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== Mbt Skor Första gången jag såg Randa Ethan ==
By [[Euclid's theorem]], there is an infinite number of [[prime number]]s. Subsets of the prime numbers may be generated with various [[formulas for primes]]. The first 500 primes are listed below, followed by lists of notable types of prime numbers in alphabetical order, giving their respective first terms.


== The first 500 prime numbers ==
Denna notebook försöker åtgärda några "resurs brister" i att lära och tillämpa den Revit API i samband med en tekniker design arbetsflöde: De API-exempel som jag har hittat på nätet är relaterade till Model Management. För formgivare intresserade av beräkning och automation kan hitta bra designrelated exempel vara en frustrerande upplevelse. Exemplen här visar hur Revit API kan användas som ett designverktyg specifikt inom miljöer [http://www.krekula-lauri.se/inc/header.asp Mbt Skor] familj skapande såsom konceptuella massan ..<br><br>Första gången jag såg Randa Ethan, kände jag genast deras varma kemi tillsammans. Men deras [http://www.lunacafe.se/uploads/menyer/include.php Michael Kors Väska] bröllop var så mycket mer. Ett par funloving människor som också är hopplösa romantiker. Använd din favorit lasagne recept, men istället för att använda kött använder ett vegetariskt kött substitut. Min favorit är Morningstar Farms smular. Detta är en soja / mejeriprodukt med en bra konsistens och inte så mycket smak i sig.<br><br>Hur att utnyttja PPC att upptäcka HighConverting sökord för Search Engine Optimization Austin, Texas sökmotor LandWhen börjat med en ny sökning ansträngning eller pe [http://www.lidingovox.se/bilder/Ansgarskyrkan.asp Longchamp Stockholm] rforming ett sökord refresh för en befintlig webbplats, är alternativen för upptäckte ring nya sökord begränsas bara av SEO fantasin . Fro m den Adwords Keyword Tool, att gräva igenom analytics, släpper Visa alla historier om detta Search Engine Land och ändra det digitala landskapet i Nya Zeeland med vit Francisco ChroniclePure SEO, Nya [http://www.vapendepan.se/images/news/confirm.asp Ray Ban Solglasögon] Zeeland ledande sökmotoroptimering företag, resultaten av deras digitala genomfört marknadsundersökning bland affärs samheter påverkas av Panda och Penguin uppdateringar. senaste uppdat es har haft en betydande inverkan alla historier om detta Francisco ChronicleThings Folk Ska n säga om din SEOSearch Engine Jour nalEverybody tycker att deras SEO är bäst.<br><br>Dessutom är de auktionssajter som eBay rapporterade att sälja 50% till 90%. Tveka. 23 maj 2007. Även om detta är vettigt, det verkar som om varje gång vi hör om rättsfall som rör BREIN, kommer gruppen ut på toppen. Så om jag skulle gissa, jag antar att BREIN vinner igen. Förhoppningsvis ska jag bli förvånad och de nederländska domstolarna kommer att plocka upp lite sunt förnuft någonstans på vägen ..<br><br>Det är lätt för företag att fastna i Googles förväntningar på sina webbplatser, när man försöker marknaden genom sökning. Det är verkligen en klok sak att göra, med tanke på Google dominerar sökmarknaden med stor marginal. Fortfarande finns det andra sökmotorer som människor använder, och det är också klokt att se till att din webbplats fungerar till det bästa av sin förmåga i dem också ..
The following table lists the first 500 primes; 20 consecutive primes in each of the 25 rows.<ref>{{Cite book | last = Lehmer | first = D. N. | authorlink = Derrick Norman Lehmer | title = List of prime numbers from 1 to 10,006,721 | publisher = Carnegie Institution of Washington | volume = 165 | year = 1982 | location = Washington D.C. | url = http://openlibrary.org/books/OL16553580M/List_of_prime_numbers_from_1_to_10_006_721 | id = OL16553580M}}</ref>
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{| class="wikitable"
<ul>
!
 
! 1 !! 2 !! 3 !! 4 !! 5 !! 6 !! 7 !! 8 !! 9 !! 10 !! 11 !! 12 !! 13 !! 14 !! 15 !! 16 !! 17 !! 18 !! 19 !! 20
  <li>[http://www.hnyrlp.com/news/html/?35804.html http://www.hnyrlp.com/news/html/?35804.html]</li>
|- align=center
 
! 1–20
  <li>[http://www.observatoiredesreligions.fr/spip.php?article8 http://www.observatoiredesreligions.fr/spip.php?article8]</li>
| [[2 (number)|2]] || [[3 (number)|3]] || [[5 (number)|5]] || [[7 (number)|7]] || [[11 (number)|11]] || [[13 (number)|13]] ||[[17 (number)|17]] || [[19 (number)|19]] || [[23 (number)|23]] || [[29 (number)|29]] || [[31 (number)|31]] || [[37 (number)|37]] || [[41 (number)|41]] || [[43 (number)|43]] || [[47 (number)|47]] || [[53 (number)|53]] || [[59 (number)|59]] || [[61 (number)|61]] || [[67 (number)|67]] || [[71 (number)|71]]
 
|- align=center
  <li>[http://taobaohunter.imotor.com/viewthread.php?tid=217075&extra= http://taobaohunter.imotor.com/viewthread.php?tid=217075&extra=]</li>
! 21–40
 
| [[73 (number)|73]] || [[79 (number)|79]] || [[83 (number)|83]] || [[89 (number)|89]] || [[97 (number)|97]] || [[101 (number)|101]]|| [[103 (number)|103]] || [[107 (number)|107]] || [[109 (number)|109]] || [[113 (number)|113]]|| [[127 (number)|127]] || [[131 (number)|131]] || [[137 (number)|137]] || [[139 (number)|139]] || [[149 (number)|149]] || [[151 (number)|151]] || [[157 (number)|157]] || [[163 (number)|163]] || [[167 (number)|167]] || [[173 (number)|173]]
  <li>[http://woyaopeiyin.com/news/html/?103021.html http://woyaopeiyin.com/news/html/?103021.html]</li>
|- align=center
 
! 41–60
  <li>[http://www.middleeasttransparent.com/spip.php?article9467&lang=ar&id_forum=10581/ http://www.middleeasttransparent.com/spip.php?article9467&lang=ar&id_forum=10581/]</li>
| [[179 (number)|179]] || [[181 (number)|181]] || [[191 (number)|191]] || [[193 (number)|193]] || [[197 (number)|197]] || [[199 (number)|199]] || [[211 (number)|211]] || [[223 (number)|223]] || [[227 (number)|227]] || [[229 (number)|229]]|| [[233 (number)|233]] || [[239 (number)|239]] || [[241 (number)|241]] || [[251 (number)|251]] || [[257 (number)|257]] || [[263 (number)|263]] || [[269 (number)|269]] || [[271 (number)|271]] || [[277 (number)|277]] || [[281 (number)|281]]
 
|- align=center
</ul>
! 61–80
| [[283 (number)|283]] || [[293 (number)|293]] || [[307 (number)|307]] || [[311 (number)|311]] || [[313 (number)|313]] || [[317 (number)|317]] || [[331 (number)|331]] || [[337 (number)|337]] || [[347 (number)|347]] || [[349 (number)|349]]|| [[353 (number)|353]] || [[359 (number)|359]] || [[367 (number)|367]] || [[373 (number)|373]] || [[379 (number)|379]] || [[383 (number)|383]] || [[389 (number)|389]] || [[397 (number)|397]] || [[401 (number)|401]] || [[409 (number)|409]]
|- align=center
! 81–100
| [[419 (number)|419]] || [[421 (number)|421]] || [[431 (number)|431]] || [[433 (number)|433]] || [[439 (number)|439]] || [[443 (number)|443]] || [[449 (number)|449]] || [[457 (number)|457]] || [[461 (number)|461]] || [[463 (number)|463]]|| [[467 (number)|467]] || [[479 (number)|479]] || [[487 (number)|487]] || [[491 (number)|491]] || [[499 (number)|499]] || [[503 (number)|503]] || [[509 (number)|509]] || [[521 (number)|521]] || [[523 (number)|523]] || [[541 (number)|541]]
|- align=center
! 101–120
| [[547 (number)|547]] || [[557 (number)|557]] || [[563 (number)|563]] || [[569 (number)|569]] || [[571 (number)|571]] || [[577 (number)|577]] || [[587 (number)|587]] || [[593 (number)|593]] || [[599 (number)|599]] || [[601 (number)|601]]|| [[607 (number)|607]] || [[613 (number)|613]] || [[617 (number)|617]] || [[619 (number)|619]] || [[631 (number)|631]] || [[641 (number)|641]] || [[643 (number)|643]] || [[647 (number)|647]]
|| [[653 (number)|653]] || [[659 (number)|659]]
|- align=center
! 121–140
| [[661 (number)|661]] || [[673 (number)|673]] || [[677 (number)|677]] || [[683 (number)|683]] || [[691 (number)|691]] || [[701 (number)|701]] || [[709 (number)|709]] || [[719 (number)|719]] || [[727 (number)|727]] || [[733 (number)|733]]|| [[739 (number)|739]] || [[743 (number)|743]] || [[751 (number)|751]] || [[757 (number)|757]] || [[761 (number)|761]] || [[769 (number)|769]] || [[773 (number)|773]] || [[787 (number)|787]] || [[797 (number)|797]] || [[809 (number)|809]]
|- align=center
! 141–160
| [[811 (number)|811]] || [[821 (number)|821]] || [[823 (number)|823]] || [[827 (number)|827]] || [[829 (number)|829]] || [[839 (number)|839]] || [[853 (number)|853]] || [[857 (number)|857]] || [[859 (number)|859]] || [[863 (number)|863]]|| [[877 (number)|877]] || [[881 (number)|881]] || [[883 (number)|883]] || [[887 (number)|887]] || [[907 (number)|907]] || [[911 (number)|911]] || [[919 (number)|919]] || [[929 (number)|929]] || [[937 (number)|937]] || [[941 (number)|941]]
|- align=center
! 161–180
| [[947 (number)|947]] || [[953 (number)|953]] || [[967 (number)|967]] || [[971 (number)|971]] || [[977 (number)|977]] || [[983 (number)|983]] || [[991 (number)|991]] || [[997 (number)|997]] || [[1009 (number)|1009]] || [[1013 (number)|1013]]|| [[1019 (number)|1019]] || [[1021 (number)|1021]] || [[1031 (number)|1031]] || [[1033 (number)|1033]] || [[1039 (number)|1039]] || [[1049 (number)|1049]] || [[1051 (number)|1051]] || [[1061 (number)|1061]] || [[1063 (number)|1063]] || [[1069 (number)|1069]]
|- align=center
! 181–200
| [[1087 (number)|1087]] || [[1091 (number)|1091]] || [[1093 (number)|1093]] || [[1097 (number)|1097]] || [[1103 (number)|1103]] || [[1109 (number)|1109]] || [[1117 (number)|1117]] || [[1123 (number)|1123]] || [[1129 (number)|1129]] || [[1151 (number)|1151]]|| [[1153 (number)|1153]] || [[1163 (number)|1163]] || [[1171 (number)|1171]] || [[1181 (number)|1181]] || [[1187 (number)|1187]] || [[1193 (number)|1193]] || [[1201 (number)|1201]] || [[1213 (number)|1213]] || [[1217 (number)|1217]] || [[1223 (number)|1223]]
|- align=center
! 201–220
| [[1229 (number)|1229]] || [[1231 (number)|1231]] || [[1237 (number)|1237]] || [[1249 (number)|1249]] || [[1259 (number)|1259]] || [[1277 (number)|1277]] || [[1279 (number)|1279]] || [[1283 (number)|1283]] || [[1289 (number)|1289]] || [[1291 (number)|1291]]|| [[1297 (number)|1297]] || [[1301 (number)|1301]] || [[1303 (number)|1303]] || [[1307 (number)|1307]] || [[1319 (number)|1319]] || [[1321 (number)|1321]] || [[1327 (number)|1327]] || [[1361 (number)|1361]] || [[1367 (number)|1367]] || [[1373 (number)|1373]]
|- align=center
! 221–240
| [[1381 (number)|1381]] || [[1399 (number)|1399]] || [[1409 (number)|1409]] || [[1423 (number)|1423]] || [[1427 (number)|1427]] || [[1429 (number)|1429]] || [[1433 (number)|1433]] || [[1439 (number)|1439]] || [[1447 (number)|1447]] || [[1451 (number)|1451]]|| [[1453 (number)|1453]] || [[1459 (number)|1459]] || [[1471 (number)|1471]] || [[1481 (number)|1481]] || [[1483 (number)|1483]] || [[1487 (number)|1487]] || [[1489 (number)|1489]] || [[1493 (number)|1493]] || [[1499 (number)|1499]] || [[1511 (number)|1511]]
|- align=center
! 241–260
| [[1523 (number)|1523]] || [[1531 (number)|1531]] || [[1543 (number)|1543]] || [[1549 (number)|1549]] || [[1553 (number)|1553]] || [[1559 (number)|1559]] || [[1567 (number)|1567]] || [[1571 (number)|1571]] || [[1579 (number)|1579]] || [[1583 (number)|1583]]|| [[1597 (number)|1597]] || [[1601 (number)|1601]] || [[1607 (number)|1607]] || [[1609 (number)|1609]] || [[1613 (number)|1613]] || [[1619 (number)|1619]] || [[1621 (number)|1621]] || [[1627 (number)|1627]] || [[1637 (number)|1637]] || [[1657 (number)|1657]]
|- align=center
! 261–280
| [[1663 (number)|1663]] || [[1667 (number)|1667]] || [[1669 (number)|1669]] || [[1693 (number)|1693]] || [[1697 (number)|1697]] || [[1699 (number)|1699]] || [[1709 (number)|1709]] || [[1721 (number)|1721]] || [[1723 (number)|1723]] || [[1733 (number)|1733]]|| [[1741 (number)|1741]] || [[1747 (number)|1747]] || [[1753 (number)|1753]] || [[1759 (number)|1759]] || [[1777 (number)|1777]] || [[1783 (number)|1783]] || [[1787 (number)|1787]] || [[1789 (number)|1789]] || [[1801 (number)|1801]] || [[1811 (number)|1811]]
|- align=center
! 281–300
| [[1823 (number)|1823]] || [[1831 (number)|1831]] || [[1847 (number)|1847]] || [[1861 (number)|1861]] || [[1867 (number)|1867]] || [[1871 (number)|1871]] || [[1873 (number)|1873]] || [[1877 (number)|1877]] || [[1879 (number)|1879]] || [[1889 (number)|1889]]|| [[1901 (number)|1901]] || [[1907 (number)|1907]] || [[1913 (number)|1913]] || [[1931 (number)|1931]] || [[1933 (number)|1933]] || [[1949 (number)|1949]] || [[1951 (number)|1951]] || [[1973 (number)|1973]] || [[1979 (number)|1979]] || [[1987 (number)|1987]]
|- align=center
! 301–320
| [[1993 (number)|1993]] || [[1997 (number)|1997]] || [[1999 (number)|1999]] || [[2003 (number)|2003]] || [[2011 (number)|2011]] || [[2017 (number)|2017]] || [[2027 (number)|2027]] || [[2029 (number)|2029]] || [[2039 (number)|2039]] || [[2053 (number)|2053]]|| [[2063 (number)|2063]] || [[2069 (number)|2069]] || [[2081 (number)|2081]] || [[2083 (number)|2083]] || [[2087 (number)|2087]] || [[2089 (number)|2089]] || [[2099 (number)|2099]] || [[2111 (number)|2111]] || [[2113 (number)|2113]] || [[2129 (number)|2129]]
|- align=center
! 321–340
| [[2131 (number)|2131]] || [[2137 (number)|2137]] || [[2141 (number)|2141]] || [[2143 (number)|2143]] || [[2153 (number)|2153]] || [[2161 (number)|2161]] || [[2179 (number)|2179]] || [[2203 (number)|2203]] || [[2207 (number)|2207]] || [[2213 (number)|2213]]|| [[2221 (number)|2221]] || [[2237 (number)|2237]] || [[2239 (number)|2239]] || [[2243 (number)|2243]] || [[2251 (number)|2251]] || [[2267 (number)|2267]] || [[2269 (number)|2269]] || [[2273 (number)|2273]] || [[2281 (number)|2281]] || [[2287 (number)|2287]]
|- align=center
! 341–360
| [[2293 (number)|2293]] || [[2297 (number)|2297]] || [[2309 (number)|2309]] || [[2311 (number)|2311]] || [[2333 (number)|2333]] || [[2339 (number)|2339]] || [[2341 (number)|2341]] || [[2347 (number)|2347]] || [[2351 (number)|2351]] || [[2357 (number)|2357]]|| [[2371 (number)|2371]] || [[2377 (number)|2377]] || [[2381 (number)|2381]] || [[2383 (number)|2383]] || [[2389 (number)|2389]] || [[2393 (number)|2393]] || [[2399 (number)|2399]] || [[2411 (number)|2411]] || [[2417 (number)|2417]] || [[2423 (number)|2423]]
|- align=center
! 361–380
| [[2437 (number)|2437]] || [[2441 (number)|2441]] || [[2447 (number)|2447]] || [[2459 (number)|2459]] || [[2467 (number)|2467]] || [[2473 (number)|2473]] || [[2477 (number)|2477]] || [[2503 (number)|2503]] || [[2521 (number)|2521]] || [[2531 (number)|2531]]|| [[2539 (number)|2539]] || [[2543 (number)|2543]] || [[2549 (number)|2549]] || [[2551 (number)|2551]] || [[2557 (number)|2557]] || [[2579 (number)|2579]] || [[2591 (number)|2591]] || [[2593 (number)|2593]] || [[2609 (number)|2609]] || [[2617 (number)|2617]]
|- align=center
! 381–400
| [[2621 (number)|2621]] || [[2633 (number)|2633]] || [[2647 (number)|2647]] || [[2657 (number)|2657]] || [[2659 (number)|2659]] || [[2663 (number)|2663]] || [[2671 (number)|2671]] || [[2677 (number)|2677]] || [[2683 (number)|2683]] || [[2687 (number)|2687]]|| [[2689 (number)|2689]] || [[2693 (number)|2693]] || [[2699 (number)|2699]] || [[2707 (number)|2707]] || [[2711 (number)|2711]] || [[2713 (number)|2713]] || [[2719 (number)|2719]] || [[2729 (number)|2729]] || [[2731 (number)|2731]] || [[2741 (number)|2741]]
|- align=center
! 401–420
| [[2749 (number)|2749]] || [[2753 (number)|2753]] || [[2767 (number)|2767]] || [[2777 (number)|2777]] || [[2789 (number)|2789]] || [[2791 (number)|2791]] || [[2797 (number)|2797]] || [[2801 (number)|2801]] || [[2803 (number)|2803]] || [[2819 (number)|2819]]|| [[2833 (number)|2833]] || [[2837 (number)|2837]] || [[2843 (number)|2843]] || [[2851 (number)|2851]] || [[2857 (number)|2857]] || [[2861 (number)|2861]] || [[2879 (number)|2879]] || [[2887 (number)|2887]] || [[2897 (number)|2897]] || [[2903 (number)|2903]]
|- align=center
! 421–440
| [[2909 (number)|2909]] || [[2917 (number)|2917]] || [[2927 (number)|2927]] || [[2939 (number)|2939]] || [[2953 (number)|2953]] || [[2957 (number)|2957]] || [[2963 (number)|2963]] || [[2969 (number)|2969]] || [[2971 (number)|2971]] || [[2999 (number)|2999]]|| [[3001 (number)|3001]] || [[3011 (number)|3011]] || [[3019 (number)|3019]] || [[3023 (number)|3023]] || [[3037 (number)|3037]] || [[3041 (number)|3041]] || [[3049 (number)|3049]] || [[3061 (number)|3061]] || [[3067 (number)|3067]] || [[3079 (number)|3079]]
|- align=center
! 441–460
| [[3083 (number)|3083]] || [[3089 (number)|3089]] || [[3109 (number)|3109]] || [[3119 (number)|3119]] || [[3121 (number)|3121]] || [[3137 (number)|3137]] || [[3163 (number)|3163]] || [[3167 (number)|3167]] || [[3169 (number)|3169]] || [[3181 (number)|3181]]|| [[3187 (number)|3187]] || [[3191 (number)|3191]] || [[3203 (number)|3203]] || [[3209 (number)|3209]] || [[3217 (number)|3217]] || [[3221 (number)|3221]] || [[3229 (number)|3229]] || [[3251 (number)|3251]] || [[3253 (number)|3253]] || [[3257 (number)|3257]]
|- align=center
! 461–480
| [[3259 (number)|3259]] || [[3271 (number)|3271]] || [[3299 (number)|3299]] || [[3301 (number)|3301]] || [[3307 (number)|3307]] || [[3313 (number)|3313]] || [[3319 (number)|3319]] || [[3323 (number)|3323]] || [[3329 (number)|3329]] || [[3331 (number)|3331]]|| [[3343 (number)|3343]] || [[3347 (number)|3347]] || [[3359 (number)|3359]] || [[3361 (number)|3361]] || [[3371 (number)|3371]] || [[3373 (number)|3373]] || [[3389 (number)|3389]] || [[3391 (number)|3391]] || [[3407 (number)|3407]] || [[3413 (number)|3413]]
|- align=center
! 481–500
| [[3433 (number)|3433]] || [[3449 (number)|3449]] || [[3457 (number)|3457]]|| [[3461 (number)|3461]] || [[3463 (number)|3463]] || [[3467 (number)|3467]] || [[3469 (number)|3469]] || [[3491 (number)|3491]] || [[3499 (number)|3499]] || [[3511 (number)|3511]]|| [[3517 (number)|3517]] || [[3527 (number)|3527]] || [[3529 (number)|3529]] || [[3533 (number)|3533]] || [[3539 (number)|3539]] || [[3541 (number)|3541]] || [[3547 (number)|3547]] || [[3557 (number)|3557]] || [[3559 (number)|3559]] || [[3571 (number)|3571]]
|}


{{OEIS|A000040}}.
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The [[Goldbach's conjecture|Goldbach conjecture]] verification project reports that it has computed all primes below 4×10{{sup|18}}.<ref>Tomás Oliveira e Silva, [http://www.ieeta.pt/~tos/goldbach.html Goldbach conjecture verification]. Retrieved 16 July 2013</ref> That means 95676260903887607 primes<ref>{{OEIS|id=A080127}}</ref> (nearly 10{{sup|17}}), but they were not stored. There are known formulae to evaluate the [[prime-counting function]] (the number of primes below a given value) faster than computing the primes. This has been used to compute that there are 1,925,320,391,606,803,968,923 primes (roughly 2{{e|21}}) below 10{{sup|23}}. A different computation found that there are 18,435,599,767,349,200,867,866 primes (roughly 2{{e|22}}) below 10{{sup|24}} if the [[Riemann hypothesis]] is true.<ref name="Franke">{{cite web |title=Conditional Calculation of pi(10{{sup|24}}) |url=http://primes.utm.edu/notes/pi(10%5E24).html |author=Jens Franke|date=29 July 2010|accessdate=2011-05-17}}</ref>
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== Lists of primes by type ==
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Below are listed the first prime numbers of many named forms and types. More details are in the article for the name. ''n'' is a [[natural number]] (including 0) in the definitions. A prime number is a number that cannot be divided by a number other than 1 and itself.


=== Additive primes ===
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Primes such that the sum of digits is a prime.
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[[2 (number)|2]], [[3 (number)|3]], [[5 (number)|5]], [[7 (number)|7]], [[11 (number)|11]], [[23 (number)|23]], [[29 (number)|29]], [[41 (number)|41]], [[43 (number)|43]], [[47 (number)|47]], [[61 (number)|61]], [[67 (number)|67]], [[83 (number)|83]], [[89 (number)|89]], [[101 (number)|101]], [[113 (number)|113]], [[131 (number)|131]] ({{OEIS2C|A046704}})
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=== Annihilating primes ===
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Let d(''p'') be the shadow of the sequence f(''n'') = ''seq''<sup>1-1</sup>(''n'') (which gives the number of sequences without repetitions that can be obtained from ''n'' distinct objects), i.e. the count of sequence entries f(0), f(1), f(2), ...., f(''h''-1) divisible by an integer ''h''. If d(''p'') = 0, then ''p'' is an annihilating prime.<ref>L. Halbeisen, N. Hungerbühler, [http://www.iam.unibe.ch/~halbeis//publications/pdf/seq.pdf Number theoretic aspects of a combinatorial function]</ref>
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[[3 (number)|3]], [[7 (number)|7]], [[11 (number)|11]], [[17 (number)|17]], [[47 (number)|47]], [[53 (number)|53]], [[61 (number)|61]], [[67 (number)|67]], [[73 (number)|73]], [[79 (number)|79]], [[89 (number)|89]], [[101 (number)|101]], [[139 (number)|139]], [[151 (number)|151]], [[157 (number)|157]], [[191 (number)|191]], [[199 (number)|199]] ({{OEIS2C|A072456}})
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=== [[Bell number#Prime Bell numbers|Bell number]] primes ===
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Primes that are the number of [[Partition of a set|partitions of a set]] with ''n'' members.
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<ul>
[[2 (number)|2]], [[5 (number)|5]], [[877 (number)|877]], [[27644437 (number)|27644437]], [[35742549198872617291353508656626642567 (number)|35742549198872617291353508656626642567]], [[359334085968622831041960188598043661065388726959079837 (number)|359334085968622831041960188598043661065388726959079837]].
 
The next term has 6,539 digits. ({{OEIS2C|A051131}})
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=== [[Carol number|Carol]] primes ===
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Of the form (2{{sup|''n''}}−1){{sup|2}}&nbsp;−&nbsp;2.
 
 
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[[7 (number)|7]], [[47 (number)|47]], [[223 (number)|223]], [[3967 (number)|3967]], [[16127 (number)|16127]], [[1046527 (number)|1046527]], [[16769023 (number)|16769023]], [[1073676287 (number)|1073676287]], [[68718952447 (number)|68718952447]], [[274876858367 (number)|274876858367]], [[4398042316799 (number)|4398042316799]], [[1125899839733759 (number)|1125899839733759]], [[18014398241046527 (number)|18014398241046527]], [[1298074214633706835075030044377087 (number)|1298074214633706835075030044377087]] ({{OEIS2C|A091516}})
 
 
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=== [[Centered decagonal number|Centered decagonal]] primes ===
 
Of the form 5(''n''{{sup|2}}&nbsp;−&nbsp;''n'')&nbsp;+&nbsp;1.
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[[11 (number)|11]], [[31 (number)|31]], [[61 (number)|61]], [[101 (number)|101]], [[151 (number)|151]], [[211 (number)|211]], [[281 (number)|281]], [[661 (number)|661]], [[911 (number)|911]], [[1051 (number)|1051]], [[1201 (number)|1201]], [[1361 (number)|1361]], [[1531 (number)|1531]], [[1901 (number)|1901]], [[2311 (number)|2311]], [[2531 (number)|2531]], [[3001 (number)|3001]], [[3251 (number)|3251]], [[3511 (number)|3511]], [[4651 (number)|4651]], [[5281 (number)|5281]], [[6301 (number)|6301]], [[6661 (number)|6661]], [[7411 (number)|7411]], [[9461 (number)|9461]], [[9901 (number)|9901]], [[12251 (number)|12251]], [[13781 (number)|13781]], [[14851 (number)|14851]], [[15401 (number)|15401]], [[18301 (number)|18301]], [[18911 (number)|18911]], [[19531 (number)|19531]], [[20161 (number)|20161]], [[22111 (number)|22111]], [[24151 (number)|24151]], [[24851 (number)|24851]], [[25561 (number)|25561]], [[27011 (number)|27011]], [[27751 (number)|27751]] ({{OEIS2C|A090562}})
</ul>
 
=== [[Centered heptagonal number|Centered heptagonal]] primes ===
Of the form (7''n''{{sup|2}}&nbsp;−&nbsp;7''n''&nbsp;+&nbsp;2)&nbsp;/&nbsp;2.
 
[[43 (number)|43]], [[71 (number)|71]], [[197 (number)|197]], [[463 (number)|463]], [[547 (number)|547]], [[953 (number)|953]], [[1471 (number)|1471]], [[1933 (number)|1933]], [[2647 (number)|2647]], [[2843 (number)|2843]], [[3697 (number)|3697]], [[4663 (number)|4663]], [[5741 (number)|5741]], [[8233 (number)|8233]], [[9283 (number)|9283]], [[10781 (number)|10781]], [[11173 (number)|11173]], [[12391 (number)|12391]], [[14561 (number)|14561]], [[18397 (number)|18397]], [[20483 (number)|20483]], [[29303 (number)|29303]], [[29947 (number)|29947]], [[34651 (number)|34651]], [[37493 (number)|37493]], [[41203 (number)|41203]], [[46691 (number)|46691]], [[50821 (number)|50821]], [[54251 (number)|54251]], [[56897 (number)|56897]], [[57793 (number)|57793]], [[65213 (number)|65213]], [[68111 (number)|68111]], [[72073 (number)|72073]], [[76147 (number)|76147]], [[84631 (number)|84631]], [[89041 (number)|89041]], [[93563 (number)|93563]] (primes in {{OEIS2C|A069099}})
 
=== [[Centered square number|Centered square]] primes ===
Of the form ''n''{{sup|2}}&nbsp;+&nbsp;(''n''+1){{sup|2}}.
 
[[5 (number)|5]], [[13 (number)|13]], [[41 (number)|41]], [[61 (number)|61]], [[113 (number)|113]], [[181 (number)|181]], [[313 (number)|313]], [[421 (number)|421]], [[613 (number)|613]], [[761 (number)|761]], [[1013 (number)|1013]], [[1201 (number)|1201]], [[1301 (number)|1301]], [[1741 (number)|1741]], [[1861 (number)|1861]], [[2113 (number)|2113]], [[2381 (number)|2381]], [[2521 (number)|2521]], [[3121 (number)|3121]], [[3613 (number)|3613]], [[4513 (number)|4513]], [[5101 (number)|5101]], [[7321 (number)|7321]], [[8581 (number)|8581]], [[9661 (number)|9661]], [[9941 (number)|9941]], [[10513 (number)|10513]], [[12641 (number)|12641]], [[13613 (number)|13613]], [[14281 (number)|14281]], [[14621 (number)|14621]], [[15313 (number)|15313]], [[16381 (number)|16381]], [[19013 (number)|19013]], [[19801 (number)|19801]], [[20201 (number)|20201]], [[21013 (number)|21013]], [[21841 (number)|21841]], [[23981 (number)|23981]], [[24421 (number)|24421]], [[26681 (number)|26681]] ({{OEIS2C|A027862}})
 
=== [[Centered triangular number|Centered triangular]] primes ===
Of the form (3''n''{{sup|2}}&nbsp;+&nbsp;3''n''&nbsp;+&nbsp;2)&nbsp;/&nbsp;2.
 
[[19 (number)|19]], [[31 (number)|31]], [[109 (number)|109]], [[199 (number)|199]], [[409 (number)|409]], [[571 (number)|571]], [[631 (number)|631]], [[829 (number)|829]], [[1489 (number)|1489]], [[1999 (number)|1999]], [[2341 (number)|2341]], [[2971 (number)|2971]], [[3529 (number)|3529]], [[4621 (number)|4621]], [[4789 (number)|4789]], [[7039 (number)|7039]], [[7669 (number)|7669]], [[8779 (number)|8779]], [[9721 (number)|9721]], [[10459 (number)|10459]], [[10711 (number)|10711]], [[13681 (number)|13681]], [[14851 (number)|14851]], [[16069 (number)|16069]], [[16381 (number)|16381]], [[17659 (number)|17659]], [[20011 (number)|20011]], [[20359 (number)|20359]], [[23251 (number)|23251]], [[25939 (number)|25939]], [[27541 (number)|27541]], [[29191 (number)|29191]], [[29611 (number)|29611]], [[31321 (number)|31321]], [[34429 (number)|34429]], [[36739 (number)|36739]], [[40099 (number)|40099]], [[40591 (number)|40591]], [[42589 (number)|42589]] ({{OEIS2C|A125602}})
 
=== [[Chen prime]]s ===
Where ''p'' is prime and ''p''+2 is either a prime or [[semiprime]].
 
[[2 (number)|2]], [[3 (number)|3]], [[5 (number)|5]], [[7 (number)|7]], [[11 (number)|11]], [[13 (number)|13]], [[17 (number)|17]], [[19 (number)|19]], [[23 (number)|23]], [[29 (number)|29]], [[31 (number)|31]], [[37 (number)|37]], [[41 (number)|41]], [[47 (number)|47]], [[53 (number)|53]], [[59 (number)|59]], [[67 (number)|67]], [[71 (number)|71]], [[83 (number)|83]], [[89 (number)|89]], [[101 (number)|101]], [[107 (number)|107]], [[109 (number)|109]], [[113 (number)|113]], [[127 (number)|127]], [[131 (number)|131]], [[137 (number)|137]], [[139 (number)|139]], [[149 (number)|149]], [[157 (number)|157]], [[167 (number)|167]], [[179 (number)|179]], [[181 (number)|181]], [[191 (number)|191]], [[197 (number)|197]], [[199 (number)|199]], [[211 (number)|211]], [[227 (number)|227]], [[233 (number)|233]], [[239 (number)|239]], [[251 (number)|251]], [[257 (number)|257]], [[263 (number)|263]], [[269 (number)|269]], [[281 (number)|281]], [[293 (number)|293]], [[307 (number)|307]], [[311 (number)|311]], [[317 (number)|317]], [[337 (number)|337]], [[347 (number)|347]], [[353 (number)|353]], [[359 (number)|359]], [[379 (number)|379]], [[389 (number)|389]], [[401 (number)|401]], [[409 (number)|409]] ({{OEIS2C|A109611}})
 
=== [[Circular prime]]s ===
A circular prime number is a number that remains prime on any cyclic rotation of its digits (in base 10).
 
[[2 (number)|2]], [[3 (number)|3]], [[5 (number)|5]], [[7 (number)|7]], [[11 (number)|11]], [[13 (number)|13]], [[17 (number)|17]], [[31 (number)|31]], [[37 (number)|37]], [[71 (number)|71]], [[73 (number)|73]], [[79 (number)|79]], [[97 (number)|97]], [[113 (number)|113]], [[131 (number)|131]], [[197 (number)|197]], [[199 (number)|199]], [[311 (number)|311]], [[337 (number)|337]], [[373 (number)|373]], [[719 (number)|719]], [[733 (number)|733]], [[919 (number)|919]], [[971 (number)|971]], [[991 (number)|991]], [[1193 (number)|1193]], [[1931 (number)|1931]], [[3119 (number)|3119]], [[3779 (number)|3779]], [[7793 (number)|7793]], [[7937 (number)|7937]], [[9311 (number)|9311]], [[9377 (number)|9377]], [[11939 (number)|11939]], [[19391 (number)|19391]], [[19937 (number)|19937]], [[37199 (number)|37199]], [[39119 (number)|39119]], [[71993 (number)|71993]], [[91193 (number)|91193]], [[93719 (number)|93719]], [[93911 (number)|93911]], [[99371 (number)|99371]], [[193939 (number)|193939]], [[199933 (number)|199933]], [[319993 (number)|319993]], [[331999 (number)|331999]], [[391939 (number)|391939]], [[393919 (number)|393919]], [[919393 (number)|919393]], [[933199 (number)|933199]], [[939193 (number)|939193]], [[939391 (number)|939391]], [[993319 (number)|993319]], [[999331 (number)|999331]] ({{OEIS2C|A068652}})
 
Some sources only list the smallest prime in each cycle, for example listing 13 but omitting 31 ([[OEIS]] really calls this sequence circular primes, but not the above sequence):
 
2, 3, 5, 7, 11, 13, 17, 37, 79, 113, 197, 199, 337, 1193, 3779, 11939, 19937, 193939, 199933, 1111111111111111111, 11111111111111111111111 ({{OEIS2C|A016114}})
 
All [[repunit]] primes are circular.
 
=== [[Cousin prime]]s ===
{{see also|#Twin primes|#Prime triplets|#Prime quadruplets}}
 
Where (''p'', ''p''+4) are both prime.
 
([[3 (number)|3]], [[7 (number)|7]]), (7, [[11 (number)|11]]), ([[13 (number)|13]], [[17 (number)|17]]), ([[19 (number)|19]], [[23 (number)|23]]), ([[37 (number)|37]], [[41 (number)|41]]), ([[43 (number)|43]], [[47 (number)|47]]), ([[67 (number)|67]], [[71 (number)|71]]), ([[79 (number)|79]], [[83 (number)|83]]), ([[97 (number)|97]], [[101 (number)|101]]), ([[103 (number)|103]], [[107 (number)|107]]), ([[109 (number)|109]], [[113 (number)|113]]), ([[127 (number)|127]], [[131 (number)|131]]), ([[163 (number)|163]], [[167 (number)|167]]), ([[193 (number)|193]], [[197 (number)|197]]), ([[223 (number)|223]], [[227 (number)|227]]), ([[229 (number)|229]], [[233 (number)|233]]), ([[277 (number)|277]], [[281 (number)|281]]) ({{OEIS2C|A023200}}, {{OEIS2C|A046132}})
 
=== [[Cuban prime]]s ===
Of the form <math>\tfrac{x^3-y^3}{x-y},</math> ''x''&nbsp;=&nbsp;''y''+1.
 
[[7 (number)|7]], [[19 (number)|19]], [[37 (number)|37]], [[61 (number)|61]], [[127 (number)|127]], [[271 (number)|271]], [[331 (number)|331]], [[397 (number)|397]], [[547 (number)|547]], [[631 (number)|631]], [[919 (number)|919]], [[1657 (number)|1657]], [[1801 (number)|1801]], [[1951 (number)|1951]], [[2269 (number)|2269]], [[2437 (number)|2437]], [[2791 (number)|2791]], [[3169 (number)|3169]], [[3571 (number)|3571]], [[4219 (number)|4219]], [[4447 (number)|4447]], [[5167 (number)|5167]], [[5419 (number)|5419]], [[6211 (number)|6211]], [[7057 (number)|7057]], [[7351 (number)|7351]], [[8269 (number)|8269]], [[9241 (number)|9241]], [[10267 (number)|10267]], [[11719 (number)|11719]], [[12097 (number)|12097]], [[13267 (number)|13267]], [[13669 (number)|13669]], [[16651 (number)|16651]], [[19441 (number)|19441]], [[19927 (number)|19927]], [[22447 (number)|22447]], [[23497 (number)|23497]], [[24571 (number)|24571]], [[25117 (number)|25117]], [[26227 (number)|26227]], [[27361 (number)|27361]], [[33391 (number)|33391]], [[35317 (number)|35317]] ({{OEIS2C|A002407}})
 
Of the form <math>\tfrac{x^3-y^3}{x-y},</math> ''x''&nbsp;=&nbsp;''y''+2.
 
[[13 (number)|13]], [[109 (number)|109]], [[193 (number)|193]], [[433 (number)|433]], [[769 (number)|769]], [[1201 (number)|1201]], [[1453 (number)|1453]], [[2029 (number)|2029]], [[3469 (number)|3469]], [[3889 (number)|3889]], [[4801 (number)|4801]], [[10093 (number)|10093]], [[12289 (number)|12289]], [[13873 (number)|13873]], [[18253 (number)|18253]], [[20173 (number)|20173]], [[21169 (number)|21169]], [[22189 (number)|22189]], [[28813 (number)|28813]], [[37633 (number)|37633]], [[43201 (number)|43201]], [[47629 (number)|47629]], [[60493 (number)|60493]], [[63949 (number)|63949]], [[65713 (number)|65713]], [[69313 (number)|69313]], [[73009 (number)|73009]], [[76801 (number)|76801]], [[84673 (number)|84673]], [[106033 (number)|106033]], [[108301 (number)|108301]], [[112909 (number)|112909]], [[115249 (number)|115249]] ({{OEIS2C|A002648}})
 
=== [[Cullen number|Cullen]] primes ===
Of the form ''n''×2{{sup|''n''}} + 1.
 
[[3 (number)|3]], [[393050634124102232869567034555427371542904833 (number)|393050634124102232869567034555427371542904833]] ({{OEIS2C|A050920}})
 
=== [[Dihedral prime]]s ===
Primes that remain prime when read upside down or mirrored in a [[seven-segment display]].
 
[[2 (number)|2]], [[5 (number)|5]], [[11 (number)|11]], [[101 (number)|101]], [[181 (number)|181]], [[1181 (number)|1181]], 1811, 18181, 108881, 110881, 118081, 120121,
121021, 121151, 150151, 151051, 151121, 180181, 180811, 181081 ({{OEIS2C|A134996}})
 
=== [[Double factorial]] primes ===
Of the form ''n''!! + 1. Values of ''n'':
 
[[0 (number)|0]], [[1 (number)|1]], [[2 (number)|2]], [[518 (number)|518]], [[33416 (number)|33416]], [[37310 (number)|37310]], [[52608 (number)|52608]] ({{OEIS2C|A080778}})
 
Note that ''n'' = 0 and ''n'' = 1 produce the same prime, namely 2.
 
Of the form ''n''!! − 1. Values of ''n'':
 
[[3 (number)|3]], [[4 (number)|4]], [[6 (number)|6]], [[8 (number)|8]], [[16 (number)|16]], [[26 (number)|26]], [[64 (number)|64]], [[82 (number)|82]], [[90 (number)|90]], [[118 (number)|118]], [[194 (number)|194]], [[214 (number)|214]], [[728 (number)|728]], [[842 (number)|842]], [[888 (number)|888]], [[2328 (number)|2328]], [[3326 (number)|3326]], [[6404 (number)|6404]], [[8670 (number)|8670]], [[9682 (number)|9682]], [[27056 (number)|27056]], [[44318 (number)|44318]] ({{OEIS2C|A007749}})
 
=== [[Double Mersenne prime]]s ===
A subset of Mersenne primes of the form 2{{sup|2{{sup|''p''}}−1}}&nbsp;−&nbsp;1 for prime ''p''.
 
[[7 (number)|7]], [[127 (number)|127]], [[2147483647]], 170141183460469231731687303715884105727 (primes in {{OEIS2C|A077586}})
 
{{As of|2011}}, these are the only known double Mersenne primes, and number theorists think these are probably the only double Mersenne primes.
 
=== [[Eisenstein prime]]s without imaginary part ===
[[Eisenstein integer]]s that are [[Irreducible element|irreducible]] and real numbers (primes of the form 3''n''&nbsp;−&nbsp;1).
 
[[2 (number)|2]], [[5 (number)|5]], [[11 (number)|11]], [[17 (number)|17]], [[23 (number)|23]], [[29 (number)|29]], [[41 (number)|41]], [[47 (number)|47]], [[53 (number)|53]], [[59 (number)|59]], [[71 (number)|71]], [[83 (number)|83]], [[89 (number)|89]], [[101 (number)|101]], [[107 (number)|107]], [[113 (number)|113]], [[131 (number)|131]], [[137 (number)|137]], [[149 (number)|149]], [[167 (number)|167]], [[173 (number)|173]], [[179 (number)|179]], [[191 (number)|191]], [[197 (number)|197]], [[227 (number)|227]], [[233 (number)|233]], [[239 (number)|239]], [[251 (number)|251]], [[257 (number)|257]], [[263 (number)|263]], [[269 (number)|269]], [[281 (number)|281]], [[293 (number)|293]], [[311 (number)|311]], [[317 (number)|317]], [[347 (number)|347]], [[353 (number)|353]], [[359 (number)|359]], [[383 (number)|383]], [[389 (number)|389]], [[401 (number)|401]] ({{OEIS2C|A003627}})
 
=== [[Emirp]]s ===
Primes which become a different prime when their decimal digits are reversed.
 
[[13 (number)|13]], [[17 (number)|17]], [[31 (number)|31]], [[37 (number)|37]], [[71 (number)|71]], [[73 (number)|73]], [[79 (number)|79]], [[97 (number)|97]], [[107 (number)|107]], [[113 (number)|113]], [[149 (number)|149]], [[157 (number)|157]], [[167 (number)|167]], [[179 (number)|179]], [[199 (number)|199]], [[311 (number)|311]], [[337 (number)|337]], [[347 (number)|347]], [[359 (number)|359]], [[389 (number)|389]], [[701 (number)|701]], [[709 (number)|709]], [[733 (number)|733]], [[739 (number)|739]], [[743 (number)|743]], [[751 (number)|751]], [[761 (number)|761]], [[769 (number)|769]], [[907 (number)|907]], [[937 (number)|937]], [[941 (number)|941]], [[953 (number)|953]], [[967 (number)|967]], [[971 (number)|971]], [[983 (number)|983]], [[991 (number)|991]] ({{OEIS2C|A006567}})
 
=== [[Euclid number|Euclid]] primes ===
Of the form ''p''{{sub|''n''}}#&nbsp;+&nbsp;1 (a subset of [[primorial prime]]s).
 
[[3 (number)|3]], [[7 (number)|7]], [[31 (number)|31]], [[211 (number)|211]], [[2311 (number)|2311]], [[200560490131 (number)|200560490131]] ({{OEIS2C|A018239}}<ref name="A018239">{{OEIS2C|A018239}} includes 2 = [[empty product]] of first 0 primes plus 1, but 2 is excluded in this list.</ref>)
 
=== [[Even number|Even]] prime ===
Of the form 2''n''.
 
[[2 (number)|2]]
 
The only even prime is 2. It is therefore sometimes called "the oddest prime" as a pun on the non-mathematical meaning of "[[Even and odd numbers|odd]]".<ref>http://mathworld.wolfram.com/OddPrime.html</ref>
 
=== [[Factorial prime]]s ===
Of the form ''n''[[factorial|!]] − 1 or ''n''! + 1.
 
[[2 (number)|2]], [[3 (number)|3]], [[5 (number)|5]], [[7 (number)|7]], [[23 (number)|23]], [[719 (number)|719]], 5039, 39916801, 479001599, 87178291199, 10888869450418352160768000001, 265252859812191058636308479999999, 263130836933693530167218012159999999, 8683317618811886495518194401279999999 ({{OEIS2C|A088054}})
 
=== [[Fermat number#Primality of Fermat numbers|Fermat primes]] ===
Of the form 2{{sup|2{{sup|''n''}}}}&nbsp;+&nbsp;1.
 
[[3 (number)|3]], [[5 (number)|5]], [[17 (number)|17]], [[257 (number)|257]], [[65537 (number)|65537]] ({{OEIS2C|A019434}})
 
{{As of|2013}} these are the only known Fermat primes, and conjecturally the only Fermat primes.
 
=== [[Fibonacci prime]]s ===
Primes in the [[Fibonacci sequence]] ''F''{{sub|0}}&nbsp;=&nbsp;0, ''F''{{sub|1}}&nbsp;=&nbsp;1,
''F''{{sub|''n''}} = ''F''{{sub|''n''−1}} + ''F''{{sub|''n''−2}}.
 
[[2 (number)|2]], [[3 (number)|3]], [[5 (number)|5]], [[13 (number)|13]], [[89 (number)|89]], [[233 (number)|233]], [[1597 (number)|1597]], [[28657 (number)|28657]], [[514229 (number)|514229]], [[433494437 (number)|433494437]], [[2971215073 (number)|2971215073]], [[99194853094755497 (number)|99194853094755497]], [[1066340417491710595814572169 (number)|1066340417491710595814572169]], [[19134702400093278081449423917 (number)|19134702400093278081449423917]] ({{OEIS2C|A005478}})
 
=== [[Fortunate prime]]s ===
[[Fortunate number]]s that are prime (it has been conjectured they all are).
 
[[3 (number)|3]], [[5 (number)|5]], [[7 (number)|7]], [[13 (number)|13]], [[17 (number)|17]], [[19 (number)|19]], [[23 (number)|23]], [[37 (number)|37]], [[47 (number)|47]], [[59 (number)|59]], [[61 (number)|61]], [[67 (number)|67]], [[71 (number)|71]], [[79 (number)|79]], [[89 (number)|89]], [[101 (number)|101]], [[103 (number)|103]], [[107 (number)|107]], [[109 (number)|109]], [[127 (number)|127]], [[151 (number)|151]], [[157 (number)|157]], [[163 (number)|163]], [[167 (number)|167]], [[191 (number)|191]], [[197 (number)|197]], [[199 (number)|199]], [[223 (number)|223]], [[229 (number)|229]], [[233 (number)|233]], [[239 (number)|239]], [[271 (number)|271]], [[277 (number)|277]], [[283 (number)|283]], [[293 (number)|293]], [[307 (number)|307]], [[311 (number)|311]], [[313 (number)|313]], [[331 (number)|331]], [[353 (number)|353]], [[373 (number)|373]], [[379 (number)|379]], [[383 (number)|383]], [[397 (number)|397]] ({{OEIS2C|A046066}})
 
=== [[Gaussian integer|Gaussian primes]] ===
[[Prime element]]s of the Gaussian integers (primes of the form 4''n''&nbsp;+&nbsp;3).
 
[[3 (number)|3]], [[7 (number)|7]], [[11 (number)|11]], [[19 (number)|19]], [[23 (number)|23]], [[31 (number)|31]], [[43 (number)|43]], [[47 (number)|47]], [[59 (number)|59]], [[67 (number)|67]], [[71 (number)|71]], [[79 (number)|79]], [[83 (number)|83]], [[103 (number)|103]], [[107 (number)|107]], [[127 (number)|127]], [[131 (number)|131]], [[139 (number)|139]], [[151 (number)|151]], [[163 (number)|163]], [[167 (number)|167]], [[179 (number)|179]], [[191 (number)|191]], [[199 (number)|199]], [[211 (number)|211]], [[223 (number)|223]], [[227 (number)|227]], [[239 (number)|239]], [[251 (number)|251]], [[263 (number)|263]], [[271 (number)|271]], [[283 (number)|283]], [[307 (number)|307]], [[311 (number)|311]], [[331 (number)|331]], [[347 (number)|347]], [[359 (number)|359]], [[367 (number)|367]], [[379 (number)|379]], [[383 (number)|383]], [[419 (number)|419]], [[431 (number)|431]], [[439 (number)|439]], [[443 (number)|443]], [[463 (number)|463]], [[467 (number)|467]], [[479 (number)|479]], [[487 (number)|487]], [[491 (number)|491]], [[499 (number)|499]], [[503 (number)|503]] ({{OEIS2C|A002145}})
 
=== Generalized Fermat primes base 10 ===
Of the form 10{{sup|''n''}}&nbsp;+&nbsp;1, where ''n''&nbsp;>&nbsp;0.
 
[[11 (number)|11]], [[101 (number)|101]]
 
{{As of|2011|04}}, these are the only known generalized Fermat primes in base 10.<ref>{{cite web
  | last = Caldwell
  | first = C.
  | authorlink = Chris Caldwell
  | coauthors = Honaker, Jr., G. L.
  | title = 101
  | work = Prime Curios!
  | url = http://primes.utm.edu/curios/page.php?short=101
  | accessdate = 1 April 2011}}
</ref>
 
=== [[Genocchi number]] primes ===
[[17 (number)|17]]
 
The only positive prime Genocchi number is 17.<ref>{{MathWorld|urlname=GenocchiNumber|title=Genocchi Number}}</ref>
 
=== Gilda's primes ===
Gilda's numbers that are prime. A number ''n'' is a Gilda's number, if when a [[Fibonacci sequence]] is formed with the first term equal to the absolute value of the successive differences between consecutive digits of ''n'' and the second term equal to the sum of the decimal digits of ''n'', ''n'' itself appears as a term in this Fibonacci sequence.<ref>{{Citation|last=Russo|first=F.|title=A Set of New Samarandache Functions, Sequences and Conjectures in Number Theory|pages=73–74|url=http://fs.gallup.unm.edu//Felice-Russo-book1.pdf}}</ref>
 
[[29 (number)|29]], [[683 (number)|683]], [[997 (number)|997]], [[2207 (number)|2207]], [[30571351 (number)|30571351]] ({{OEIS2C|A046850}}; another entry {{OEIS2C|A135995}} is erroneous)
 
=== [[Good prime]]s ===
Primes ''p''{{sub|''n''}} for which ''p''{{sub|''n''}}{{sup|2}}&nbsp;>&nbsp;''p''{{sub|''n''−''i''}}&nbsp;''p''{{sub|''n''+''i''}} for all 1&nbsp;≤&nbsp;''i''&nbsp;≤&nbsp;''n''−1, where ''p''{{sub|''n''}} is the ''n''th prime.
 
[[5 (number)|5]], [[11 (number)|11]], [[17 (number)|17]], [[29 (number)|29]], [[37 (number)|37]], [[41 (number)|41]], [[53 (number)|53]], [[59 (number)|59]], [[67 (number)|67]], [[71 (number)|71]], [[97 (number)|97]], [[101 (number)|101]], [[127 (number)|127]], [[149 (number)|149]], [[179 (number)|179]], [[191 (number)|191]], [[223 (number)|223]], [[227 (number)|227]], [[251 (number)|251]], [[257 (number)|257]], [[269 (number)|269]], [[307 (number)|307]] ({{OEIS2C|A028388}})
 
=== [[Happy number|Happy primes]] ===
Happy numbers that are prime.
 
[[7 (number)|7]], [[13 (number)|13]], [[19 (number)|19]], [[23 (number)|23]], [[31 (number)|31]], [[79 (number)|79]], [[97 (number)|97]], [[103 (number)|103]], [[109 (number)|109]], [[139 (number)|139]], [[167 (number)|167]], [[193 (number)|193]], [[239 (number)|239]], [[263 (number)|263]], [[293 (number)|293]], [[313 (number)|313]], [[331 (number)|331]], [[367 (number)|367]], [[379 (number)|379]], [[383 (number)|383]], [[397 (number)|397]], [[409 (number)|409]], [[487 (number)|487]], [[563 (number)|563]], [[617 (number)|617]], [[653 (number)|653]], [[673 (number)|673]], [[683 (number)|683]], [[709 (number)|709]], [[739 (number)|739]], [[761 (number)|761]], [[863 (number)|863]], [[881 (number)|881]], [[907 (number)|907]], [[937 (number)|937]], [[1009 (number)|1009]], [[1033 (number)|1033]], [[1039 (number)|1039]], [[1093 (number)|1093]] ({{OEIS2C|A035497}})
 
=== Harmonic primes ===
Primes ''p'' for which there are no solutions to ''H''{{sub|''k''}}&nbsp;≡&nbsp;0&nbsp;(mod&nbsp;''p'') and ''H''{{sub|''k''}}&nbsp;≡&nbsp;−''ω''{{sub|''p''}}&nbsp;(mod&nbsp;''p'') for 1&nbsp;≤&nbsp;''k''&nbsp;≤&nbsp;''p''−2, where ''ω''{{sub|''p''}} is the [[Wolstenholme quotient]].<ref>{{cite doi|10.1080/10586458.1994.10504298}}</ref>
 
[[5 (number)|5]], [[13 (number)|13]], [[17 (number)|17]], [[23 (number)|23]], [[41 (number)|41]], [[67 (number)|67]], [[73 (number)|73]], [[79 (number)|79]], [[107 (number)|107]], [[113 (number)|113]], [[139 (number)|139]], [[149 (number)|149]], [[157 (number)|157]], [[179 (number)|179]], [[191 (number)|191]], [[193 (number)|193]], [[223 (number)|223]], [[239 (number)|239]], [[241 (number)|241]], [[251 (number)|251]], [[263 (number)|263]], [[277 (number)|277]], [[281 (number)|281]], [[293 (number)|293]], [[307 (number)|307]], [[311 (number)|311]], [[317 (number)|317]], [[331 (number)|331]], [[337 (number)|337]], [[349 (number)|349]] ({{OEIS2C|A092101}})
 
=== [[Higgs prime]]s for squares ===
Primes ''p'' for which ''p''−1 divides the square of the product of all earlier terms.
 
[[2 (number)|2]], [[3 (number)|3]], [[5 (number)|5]], [[7 (number)|7]], [[11 (number)|11]], [[13 (number)|13]], [[19 (number)|19]], [[23 (number)|23]], [[29 (number)|29]], [[31 (number)|31]], [[37 (number)|37]], [[43 (number)|43]], [[47 (number)|47]], [[53 (number)|53]], [[59 (number)|59]], [[61 (number)|61]], [[67 (number)|67]], [[71 (number)|71]], [[79 (number)|79]], [[101 (number)|101]], [[107 (number)|107]], [[127 (number)|127]], [[131 (number)|131]], [[139 (number)|139]], [[149 (number)|149]], [[151 (number)|151]], [[157 (number)|157]], [[173 (number)|173]], [[181 (number)|181]], [[191 (number)|191]], [[197 (number)|197]], [[199 (number)|199]], [[211 (number)|211]], [[223 (number)|223]], [[229 (number)|229]], [[263 (number)|263]], [[269 (number)|269]], [[277 (number)|277]], [[283 (number)|283]], [[311 (number)|311]], [[317 (number)|317]], [[331 (number)|331]], [[347 (number)|347]], [[349 (number)|349]] ({{OEIS2C|A007459}})
 
=== [[Highly cototient number]] primes ===
Primes that are a [[cototient]] more often than any integer below it except 1.
 
[[2 (number)|2]], [[23 (number)|23]], [[47 (number)|47]], [[59 (number)|59]], [[83 (number)|83]], [[89 (number)|89]], [[113 (number)|113]], [[167 (number)|167]], [[269 (number)|269]], [[389 (number)|389]], [[419 (number)|419]], [[509 (number)|509]], [[659 (number)|659]], [[839 (number)|839]], [[1049 (number)|1049]], [[1259 (number)|1259]], [[1889 (number)|1889]] ({{OEIS2C|A105440}})
 
=== [[Irregular prime]]s ===
Odd primes ''p'' which divide the [[Class number (number theory)|class number]] of the ''p''-th [[cyclotomic field]].
 
[[37 (number)|37]], [[59 (number)|59]], [[67 (number)|67]], [[101 (number)|101]], [[103 (number)|103]], [[131 (number)|131]], [[149 (number)|149]], [[157 (number)|157]], [[233 (number)|233]], [[257 (number)|257]], [[263 (number)|263]], [[271 (number)|271]], [[283 (number)|283]], [[293 (number)|293]], [[307 (number)|307]], [[311 (number)|311]], [[347 (number)|347]], [[353 (number)|353]], [[379 (number)|379]], [[389 (number)|389]], [[401 (number)|401]], [[409 (number)|409]], [[421 (number)|421]], [[433 (number)|433]], [[461 (number)|461]], [[463 (number)|463]], [[467 (number)|467]], [[491 (number)|491]], [[523 (number)|523]], [[541 (number)|541]], [[547 (number)|547]], [[557 (number)|557]], [[577 (number)|577]], [[587 (number)|587]], [[593 (number)|593]], [[607 (number)|607]], [[613 (number)|613]], [[617 (number)|617]], 619 ({{OEIS2C|A000928}})
 
=== [[Regular prime#Irregular pairs|(p, p−5) irregular primes]] ===
Primes ''p'' such that (''p'', ''p''−5) is an irregular pair.<ref name="Johnson">{{cite journal | last = Johnson | first = W. | authorlink = Wells Johnson | title = Irregular Primes and Cyclotomic Invariants
| journal = [[Mathematics of Computation]] | volume = 29 | issue = 129 | pages = 113–120 | publisher = [[American Mathematical Society|AMS]] | year = 1975 | url = http://www.ams.org/journals/mcom/1975-29-129/S0025-5718-1975-0376606-9/S0025-5718-1975-0376606-9.pdf}}</ref>
 
[[37 (number)|37]]
 
=== [[Regular prime#Irregular pairs|(p, p−9) irregular primes]] ===
Primes ''p'' such that (''p'', ''p''−9) is an irregular pair.<ref name="Johnson" />
 
[[67 (number)|67]], [[877 (number)|877]] ({{OEIS2C|A212557}})
 
=== [[Twin prime|Isolated primes]] ===
Primes ''p'' such that neither ''p''−2 nor ''p''+2 is prime.
 
[[2 (number)|2]], [[23 (number)|23]], [[37 (number)|37]], [[47 (number)|47]], [[53 (number)|53]], [[67 (number)|67]], [[79 (number)|79]], [[83 (number)|83]], [[89 (number)|89]], [[97 (number)|97]], [[113 (number)|113]], [[127 (number)|127]], [[131 (number)|131]], [[157 (number)|157]], [[163 (number)|163]], [[167 (number)|167]], [[173 (number)|173]], [[211 (number)|211]], [[223 (number)|223]], [[233 (number)|233]], [[251 (number)|251]], [[257 (number)|257]], [[263 (number)|263]], [[277 (number)|277]], [[293 (number)|293]], [[307 (number)|307]], [[317 (number)|317]], [[331 (number)|331]], [[337 (number)|337]], [[353 (number)|353]], [[359 (number)|359]], [[367 (number)|367]], [[373 (number)|373]], [[379 (number)|379]], [[383 (number)|383]], [[389 (number)|389]], [[397 (number)|397]], [[401 (number)|401]], [[409 (number)|409]], [[439 (number)|439]], [[443 (number)|443]], [[449 (number)|449]], [[457 (number)|457]], [[467 (number)|467]], [[479 (number)|479]], [[487 (number)|487]], [[491 (number)|491]], [[499 (number)|499]], [[503 (number)|503]], [[509 (number)|509]], [[541 (number)|541]], [[547 (number)|547]], [[557 (number)|557]], [[563 (number)|563]], [[577 (number)|577]], [[587 (number)|587]], [[593 (number)|593]], [[607 (number)|607]], [[613 (number)|613]], [[631 (number)|631]], [[647 (number)|647]], [[653 (number)|653]], [[673 (number)|673]], [[677 (number)|677]], [[683 (number)|683]], [[691 (number)|691]], [[701 (number)|701]], [[709 (number)|709]], [[719 (number)|719]], [[727 (number)|727]], [[733 (number)|733]], [[739 (number)|739]], [[743 (number)|743]], [[751 (number)|751]], [[757 (number)|757]], [[761 (number)|761]], [[769 (number)|769]], [[773 (number)|773]], [[787 (number)|787]], [[797 (number)|797]], [[839 (number)|839]], [[853 (number)|853]], [[863 (number)|863]], [[877 (number)|877]], [[887 (number)|887]], [[907 (number)|907]], [[911 (number)|911]], [[919 (number)|919]], [[929 (number)|929]], [[937 (number)|937]], [[941 (number)|941]], [[947 (number)|947]], [[953 (number)|953]], [[967 (number)|967]], [[971 (number)|971]], [[977 (number)|977]], [[983 (number)|983]], [[991 (number)|991]], [[997 (number)|997]] ({{OEIS2C|A007510}})
 
=== [[Kynea number|Kynea primes]] ===
Of the form (2{{sup|''n''}}&nbsp;+&nbsp;1){{sup|2}}&nbsp;−&nbsp;2.
 
[[7 (number)|7]], [[23 (number)|23]], [[79 (number)|79]], [[1087 (number)|1087]], [[66047 (number)|66047]], [[263167 (number)|263167]], [[16785407 (number)|16785407]], [[1073807359 (number)|1073807359]], [[17180131327 (number)|17180131327]], [[68720001023 (number)|68720001023]], [[4398050705407 (number)|4398050705407]], [[70368760954879 (number)|70368760954879]], [[18014398777917439 (number)|18014398777917439]], [[18446744082299486207 (number)|18446744082299486207]] ({{OEIS2C|A091514}})
 
=== [[Truncatable prime|Left-truncatable primes]] ===
{{see also|#Right-truncatable primes|#Two-sided primes}}
 
Primes that remain prime when the leading decimal digit is successively removed.
 
[[2 (number)|2]], [[3 (number)|3]], [[5 (number)|5]], [[7 (number)|7]], [[13 (number)|13]], [[17 (number)|17]], [[23 (number)|23]], [[37 (number)|37]], [[43 (number)|43]], [[47 (number)|47]], [[53 (number)|53]], [[67 (number)|67]], [[73 (number)|73]], [[83 (number)|83]], [[97 (number)|97]], [[113 (number)|113]], [[137 (number)|137]], [[167 (number)|167]], [[173 (number)|173]], [[197 (number)|197]], [[223 (number)|223]], [[283 (number)|283]], [[313 (number)|313]], [[317 (number)|317]], [[337 (number)|337]], [[347 (number)|347]], [[353 (number)|353]], [[367 (number)|367]], [[373 (number)|373]], [[383 (number)|383]], [[397 (number)|397]], [[443 (number)|443]], [[467 (number)|467]], [[523 (number)|523]], [[547 (number)|547]], [[613 (number)|613]], [[617 (number)|617]], [[643 (number)|643]], [[647 (number)|647]], [[653 (number)|653]], [[673 (number)|673]], [[683 (number)|683]] ({{OEIS2C|A024785}})
 
=== [[Leyland number|Leyland]] primes ===
Of the form ''x''{{sup|''y''}}&nbsp;+&nbsp;''y''{{sup|''x''}}, with 1&nbsp;<&nbsp;''x''&nbsp;≤&nbsp;''y''.
 
[[17 (number)|17]], [[593 (number)|593]], [[32993 (number)|32993]], [[2097593 (number)|2097593]], [[8589935681 (number)|8589935681]], [[59604644783353249 (number)|59604644783353249]], [[523347633027360537213687137 (number)|523347633027360537213687137]], [[43143988327398957279342419750374600193 (number)|43143988327398957279342419750374600193]] ({{OEIS2C|A094133}})
 
=== [[Full reptend prime|Long primes]] ===
Primes ''p'' for which, in a given base ''b'', <math>\frac{b^{p-1}-1}{p}</math> gives a [[cyclic number]]. They are also called full reptend primes. Primes ''p'' for base 10:
 
[[7 (number)|7]], [[17 (number)|17]], [[19 (number)|19]], [[23 (number)|23]], [[29 (number)|29]], [[47 (number)|47]], [[59 (number)|59]], [[61 (number)|61]], [[97 (number)|97]], [[109 (number)|109]], [[113 (number)|113]], [[131 (number)|131]], [[149 (number)|149]], [[167 (number)|167]], [[179 (number)|179]], [[181 (number)|181]], [[193 (number)|193]], [[223 (number)|223]], [[229 (number)|229]], [[233 (number)|233]], [[257 (number)|257]], [[263 (number)|263]], [[269 (number)|269]], [[313 (number)|313]], [[337 (number)|337]], [[367 (number)|367]], [[379 (number)|379]], [[383 (number)|383]], [[389 (number)|389]], [[419 (number)|419]], [[433 (number)|433]], [[461 (number)|461]], [[487 (number)|487]], [[491 (number)|491]], [[499 (number)|499]], [[503 (number)|503]], [[509 (number)|509]], [[541 (number)|541]], [[571 (number)|571]], [[577 (number)|577]], [[593 (number)|593]] ({{OEIS2C|A001913}})
 
=== [[Lucas number|Lucas primes]] ===
Primes in the Lucas number sequence ''L''{{sub|0}}&nbsp;=&nbsp;2, ''L''{{sub|1}}&nbsp;=&nbsp;1,
''L''{{sub|''n''}}&nbsp;=&nbsp;''L''{{sub|''n''−1}}&nbsp;+&nbsp;''L''{{sub|''n''−2}}.
 
[[2 (number)|2]],<ref>It varies whether ''L''{{sub|0}}&nbsp;=&nbsp;2 is included in the Lucas numbers.</ref> [[3 (number)|3]], [[7 (number)|7]], [[11 (number)|11]], [[29 (number)|29]], [[47 (number)|47]], [[199 (number)|199]], [[521 (number)|521]], [[2207 (number)|2207]], [[3571 (number)|3571]], [[9349 (number)|9349]], [[3010349 (number)|3010349]], [[54018521 (number)|54018521]], [[370248451 (number)|370248451]], [[6643838879 (number)|6643838879]], [[119218851371 (number)|119218851371]], [[5600748293801 (number)|5600748293801]], [[688846502588399 (number)|688846502588399]], [[32361122672259149 (number)|32361122672259149]] ({{OEIS2C|A005479}})
 
=== [[Lucky number|Lucky primes]] ===
Lucky numbers that are prime.
 
[[3 (number)|3]], [[7 (number)|7]], [[13 (number)|13]], [[31 (number)|31]], [[37 (number)|37]], [[43 (number)|43]], [[67 (number)|67]], [[73 (number)|73]], [[79 (number)|79]], [[127 (number)|127]], [[151 (number)|151]], [[163 (number)|163]], [[193 (number)|193]], [[211 (number)|211]], [[223 (number)|223]], [[241 (number)|241]], [[283 (number)|283]], [[307 (number)|307]], [[331 (number)|331]], [[349 (number)|349]], [[367 (number)|367]], [[409 (number)|409]], [[421 (number)|421]], [[433 (number)|433]], [[463 (number)|463]], [[487 (number)|487]], [[541 (number)|541]], [[577 (number)|577]], [[601 (number)|601]], [[613 (number)|613]], 619, [[631 (number)|631]], [[643 (number)|643]], [[673 (number)|673]], [[727 (number)|727]], [[739 (number)|739]], [[769 (number)|769]], [[787 (number)|787]], [[823 (number)|823]], [[883 (number)|883]], [[937 (number)|937]], [[991 (number)|991]], [[997 (number)|997]] ({{OEIS2C|A031157}})
 
=== [[Markov number|Markov]] primes ===
Primes ''p'' for which there exist integers ''x'' and ''y'' such that ''x''{{sup|2}}&nbsp;+&nbsp;''y''{{sup|2}}&nbsp;+&nbsp;''p''{{sup|2}}&nbsp;=&nbsp;3''xyp''.
 
[[2 (number)|2]], [[5 (number)|5]], [[13 (number)|13]], [[29 (number)|29]], [[89 (number)|89]], [[233 (number)|233]], [[433 (number)|433]], [[1597 (number)|1597]], [[2897 (number)|2897]], [[5741 (number)|5741]], [[7561 (number)|7561]], [[28657 (number)|28657]], [[33461 (number)|33461]], [[43261 (number)|43261]], [[96557 (number)|96557]], [[426389 (number)|426389]], [[514229 (number)|514229]], [[1686049 (number)|1686049]], [[2922509 (number)|2922509]], [[3276509 (number)|3276509]], [[94418953 (number)|94418953]], [[321534781 (number)|321534781]], [[433494437 (number)|433494437]], [[780291637 (number)|780291637]], [[1405695061 (number)|1405695061]], [[2971215073 (number)|2971215073]], [[19577194573 (number)|19577194573]], [[25209506681 (number)|25209506681]] (primes in {{OEIS2C|A002559}})
 
=== [[Mersenne prime]]s ===
Of the form 2{{sup|''n''}} − 1.
 
[[3 (number)|3]], [[7 (number)|7]], [[31 (number)|31]], [[127 (number)|127]], [[8191 (number)|8191]], [[131071 (number)|131071]], [[524287 (number)|524287]], [[2147483647]], [[2305843009213693951 (number)|2305843009213693951]], [[618970019642690137449562111 (number)|618970019642690137449562111]], [[162259276829213363391578010288127 (number)|162259276829213363391578010288127]], [[170141183460469231731687303715884105727 (number)|170141183460469231731687303715884105727]] ({{OEIS2C|A000668}})
 
{{As of|2013}}, there are 48 known Mersenne primes. The 13th, 14th, and 48th have respectively 157, 183, and  17,425,170 digits.
 
=== Mersenne prime exponents ===
Primes ''p'' such that 2{{sup|''p''}} − 1 is prime.
 
[[2 (number)|2]], [[3 (number)|3]], [[5 (number)|5]], [[7 (number)|7]], [[13 (number)|13]], [[17 (number)|17]], [[19 (number)|19]], [[31 (number)|31]], [[61 (number)|61]], [[89 (number)|89]], [[107 (number)|107]], [[127 (number)|127]], [[521 (number)|521]], [[607 (number)|607]], [[1279 (number)|1279]], [[2203 (number)|2203]], [[2281 (number)|2281]], [[3217 (number)|3217]], [[4253 (number)|4253]], [[4423 (number)|4423]], [[9689 (number)|9689]], [[9941 (number)|9941]], [[11213 (number)|11213]], [[19937 (number)|19937]], [[21701 (number)|21701]], [[23209 (number)|23209]], [[44497 (number)|44497]], [[86243 (number)|86243]], [[110503 (number)|110503]], [[132049 (number)|132049]], [[216091 (number)|216091]], [[756839 (number)|756839]], [[859433 (number)|859433]], [[1257787 (number)|1257787]], [[1398269 (number)|1398269]], [[2976221 (number)|2976221]], [[3021377 (number)|3021377]], [[6972593 (number)|6972593]], [[13466917 (number)|13466917]], [[20996011 (number)|20996011]], [[24036583 (number)|24036583]], [[25964951 (number)|25964951]] ({{OEIS2C|A000043}})
 
=== [[Mills' constant|Mills primes]] ===
Of the form ⌊θ{{sup|3{{sup|''n''}}}}⌋, where θ is Mills' constant. This form is prime for all positive integers ''n''.
 
[[2 (number)|2]], [[11 (number)|11]], [[1361 (number)|1361]], [[2521008887 (number)|2521008887]], [[16022236204009818131831320183 (number)|16022236204009818131831320183]] ({{OEIS2C|A051254}})
 
=== [[Minimal prime (number theory)|Minimal primes]] ===
Primes for which there is no shorter [[subsequence|sub-sequence]] of the decimal digits that form a prime. There are exactly 26 minimal primes:
 
[[2 (number)|2]], [[3 (number)|3]], [[5 (number)|5]], [[7 (number)|7]], [[11 (number)|11]], [[19 (number)|19]], [[41 (number)|41]], [[61 (number)|61]], [[89 (number)|89]], [[409 (number)|409]], [[449 (number)|449]], [[499 (number)|499]], [[881 (number)|881]], [[991 (number)|991]], [[6469 (number)|6469]], [[6949 (number)|6949]], [[9001 (number)|9001]], [[9049 (number)|9049]], [[9649 (number)|9649]], [[9949 (number)|9949]], [[60649 (number)|60649]], [[666649 (number)|666649]], [[946669 (number)|946669]], [[60000049 (number)|60000049]], [[66000049 (number)|66000049]], [[66600049 (number)|66600049]] ({{OEIS2C|A071062}})
 
=== [[Motzkin number|Motzkin]] primes ===
Primes that are the number of different ways of drawing non-intersecting chords on a circle between ''n'' points.
 
[[2 (number)|2]], [[127 (number)|127]], [[15511 (number)|15511]], [[953467954114363 (number)|953467954114363]] ({{OEIS2C|A092832}})
 
=== [[Newman–Shanks–Williams prime]]s ===
Newman–Shanks–Williams numbers that are prime.
 
[[7 (number)|7]], [[41 (number)|41]], [[239 (number)|239]], [[9369319 (number)|9369319]], [[63018038201 (number)|63018038201]], [[489133282872437279 (number)|489133282872437279]], [[19175002942688032928599 (number)|19175002942688032928599]] ({{OEIS2C|A088165}})
 
=== Non-generous primes ===
Primes ''p'' for which the least positive [[primitive root modulo n|primitive root]] is not a primitive root of p{{sup|2}}.
 
[[2 (number)|2]], [[40487 (number)|40487]], [[6692367337 (number)|6692367337]] ({{OEIS2C|A055578}})
 
=== [[Odd number|Odd]] primes ===
Of the form 2''n'' − 1.
 
[[3 (number)|3]], [[5 (number)|5]], [[7 (number)|7]], [[11 (number)|11]], [[13 (number)|13]], [[17 (number)|17]], [[19 (number)|19]], [[23 (number)|23]], [[29 (number)|29]], [[31 (number)|31]], [[37 (number)|37]], [[41 (number)|41]], [[43 (number)|43]], [[47 (number)|47]], [[53 (number)|53]], [[59 (number)|59]], [[61 (number)|61]], [[67 (number)|67]], [[71 (number)|71]], [[73 (number)|73]], [[79 (number)|79]], [[83 (number)|83]], [[89 (number)|89]], [[97 (number)|97]], [[101 (number)|101]], [[103 (number)|103]], [[107 (number)|107]], [[109 (number)|109]], [[113 (number)|113]], [[127 (number)|127]], [[131 (number)|131]], [[137 (number)|137]], [[139 (number)|139]], [[149 (number)|149]], [[151 (number)|151]], [[157 (number)|157]], [[163 (number)|163]], [[167 (number)|167]], [[173 (number)|173]], [[179 (number)|179]], [[181 (number)|181]], [[191 (number)|191]], [[193 (number)|193]], [[197 (number)|197]], [[199 (number)|199]]... ({{OEIS2C|A065091}})
 
All prime numbers except 2 are odd.
 
=== [[Padovan sequence|Padovan]] primes ===
Primes in the Padovan sequence ''P''(0)&nbsp;=&nbsp;''P''(1)&nbsp;=&nbsp;''P''(2)&nbsp;=&nbsp;1, ''P''(''n'')&nbsp;=&nbsp;''P''(''n''−2)&nbsp;+&nbsp;''P''(''n''−3).
 
[[2 (number)|2]], [[3 (number)|3]], [[5 (number)|5]], [[7 (number)|7]], [[37 (number)|37]], [[151 (number)|151]], [[3329 (number)|3329]], [[23833 (number)|23833]], [[13091204281 (number)|13091204281]], [[3093215881333057 (number)|3093215881333057]], [[1363005552434666078217421284621279933627102780881053358473 (number)|1363005552434666078217421284621279933627102780881053358473]] ({{OEIS2C|A100891}})
 
=== [[Palindromic prime]]s ===
Primes that remain the same when their decimal digits are read backwards.
 
[[2 (number)|2]], [[3 (number)|3]], [[5 (number)|5]], [[7 (number)|7]], [[11 (number)|11]], [[101 (number)|101]], [[131 (number)|131]], [[151 (number)|151]], [[181 (number)|181]], [[191 (number)|191]], [[313 (number)|313]], [[353 (number)|353]], [[373 (number)|373]], [[383 (number)|383]], [[727 (number)|727]], [[757 (number)|757]], [[787 (number)|787]], [[797 (number)|797]], [[919 (number)|919]], [[929 (number)|929]], [[10301 (number)|10301]], [[10501 (number)|10501]], [[10601 (number)|10601]], [[11311 (number)|11311]], [[11411 (number)|11411]], [[12421 (number)|12421]], [[12721 (number)|12721]], [[12821 (number)|12821]], [[13331 (number)|13331]], [[13831 (number)|13831]], [[13931 (number)|13931]], [[14341 (number)|14341]], [[14741 (number)|14741]] ({{OEIS2C|A002385}})
 
=== Palindromic wing primes ===
Primes of the form <math>\frac{a \big( 10^m-1 \big)}{9} \pm b \times 10^{\frac{m}{2}}</math>.<ref>{{Cite journal | last1 = Caldwell | first1 = C. | author1-link = Chris Caldwell | last2 = Dubner | first2 = H. | author2-link = Harvey Dubner | title = The near repdigit primes <math>A_{n-k-1}B_1A_k</math>, especially <math>9_{n-k-1}8_19_k</math> | journal = Journal of Recreational Mathematics | volume = 28 | issue = 1 | pages = 1–9 | year = 1996–97}}</ref>
 
[[101 (number)|101]], [[131 (number)|131]], [[151 (number)|151]], [[181 (number)|181]], [[191 (number)|191]], [[313 (number)|313]], [[353 (number)|353]], [[373 (number)|373]], [[383 (number)|383]], [[727 (number)|727]], [[757 (number)|757]], [[787 (number)|787]], [[797 (number)|797]], [[919 (number)|919]], [[929 (number)|929]], [[11311 (number)|11311]], [[11411 (number)|11411]], [[33533 (number)|33533]], [[77377 (number)|77377]], [[77477 (number)|77477]], [[77977 (number)|77977]], [[1114111 (number)|1114111]], [[1117111 (number)|1117111]], [[3331333 (number)|3331333]], [[3337333 (number)|3337333]], [[7772777 (number)|7772777]], [[7774777 (number)|7774777]], [[7778777 (number)|7778777]], [[111181111 (number)|111181111]], [[111191111 (number)|111191111]], [[777767777 (number)|777767777]], [[77777677777 (number)|77777677777]], [[99999199999 (number)|99999199999]] ({{OEIS2C|A077798}})
 
=== [[Partition (number theory)|Partition]] primes ===
Partition numbers that are prime.
 
[[2 (number)|2]], [[3 (number)|3]], [[5 (number)|5]], [[7 (number)|7]], [[11 (number)|11]], [[101 (number)|101]], [[17977 (number)|17977]], [[10619863 (number)|10619863]], [[6620830889 (number)|6620830889]], [[80630964769 (number)|80630964769]], [[228204732751 (number)|228204732751]], [[1171432692373 (number)|1171432692373]], [[1398341745571 (number)|1398341745571]], [[10963707205259 (number)|10963707205259]], [[15285151248481 (number)|15285151248481]], [[10657331232548839 (number)|10657331232548839]], [[790738119649411319 (number)|790738119649411319]], [[18987964267331664557 (number)|18987964267331664557]] ({{OEIS2C|A049575}})
 
=== [[Pell number|Pell]] primes ===
Primes in the Pell number sequence ''P''{{sub|0}}&nbsp;=&nbsp;0, ''P''{{sub|''1''}}&nbsp;=&nbsp;1,
''P''{{sub|''n''}}&nbsp;=&nbsp;2''P''{{sub|''n''−1}}&nbsp;+&nbsp;''P''{{sub|''n''−2}}.
 
[[2 (number)|2]], [[5 (number)|5]], [[29 (number)|29]], [[5741 (number)|5741]], [[33461 (number)|33461]], [[44560482149 (number)|44560482149]], [[1746860020068409 (number)|1746860020068409]], [[68480406462161287469 (number)|68480406462161287469]], [[13558774610046711780701 (number)|13558774610046711780701]], [[4125636888562548868221559797461449 (number)|4125636888562548868221559797461449]] ({{OEIS2C|A086383}})
 
=== [[Permutable prime]]s ===
Any permutation of the decimal digits is a prime.
 
[[2 (number)|2]], [[3 (number)|3]], [[5 (number)|5]], [[7 (number)|7]], [[11 (number)|11]], [[13 (number)|13]], [[17 (number)|17]], [[31 (number)|31]], [[37 (number)|37]], [[71 (number)|71]], [[73 (number)|73]], [[79 (number)|79]], [[97 (number)|97]], [[113 (number)|113]], [[131 (number)|131]], [[199 (number)|199]], [[311 (number)|311]], [[337 (number)|337]], [[373 (number)|373]], [[733 (number)|733]], [[919 (number)|919]], [[991 (number)|991]], [[1111111111111111111 (number)|1111111111111111111]], [[11111111111111111111111 (number)|11111111111111111111111]] ({{OEIS2C|A003459}})
 
It seems likely that all further permutable primes are [[repunit]]s, i.e. contain only the digit 1.
 
=== [[Perrin number|Perrin]] primes ===
Primes in the Perrin number sequence ''P''(0)&nbsp;=&nbsp;3, ''P''(1)&nbsp;=&nbsp;0, ''P''(2)&nbsp;=&nbsp;2,
''P''(''n'')&nbsp;=&nbsp;''P''(''n''−2)&nbsp;+&nbsp;''P''(''n''−3).
 
[[2 (number)|2]], [[3 (number)|3]], [[5 (number)|5]], [[7 (number)|7]], [[17 (number)|17]], [[29 (number)|29]], [[277 (number)|277]], [[367 (number)|367]], [[853 (number)|853]], [[14197 (number)|14197]], [[43721 (number)|43721]], [[1442968193 (number)|1442968193]], [[792606555396977 (number)|792606555396977]], [[187278659180417234321 (number)|187278659180417234321]], [[66241160488780141071579864797 (number)|66241160488780141071579864797]] ({{OEIS2C|A074788}})
 
=== [[Pierpont prime]]s ===
Of the form 2{{sup|''u''}}3{{sup|''v''}}&nbsp;+&nbsp;1 for some [[integer]]s ''u'',''v''&nbsp;≥&nbsp;0.
 
These are also [[Prime number#Classification of prime numbers|class 1- primes]].
 
[[2 (number)|2]], [[3 (number)|3]], [[5 (number)|5]], [[7 (number)|7]], [[13 (number)|13]], [[17 (number)|17]], [[19 (number)|19]], [[37 (number)|37]], [[73 (number)|73]], [[97 (number)|97]], [[109 (number)|109]], [[163 (number)|163]], [[193 (number)|193]], [[257 (number)|257]], [[433 (number)|433]], [[487 (number)|487]], [[577 (number)|577]], [[769 (number)|769]], [[1153 (number)|1153]], [[1297 (number)|1297]], [[1459 (number)|1459]], [[2593 (number)|2593]], [[2917 (number)|2917]], [[3457 (number)|3457]], [[3889 (number)|3889]], [[10369 (number)|10369]], [[12289 (number)|12289]], [[17497 (number)|17497]], [[18433 (number)|18433]], [[39367 (number)|39367]], [[52489 (number)|52489]], [[65537 (number)|65537]], [[139969 (number)|139969]], [[147457 (number)|147457]] ({{OEIS2C|A005109}})
 
=== [[Pillai prime]]s ===
Primes ''p'' for which there exist ''n''&nbsp;>&nbsp;0 such that ''p'' divides ''n''!+ 1 and ''n'' does not divide ''p''−1.
 
[[23 (number)|23]], [[29 (number)|29]], [[59 (number)|59]], [[61 (number)|61]], [[67 (number)|67]], [[71 (number)|71]], [[79 (number)|79]], [[83 (number)|83]], [[109 (number)|109]], [[137 (number)|137]], [[139 (number)|139]], [[149 (number)|149]], [[193 (number)|193]], [[227 (number)|227]], [[233 (number)|233]], [[239 (number)|239]], [[251 (number)|251]], [[257 (number)|257]], [[269 (number)|269]], [[271 (number)|271]], [[277 (number)|277]], [[293 (number)|293]], [[307 (number)|307]], [[311 (number)|311]], [[317 (number)|317]], [[359 (number)|359]], [[379 (number)|379]], [[383 (number)|383]], [[389 (number)|389]], [[397 (number)|397]], [[401 (number)|401]], [[419 (number)|419]], [[431 (number)|431]], [[449 (number)|449]], [[461 (number)|461]], [[463 (number)|463]], [[467 (number)|467]], [[479 (number)|479]], [[499 (number)|499]] ({{OEIS2C|A063980}})
 
=== Primes of the form ''n''<sup>4</sup> + 1 ===
Of the form ''n''<sup>4</sup> + 1.<ref>{{cite journal | last = Lal | first = M. | title = Primes of the Form n<sup>4</sup> + 1 | journal = Mathematics of Computation | volume = 21 | pages = 245-247 | publisher = [[American Mathematical Society|AMS]] | date = 1967 | url = http://www.ams.org/journals/mcom/1967-21-098/S0025-5718-1967-0222007-9/S0025-5718-1967-0222007-9.pdf | issn = 1088-6842 | doi = 10.1090/S0025-5718-1967-0222007-9}}</ref><ref>{{cite journal | last = Bohman | first = J. | title = New primes of the form ''n''<sup>4</sup> + 1 | journal = BIT Numerical Mathematics | volume = 13 | issue = 3 | pages = 370-372 | publisher = Springer | date = 1973 | issn = 1572-9125 | doi = 10.1007/BF01951947}}</ref>
 
[[2 (number)|2]], [[17 (number)|17]], [[257 (number)|257]], [[1297 (number)|1297]], [[65537 (number)|65537]], [[160001 (number)|160001]], [[331777 (number)|331777]], [[614657 (number)|614657]], [[1336337 (number)|1336337]], [[4477457 (number)|4477457]], [[5308417 (number)|5308417]], [[8503057 (number)|8503057]], [[9834497 (number)|9834497]], [[29986577 (number)|29986577]], [[40960001 (number)|40960001]], [[45212177 (number)|45212177]], [[59969537 (number)|59969537]], [[65610001 (number)|65610001]], [[126247697 (number)|126247697]], [[193877777 (number)|193877777]], [[303595777 (number)|303595777]], [[384160001 (number)|384160001]], [[406586897 (number)|406586897]], [[562448657 (number)|562448657]], [[655360001 (number)|655360001]] ({{OEIS2C|A037896}})
 
=== [[Primeval prime]]s ===
Primes for which there are more prime permutations of some or all the decimal digits than for any smaller number.
 
[[2 (number)|2]], [[13 (number)|13]], [[37 (number)|37]], [[107 (number)|107]], [[113 (number)|113]], [[137 (number)|137]], [[1013 (number)|1013]], [[1237 (number)|1237]], [[1367 (number)|1367]], [[10079 (number)|10079]] ({{OEIS2C|A119535}})
 
=== [[Primorial prime]]s ===
Of the form ''p''{{sub|''n''}}#&nbsp;−1 or ''p''{{sub|''n''}}#&nbsp;+&nbsp;1.
 
[[3 (number)|3]], [[5 (number)|5]], [[7 (number)|7]], [[29 (number)|29]], [[31 (number)|31]], [[211 (number)|211]], [[2309 (number)|2309]], [[2311 (number)|2311]], [[30029 (number)|30029]], [[200560490131 (number)|200560490131]], [[304250263527209 (number)|304250263527209]], [[23768741896345550770650537601358309 (number)|23768741896345550770650537601358309]] (union of {{OEIS2C|A057705}} and {{OEIS2C|A018239}}<ref name="A018239"/>)
 
=== [[Proth number|Proth primes]] ===
Of the form ''k''×2{{sup|''n''}}&nbsp;+&nbsp;1, with odd ''k'' and ''k''&nbsp;<&nbsp;2{{sup|''n''}}.
 
[[3 (number)|3]], [[5 (number)|5]], [[13 (number)|13]], [[17 (number)|17]], [[41 (number)|41]], [[97 (number)|97]], [[113 (number)|113]], [[193 (number)|193]], [[241 (number)|241]], [[257 (number)|257]], [[353 (number)|353]], [[449 (number)|449]], [[577 (number)|577]], [[641 (number)|641]], [[673 (number)|673]], [[769 (number)|769]], [[929 (number)|929]], [[1153 (number)|1153]], [[1217 (number)|1217]], [[1409 (number)|1409]], [[1601 (number)|1601]], [[2113 (number)|2113]], [[2689 (number)|2689]], [[2753 (number)|2753]], [[3137 (number)|3137]], [[3329 (number)|3329]], [[3457 (number)|3457]], [[4481 (number)|4481]], [[4993 (number)|4993]], [[6529 (number)|6529]], [[7297 (number)|7297]], [[7681 (number)|7681]], [[7937 (number)|7937]], [[9473 (number)|9473]], [[9601 (number)|9601]], [[9857 (number)|9857]] ({{OEIS2C|A080076}})
 
=== [[Pythagorean prime]]s ===
Of the form 4''n'' + 1.
 
[[5 (number)|5]], [[13 (number)|13]], [[17 (number)|17]], [[29 (number)|29]], [[37 (number)|37]], [[41 (number)|41]], [[53 (number)|53]], [[61 (number)|61]], [[73 (number)|73]], [[89 (number)|89]], [[97 (number)|97]], [[101 (number)|101]], [[109 (number)|109]], [[113 (number)|113]], [[137 (number)|137]], [[149 (number)|149]], [[157 (number)|157]], [[173 (number)|173]], [[181 (number)|181]], [[193 (number)|193]], [[197 (number)|197]], [[229 (number)|229]], [[233 (number)|233]], [[241 (number)|241]], [[257 (number)|257]], [[269 (number)|269]], [[277 (number)|277]], [[281 (number)|281]], [[293 (number)|293]], [[313 (number)|313]], [[317 (number)|317]], [[337 (number)|337]], [[349 (number)|349]], [[353 (number)|353]], [[373 (number)|373]], [[389 (number)|389]], [[397 (number)|397]], [[401 (number)|401]], [[409 (number)|409]], [[421 (number)|421]], [[433 (number)|433]], [[449 (number)|449]] ({{OEIS2C|A002144}})
 
=== [[Prime quadruplet]]s ===
{{see also|#Cousin primes|#Twin primes|#Prime triplets}}
 
Where (''p'', ''p''+2, ''p''+6, ''p''+8) are all prime.
 
([[5 (number)|5]], [[7 (number)|7]], [[11 (number)|11]], [[13 (number)|13]]), (11, 13, [[17 (number)|17]], [[19 (number)|19]]), ([[101 (number)|101]], [[103 (number)|103]], [[107 (number)|107]], [[109 (number)|109]]), ([[191 (number)|191]], [[193 (number)|193]], [[197 (number)|197]], [[199 (number)|199]]), ([[821 (number)|821]], [[823 (number)|823]], [[827 (number)|827]], [[829 (number)|829]]), ([[1481 (number)|1481]], [[1483 (number)|1483]], [[1487 (number)|1487]], [[1489 (number)|1489]]), ([[1871 (number)|1871]], [[1873 (number)|1873]], [[1877 (number)|1877]], [[1879 (number)|1879]]), ([[2081 (number)|2081]], [[2083 (number)|2083]], [[2087 (number)|2087]], [[2089 (number)|2089]]), ([[3251 (number)|3251]], [[3253 (number)|3253]], [[3257 (number)|3257]], [[3259 (number)|3259]]), ([[3461 (number)|3461]], [[3463 (number)|3463]], [[3467 (number)|3467]], [[3469 (number)|3469]]), ([[5651 (number)|5651]], [[5653 (number)|5653]], [[5657 (number)|5657]], [[5659 (number)|5659]]), ([[9431 (number)|9431]], [[9433 (number)|9433]], [[9437 (number)|9437]], [[9439 (number)|9439]]) ({{OEIS2C|A007530}}, {{OEIS2C|A136720}}, {{OEIS2C|A136721}}, {{OEIS2C|A090258}})
 
=== Primes of binary quadratic form ===
Of the form ''x''{{sup|2}}&nbsp;+&nbsp;''xy''&nbsp;+&nbsp;2''y''{{sup|2}}, with non-negative integers ''x'' and ''y''.
 
[[2 (number)|2]], [[11 (number)|11]], [[23 (number)|23]], [[37 (number)|37]], [[43 (number)|43]], [[53 (number)|53]], [[71 (number)|71]], [[79 (number)|79]], [[107 (number)|107]], [[109 (number)|109]], [[127 (number)|127]], [[137 (number)|137]], [[149 (number)|149]], [[151 (number)|151]], [[163 (number)|163]], [[193 (number)|193]], [[197 (number)|197]], [[211 (number)|211]], [[233 (number)|233]], [[239 (number)|239]], [[263 (number)|263]], [[281 (number)|281]], [[317 (number)|317]], [[331 (number)|331]], [[337 (number)|337]], [[373 (number)|373]], [[389 (number)|389]], [[401 (number)|401]], [[421 (number)|421]], [[431 (number)|431]], [[443 (number)|443]], [[463 (number)|463]], [[487 (number)|487]], [[491 (number)|491]], [[499 (number)|499]], [[541 (number)|541]], [[547 (number)|547]], [[557 (number)|557]], [[569 (number)|569]], [[599 (number)|599]], [[613 (number)|613]], [[617 (number)|617]], [[641 (number)|641]], [[653 (number)|653]], [[659 (number)|659]], [[673 (number)|673]], [[683 (number)|683]], [[739 (number)|739]], [[743 (number)|743]], [[751 (number)|751]], [[757 (number)|757]], [[809 (number)|809]], [[821 (number)|821]] ({{OEIS2C|A106856}})
 
=== [[Quartan prime]]s ===
Of the form ''x''{{sup|4}}&nbsp;+&nbsp;''y''{{sup|4}}, where ''x'',''y''&nbsp;>&nbsp;0.
 
[[2 (number)|2]], [[17 (number)|17]], [[97 (number)|97]], [[257 (number)|257]], [[337 (number)|337]], [[641 (number)|641]], [[881 (number)|881]] ({{OEIS2C|A002645}})
 
=== [[Ramanujan prime]]s ===
Integers ''R''{{sub|''n''}} that are the smallest to give at least ''n'' primes from ''x''/2 to ''x'' for all ''x''&nbsp;≥&nbsp;''R''{{sub|''n''}} (all such integers are primes).
 
[[2 (number)|2]], [[11 (number)|11]], [[17 (number)|17]], [[29 (number)|29]], [[41 (number)|41]], [[47 (number)|47]], [[59 (number)|59]], [[67 (number)|67]], [[71 (number)|71]], [[97 (number)|97]], [[101 (number)|101]], [[107 (number)|107]], [[127 (number)|127]], [[149 (number)|149]], [[151 (number)|151]], [[167 (number)|167]], [[179 (number)|179]], [[181 (number)|181]], [[227 (number)|227]], [[229 (number)|229]], [[233 (number)|233]], [[239 (number)|239]], [[241 (number)|241]], [[263 (number)|263]], [[269 (number)|269]], [[281 (number)|281]], [[307 (number)|307]], [[311 (number)|311]], [[347 (number)|347]], [[349 (number)|349]], [[367 (number)|367]], [[373 (number)|373]], [[401 (number)|401]], [[409 (number)|409]], [[419 (number)|419]], [[431 (number)|431]], [[433 (number)|433]], [[439 (number)|439]], [[461 (number)|461]], [[487 (number)|487]], [[491 (number)|491]] ({{OEIS2C|A104272}})
 
=== [[Regular prime]]s ===
Primes ''p'' which do not divide the [[Class number (number theory)|class number]] of the ''p''-th [[cyclotomic field]].
 
[[3 (number)|3]], [[5 (number)|5]], [[7 (number)|7]], [[11 (number)|11]], [[13 (number)|13]], [[17 (number)|17]], [[19 (number)|19]], [[23 (number)|23]], [[29 (number)|29]], [[31 (number)|31]], [[41 (number)|41]], [[43 (number)|43]], [[47 (number)|47]], [[53 (number)|53]], [[61 (number)|61]], [[71 (number)|71]], [[73 (number)|73]], [[79 (number)|79]], [[83 (number)|83]], [[89 (number)|89]], [[97 (number)|97]], [[107 (number)|107]], [[109 (number)|109]], [[113 (number)|113]], [[127 (number)|127]], [[137 (number)|137]], [[139 (number)|139]], [[151 (number)|151]], [[163 (number)|163]], [[167 (number)|167]], [[173 (number)|173]], [[179 (number)|179]], [[181 (number)|181]], [[191 (number)|191]], [[193 (number)|193]], [[197 (number)|197]], [[199 (number)|199]], [[211 (number)|211]], [[223 (number)|223]], [[227 (number)|227]], [[229 (number)|229]], [[239 (number)|239]], [[241 (number)|241]], [[251 (number)|251]], [[269 (number)|269]], [[277 (number)|277]], [[281 (number)|281]] ({{OEIS2C|A007703}})
 
=== [[Repunit]] primes ===
Primes containing only the decimal digit 1.
 
[[11 (number)|11]], [[1111111111111111111 (number)|1111111111111111111]], [[11111111111111111111111 (number)|11111111111111111111111]] ({{OEIS2C|A004022}})
 
The next have 317 and 1,031 digits.
 
=== [[Dirichlet's theorem on arithmetic progressions|Primes in residue classes]] ===
Of the form ''an'' + ''d'' for fixed ''a'' and ''d''. Also called primes congruent to ''d'' [[Modular arithmetic|modulo]] ''a''.
 
Three cases have their own entry: 2''n''+1 are the odd primes, 4''n''+1 are Pythagorean primes, 4''n''+3 are the integer Gaussian primes.
 
2''n''+1: [[3 (number)|3]], [[5 (number)|5]], [[7 (number)|7]], [[11 (number)|11]], [[13 (number)|13]], [[17 (number)|17]], [[19 (number)|19]], [[23 (number)|23]], [[29 (number)|29]], [[31 (number)|31]], [[37 (number)|37]], [[41 (number)|41]], [[43 (number)|43]], [[47 (number)|47]], [[53 (number)|53]] ({{OEIS2C|A065091}})<br>
4''n''+1: 5, 13, 17, 29, 37, 41, 53, [[61 (number)|61]], [[73 (number)|73]], [[89 (number)|89]], [[97 (number)|97]], [[101 (number)|101]], [[109 (number)|109]], [[113 (number)|113]], [[137 (number)|137]] ({{OEIS2C|A002144}})<br>
4''n''+3: 3, 7, 11, 19, 23, 31, 43, 47, [[59 (number)|59]], [[67 (number)|67]], [[71 (number)|71]], [[79 (number)|79]], [[83 (number)|83]], [[103 (number)|103]], [[107 (number)|107]] ({{OEIS2C|A002145}})<br>
6''n''+1: 7, 13, 19, 31, 37, 43, 61, 67, 73, 79, 97, 103, 109, [[127 (number)|127]], [[139 (number)|139]] ({{OEIS2C|A002476}})<br>
6''n''+5: 5, 11, 17, 23, 29, 41, 47, 53, 59, 71, 83, 89, 101, 107, 113 ({{OEIS2C|A007528}})<br>
8''n''+1: 17, 41, 73, 89, 97, 113, 137, [[193 (number)|193]], [[233 (number)|233]], [[241 (number)|241]], [[257 (number)|257]], [[281 (number)|281]], [[313 (number)|313]], [[337 (number)|337]], [[353 (number)|353]] ({{OEIS2C|A007519}})<br>
8''n''+3: 3, 11, 19, 43, 59, 67, 83, 107, [[131 (number)|131]], 139, [[163 (number)|163]], [[179 (number)|179]], [[211 (number)|211]], [[227 (number)|227]], [[251 (number)|251]] ({{OEIS2C|A007520}})<br>
8''n''+5: 5, 13, 29, 37, 53, 61, 101, 109, [[149 (number)|149]], [[157 (number)|157]], [[173 (number)|173]], [[181 (number)|181]], [[197 (number)|197]], [[229 (number)|229]], [[269 (number)|269]] ({{OEIS2C|A007521}})<br>
8''n''+7: 7, 23, 31, 47, 71, 79, 103, 127, [[151 (number)|151]], [[167 (number)|167]], [[191 (number)|191]], [[199 (number)|199]], [[223 (number)|223]], [[239 (number)|239]], [[263 (number)|263]] ({{OEIS2C|A007522}})<br>
10''n''+1: 11, 31, 41, 61, 71, 101, 131, 151, 181, 191, 211, 241, 251, [[271 (number)|271]], 281 ({{OEIS2C|A030430}})<br>
10''n''+3: 3, 13, 23, 43, 53, 73, 83, 103, 113, 163, 173, 193, 223, 233, 263 ({{OEIS2C|A030431}})<br>
10''n''+7: 7, 17, 37, 47, 67, 97, 107, 127, 137, 157, 167, 197, 227, 257, [[277 (number)|277]] ({{OEIS2C|A030432}})<br>
10''n''+9: 19, 29, 59, 79, 89, 109, 139, 149, 179, 199, 229, 239, 269, [[349 (number)|349]], [[359 (number)|359]] ({{OEIS2C|A030433}})<br>
...
 
10''n''+''d'' (''d'' = 1, 3, 7, 9) are primes ending in the decimal digit ''d''.
 
=== [[Truncatable prime|Right-truncatable primes]] ===
{{see also|#Left-truncatable primes|#Two-sided primes}}
 
Primes that remain prime when the last decimal digit is successively removed.
 
[[2 (number)|2]], [[3 (number)|3]], [[5 (number)|5]], [[7 (number)|7]], [[23 (number)|23]], [[29 (number)|29]], [[31 (number)|31]], [[37 (number)|37]], [[53 (number)|53]], [[59 (number)|59]], [[71 (number)|71]], [[73 (number)|73]], [[79 (number)|79]], [[233 (number)|233]], [[239 (number)|239]], [[293 (number)|293]], [[311 (number)|311]], [[313 (number)|313]], [[317 (number)|317]], [[373 (number)|373]], [[379 (number)|379]], [[593 (number)|593]], [[599 (number)|599]], [[719 (number)|719]], [[733 (number)|733]], [[739 (number)|739]], [[797 (number)|797]], [[2333 (number)|2333]], [[2339 (number)|2339]], [[2393 (number)|2393]], [[2399 (number)|2399]], [[2939 (number)|2939]], [[3119 (number)|3119]], [[3137 (number)|3137]], [[3733 (number)|3733]], [[3739 (number)|3739]], [[3793 (number)|3793]], [[3797 (number)|3797]] ({{OEIS2C|A024770}})
 
=== [[Safe prime]]s ===
Where ''p'' and (''p''−1)&nbsp;/&nbsp;2 are both prime.
 
[[5 (number)|5]], [[7 (number)|7]], [[11 (number)|11]], [[23 (number)|23]], [[47 (number)|47]], [[59 (number)|59]], [[83 (number)|83]], [[107 (number)|107]], [[167 (number)|167]], [[179 (number)|179]], [[227 (number)|227]], [[263 (number)|263]], [[347 (number)|347]], [[359 (number)|359]], [[383 (number)|383]], [[467 (number)|467]], [[479 (number)|479]], [[503 (number)|503]], [[563 (number)|563]], [[587 (number)|587]], [[719 (number)|719]], [[839 (number)|839]], [[863 (number)|863]], [[887 (number)|887]], [[983 (number)|983]], [[1019 (number)|1019]], [[1187 (number)|1187]], [[1283 (number)|1283]], [[1307 (number)|1307]], [[1319 (number)|1319]], [[1367 (number)|1367]], [[1439 (number)|1439]], [[1487 (number)|1487]], [[1523 (number)|1523]], [[1619 (number)|1619]], [[1823 (number)|1823]], [[1907 (number)|1907]] ({{OEIS2C|A005385}})
 
=== [[Self number|Self primes]] in base 10 ===
Primes that cannot be generated by any integer added to the sum of its decimal digits.
 
[[3 (number)|3]], [[5 (number)|5]], [[7 (number)|7]], [[31 (number)|31]], [[53 (number)|53]], [[97 (number)|97]], [[211 (number)|211]], [[233 (number)|233]], [[277 (number)|277]], [[367 (number)|367]], [[389 (number)|389]], [[457 (number)|457]], [[479 (number)|479]], [[547 (number)|547]], [[569 (number)|569]], [[613 (number)|613]], [[659 (number)|659]], [[727 (number)|727]], [[839 (number)|839]], [[883 (number)|883]], [[929 (number)|929]], [[1021 (number)|1021]], [[1087 (number)|1087]], [[1109 (number)|1109]], [[1223 (number)|1223]], [[1289 (number)|1289]], [[1447 (number)|1447]], [[1559 (number)|1559]], [[1627 (number)|1627]], [[1693 (number)|1693]], [[1783 (number)|1783]], [[1873 (number)|1873]] ({{OEIS2C|A006378}})
 
=== [[Sexy prime]]s ===
Where (''p'', ''p''+6) are both prime.
 
([[5 (number)|5]], [[11 (number)|11]]), ([[7 (number)|7]], [[13 (number)|13]]), (11, [[17 (number)|17]]), (13, [[19 (number)|19]]), (17, [[23 (number)|23]]), (23, [[29 (number)|29]]), ([[31 (number)|31]], [[37 (number)|37]]), (37, [[43 (number)|43]]), ([[41 (number)|41]], [[47 (number)|47]]), (47, [[53 (number)|53]]), (53, [[59 (number)|59]]), ([[61 (number)|61]], [[67 (number)|67]]), (67, [[73 (number)|73]]), (73, [[79 (number)|79]]), ([[83 (number)|83]], [[89 (number)|89]]), ([[97 (number)|97]], [[103 (number)|103]]), ([[101 (number)|101]], [[107 (number)|107]]), (103, [[109 (number)|109]]), (107, [[113 (number)|113]]), ([[131 (number)|131]], [[137 (number)|137]]), ([[151 (number)|151]], [[157 (number)|157]]), (157, [[163 (number)|163]]), ([[167 (number)|167]], [[173 (number)|173]]), (173, [[179 (number)|179]]), ([[191 (number)|191]], [[197 (number)|197]]), ([[193 (number)|193]], [[199 (number)|199]]) ({{OEIS2C|A023201}}, {{OEIS2C|A046117}})
 
=== [[Smarandache–Wellin number|Smarandache–Wellin]] primes ===
Primes which are the concatenation of the first ''n'' primes written in decimal.
 
[[2 (number)|2]], [[23 (number)|23]], [[2357 (number)|2357]] ({{OEIS2C|A069151}})
 
The fourth Smarandache-Wellin prime is the 355-digit concatenation of the first 128 primes which end with 719.
 
=== [[Solinas prime]]s ===
Of the form 2{{sup|''a''}}&nbsp;±&nbsp;2{{sup|''b''}}&nbsp;±&nbsp;1, where 0&nbsp;<&nbsp;''b''&nbsp;<&nbsp;''a''.
 
[[3 (number)|3]], [[5 (number)|5]], [[7 (number)|7]], [[11 (number)|11]], [[13 (number)|13]] ({{OEIS2C|A165255}})
 
=== [[Sophie Germain prime]]s ===
Where ''p'' and 2''p''+1 are both prime.
 
[[2 (number)|2]], [[3 (number)|3]], [[5 (number)|5]], [[11 (number)|11]], [[23 (number)|23]], [[29 (number)|29]], [[41 (number)|41]], [[53 (number)|53]], [[83 (number)|83]], [[89 (number)|89]], [[113 (number)|113]], [[131 (number)|131]], [[173 (number)|173]], [[179 (number)|179]], [[191 (number)|191]], [[233 (number)|233]], [[239 (number)|239]], [[251 (number)|251]], [[281 (number)|281]], [[293 (number)|293]], [[359 (number)|359]], [[419 (number)|419]], [[431 (number)|431]], [[443 (number)|443]], [[491 (number)|491]], [[509 (number)|509]], [[593 (number)|593]], [[641 (number)|641]], [[653 (number)|653]], [[659 (number)|659]], [[683 (number)|683]], [[719 (number)|719]], [[743 (number)|743]], [[761 (number)|761]], [[809 (number)|809]], [[911 (number)|911]], [[953 (number)|953]] ({{OEIS2C|A005384}})
 
=== [[Star number|Star]] primes ===
Of the form 6''n''(''n'' − 1) + 1.
 
[[13 (number)|13]], [[37 (number)|37]], [[73 (number)|73]], [[181 (number)|181]], [[337 (number)|337]], [[433 (number)|433]], [[541 (number)|541]], [[661 (number)|661]], [[937 (number)|937]], [[1093 (number)|1093]], [[2053 (number)|2053]], [[2281 (number)|2281]], [[2521 (number)|2521]], [[3037 (number)|3037]], [[3313 (number)|3313]], [[5581 (number)|5581]], [[5953 (number)|5953]], [[6337 (number)|6337]], [[6733 (number)|6733]], [[7561 (number)|7561]], [[7993 (number)|7993]], [[8893 (number)|8893]], [[10333 (number)|10333]], [[10837 (number)|10837]], [[11353 (number)|11353]], [[12421 (number)|12421]], [[12973 (number)|12973]], [[13537 (number)|13537]], [[15913 (number)|15913]], [[18481 (number)|18481]] ({{OEIS2C|A083577}})
 
=== [[Stern prime]]s ===
Primes that are not the sum of a smaller prime and twice the square of a nonzero integer.
 
[[2 (number)|2]], [[3 (number)|3]], [[17 (number)|17]], [[137 (number)|137]], [[227 (number)|227]], [[977 (number)|977]], [[1187 (number)|1187]], [[1493 (number)|1493]] ({{OEIS2C|A042978}})
 
{{As of|2011}}, these are the only known Stern primes, and possibly the only existing.
 
=== [[Super-prime]]s ===
Primes with a prime index in the sequence of prime numbers (the 2nd, 3rd, 5th, ... prime).
 
[[3 (number)|3]], [[5 (number)|5]], [[11 (number)|11]], [[17 (number)|17]], [[31 (number)|31]], [[41 (number)|41]], [[59 (number)|59]], [[67 (number)|67]], [[83 (number)|83]], [[109 (number)|109]], [[127 (number)|127]], [[157 (number)|157]], [[179 (number)|179]], [[191 (number)|191]], [[211 (number)|211]], [[241 (number)|241]], [[277 (number)|277]], [[283 (number)|283]], [[331 (number)|331]], [[353 (number)|353]], [[367 (number)|367]], [[401 (number)|401]], [[431 (number)|431]], [[461 (number)|461]], [[509 (number)|509]], [[547 (number)|547]], [[563 (number)|563]], [[587 (number)|587]], [[599 (number)|599]], [[617 (number)|617]], [[709 (number)|709]], [[739 (number)|739]], [[773 (number)|773]], [[797 (number)|797]], [[859 (number)|859]], [[877 (number)|877]], [[919 (number)|919]], [[967 (number)|967]], [[991 (number)|991]] ({{OEIS2C|A006450}})
 
=== [[Supersingular prime (moonshine theory)|Supersingular primes]] ===
There are exactly fifteen supersingular primes:
 
[[2 (number)|2]], [[3 (number)|3]], [[5 (number)|5]], [[7 (number)|7]], [[11 (number)|11]], [[13 (number)|13]], [[17 (number)|17]], [[19 (number)|19]], [[23 (number)|23]], [[29 (number)|29]], [[31 (number)|31]], [[41 (number)|41]], [[47 (number)|47]], [[59 (number)|59]], [[71 (number)|71]] ({{OEIS2C|A002267}})
 
=== Swinging primes ===
Primes of the form <math>n \wr \pm 1</math>, where <math>n \wr</math> denotes the swinging factorial, which is defined in terms of the ''double swinging factorial'' as<ref>Luschny, [http://www.luschny.de/math/swing/SwingingFactorial.html Swinging factorial]</ref> <math>n \wr = (n-1) \wr \wr n \wr \wr</math> and <math>n \wr \wr = \begin{cases} 1 \qquad \qquad \qquad \qquad \qquad \qquad \quad \ n \leqslant 0 \\ (n-2) \wr \wr n^{\big[ \text{n odd} \big]} (4/n)^{\big[ \text{n even} \big]} \quad n > 0 \end{cases}</math>
 
[[2 (number)|2]], [[3 (number)|3]], [[5 (number)|5]], [[7 (number)|7]], [[19 (number)|19]], [[29 (number)|29]], [[31 (number)|31]], [[71 (number)|71]], [[139 (number)|139]], [[251 (number)|251]], [[631 (number)|631]], [[3433 (number)|3433]], [[12011 (number)|12011]] ({{OEIS2C|A163074}})
 
=== [[Thabit number]] primes ===
Of the form 3×2{{sup|''n''}} − 1.
 
[[2 (number)|2]], [[5 (number)|5]], [[11 (number)|11]], [[23 (number)|23]], [[47 (number)|47]], [[191 (number)|191]], [[383 (number)|383]], [[6143 (number)|6143]], [[786431 (number)|786431]], [[51539607551 (number)|51539607551]], [[824633720831 (number)|824633720831]], [[26388279066623 (number)|26388279066623]], [[108086391056891903 (number)|108086391056891903]], [[55340232221128654847 (number)|55340232221128654847]], [[226673591177742970257407 (number)|226673591177742970257407]] ({{OEIS2C|A007505}})
 
The primes of the form 3×2{{sup|''n''}} + 1 are related.
 
[[7 (number)|7]], [[13 (number)|13]], [[97 (number)|97]], [[193 (number)|193]], [[769 (number)|769]], [[12289 (number)|12289]], [[786433 (number)|786433]], [[3221225473 (number)|3221225473]], [[206158430209 (number)|206158430209]], [[6597069766657 (number)|6597069766657]] ({{OEIS2C|A039687}})
 
=== [[Prime triplet]]s ===
{{see also|#Cousin primes|#Twin primes|#Prime quadruplets}}
 
Where (''p'', ''p''+2, ''p''+6) or (''p'', ''p''+4, ''p''+6) are all prime.
 
([[5 (number)|5]], [[7 (number)|7]], [[11 (number)|11]]), (7, 11, [[13 (number)|13]]), (11, 13, [[17 (number)|17]]), (13, 17, [[19 (number)|19]]), (17, 19, [[23 (number)|23]]), ([[37 (number)|37]], [[41 (number)|41]], [[43 (number)|43]]), (41, 43, [[47 (number)|47]]), ([[67 (number)|67]], [[71 (number)|71]], [[73 (number)|73]]), ([[97 (number)|97]], [[101 (number)|101]], [[103 (number)|103]]), (101, 103, [[107 (number)|107]]), (103, 107, [[109 (number)|109]]), (107, 109, [[113 (number)|113]]), ([[191 (number)|191]], [[193 (number)|193]], [[197 (number)|197]]), (193, 197, [[199 (number)|199]]), ([[223 (number)|223]], [[227 (number)|227]], [[229 (number)|229]]), (227, 229, [[233 (number)|233]]), ([[277 (number)|277]], [[281 (number)|281]], [[283 (number)|283]]), ([[307 (number)|307]], [[311 (number)|311]], [[313 (number)|313]]), (311, 313, [[317 (number)|317]]), ([[347 (number)|347]], [[349 (number)|349]], [[353 (number)|353]]) ({{OEIS2C|A007529}}, {{OEIS2C|A098414}}, {{OEIS2C|A098415}})
 
=== [[Twin prime]]s ===
{{see also|#Cousin primes|#Prime triplets|#Prime quadruplets}}
 
Where (''p'', ''p''+2) are both prime.
 
([[3 (number)|3]], [[5 (number)|5]]), (5, [[7 (number)|7]]), ([[11 (number)|11]], [[13 (number)|13]]), ([[17 (number)|17]], [[19 (number)|19]]), ([[29 (number)|29]], [[31 (number)|31]]), ([[41 (number)|41]], [[43 (number)|43]]), ([[59 (number)|59]], [[61 (number)|61]]), ([[71 (number)|71]], [[73 (number)|73]]), ([[101 (number)|101]], [[103 (number)|103]]), ([[107 (number)|107]], [[109 (number)|109]]), ([[137 (number)|137]], [[139 (number)|139]]), ([[149 (number)|149]], [[151 (number)|151]]), ([[179 (number)|179]], [[181 (number)|181]]), ([[191 (number)|191]], [[193 (number)|193]]), ([[197 (number)|197]], [[199 (number)|199]]), ([[227 (number)|227]], [[229 (number)|229]]), ([[239 (number)|239]], [[241 (number)|241]]), ([[269 (number)|269]], [[271 (number)|271]]), ([[281 (number)|281]], [[283 (number)|283]]), ([[311 (number)|311]], [[313 (number)|313]]), ([[347 (number)|347]], [[349 (number)|349]]), ([[419 (number)|419]], [[421 (number)|421]]), ([[431 (number)|431]], [[433 (number)|433]]), ([[461 (number)|461]], [[463 (number)|463]]) ({{OEIS2C|A001359}}, {{OEIS2C|A006512}})
 
=== [[Two-sided prime]]s ===
{{see also|#Right-truncatable primes|#Left-truncatable primes}}
 
Primes which are both left-truncatable and right-truncatable. There are exactly fifteen two-sided primes:
 
[[2 (number)|2]], [[3 (number)|3]], [[5 (number)|5]], [[7 (number)|7]], [[23 (number)|23]], [[37 (number)|37]], [[53 (number)|53]], [[73 (number)|73]], [[313 (number)|313]], [[317 (number)|317]], [[373 (number)|373]], [[797 (number)|797]], [[3137 (number)|3137]], [[3797 (number)|3797]], [[739397 (number)|739397]] ({{OEIS2C|A020994}})
 
=== [[Ulam number]] primes ===
Ulam numbers that are prime.
 
[[2 (number)|2]], [[3 (number)|3]], [[11 (number)|11]], [[13 (number)|13]], [[47 (number)|47]], [[53 (number)|53]], [[97 (number)|97]], [[131 (number)|131]], [[197 (number)|197]], [[241 (number)|241]], [[409 (number)|409]], [[431 (number)|431]], [[607 (number)|607]], [[673 (number)|673]], [[739 (number)|739]], [[751 (number)|751]], [[983 (number)|983]], [[991 (number)|991]], [[1103 (number)|1103]], [[1433 (number)|1433]], [[1489 (number)|1489]], [[1531 (number)|1531]], [[1553 (number)|1553]], [[1709 (number)|1709]], [[1721 (number)|1721]], [[2371 (number)|2371]], [[2393 (number)|2393]], [[2447 (number)|2447]], [[2633 (number)|2633]], [[2789 (number)|2789]], [[2833 (number)|2833]], [[2897 (number)|2897]] ({{OEIS2C|A068820}})
 
=== [[Unique prime]]s ===
The list of primes ''p'' for which the [[period length]] of the decimal expansion of 1/''p'' is unique (no other prime gives the same period).
 
[[3 (number)|3]], [[11 (number)|11]], [[37 (number)|37]], [[101 (number)|101]], [[9091 (number)|9091]], [[9901 (number)|9901]], [[333667 (number)|333667]], [[909091 (number)|909091]], [[99990001 (number)|99990001]], [[999999000001 (number)|999999000001]], [[9999999900000001 (number)|9999999900000001]], [[909090909090909091 (number)|909090909090909091]], [[1111111111111111111 (number)|1111111111111111111]], [[11111111111111111111111 (number)|11111111111111111111111]], [[900900900900990990990991 (number)|900900900900990990990991]] ({{OEIS2C|A040017}})
 
=== [[Wagstaff prime]]s ===
Of the form (2{{sup|''n''}}+1) / 3.
 
[[3 (number)|3]], [[11 (number)|11]], [[43 (number)|43]], [[683 (number)|683]], [[2731 (number)|2731]], [[43691 (number)|43691]], [[174763 (number)|174763]], [[2796203 (number)|2796203]], [[715827883 (number)|715827883]], [[2932031007403 (number)|2932031007403]], [[768614336404564651 (number)|768614336404564651]], [[201487636602438195784363 (number)|201487636602438195784363]], [[845100400152152934331135470251 (number)|845100400152152934331135470251]], [[56713727820156410577229101238628035243 (number)|56713727820156410577229101238628035243]] ({{OEIS2C|A000979}})
 
Values of ''n'':
 
3, [[5 (number)|5]], [[7 (number)|7]], 11, [[13 (number)|13]], [[17 (number)|17]], [[19 (number)|19]], [[23 (number)|23]], [[31 (number)|31]], 43, [[61 (number)|61]], [[79 (number)|79]], [[101 (number)|101]], [[127 (number)|127]], [[167 (number)|167]], [[191 (number)|191]], [[199 (number)|199]], [[313 (number)|313]], [[347 (number)|347]], [[701 (number)|701]], [[1709 (number)|1709]], [[2617 (number)|2617]], [[3539 (number)|3539]], [[5807 (number)|5807]], [[10501 (number)|10501]], [[10691 (number)|10691]], [[11279 (number)|11279]], [[12391 (number)|12391]], [[14479 (number)|14479]], [[42737 (number)|42737]], [[83339 (number)|83339]], [[95369 (number)|95369]], [[117239 (number)|117239]], [[127031 (number)|127031]], [[138937 (number)|138937]], [[141079 (number)|141079]], [[267017 (number)|267017]], [[269987 (number)|269987]], [[374321 (number)|374321]] ({{OEIS2C|A000978}})
 
=== [[Wall–Sun–Sun prime]]s ===
A prime ''p''&nbsp;>&nbsp;5 if ''p''{{sup|2}} divides the [[Fibonacci number]] <math>F_{p - \left(\frac{{p}}{{5}}\right)}</math>, where the [[Legendre symbol]] <math>\left(\frac{{p}}{{5}}\right)</math> is defined as
:<math>\left(\frac{p}{5}\right) = \begin{cases} 1 &\textrm{if}\;p \equiv \pm1 \pmod 5\\ -1 &\textrm{if}\;p \equiv \pm2 \pmod 5. \end{cases}</math>
 
{{As of|2013}}, no Wall-Sun-Sun primes are known.
 
=== [[Wedderburn-Etherington number]] primes ===
Wedderburn-Etherington numbers that are prime.
 
[[2 (number)|2]], [[3 (number)|3]], [[11 (number)|11]], [[23 (number)|23]], [[983 (number)|983]], [[2179 (number)|2179]], [[24631 (number)|24631]], [[3626149 (number)|3626149]], [[253450711 (number)|253450711]], [[596572387 (number)|596572387]] (primes in {{OEIS2C|A001190}})
 
=== [[Weakly prime number]]s ===
Primes that having any one of their (base 10) digits changed to any other value will always result in a composite number.
 
[[294001 (number)|294001]], [[505447 (number)|505447]], [[584141 (number)|584141]], [[604171 (number)|604171]], [[971767 (number)|971767]], [[1062599 (number)|1062599]], [[1282529 (number)|1282529]], [[1524181 (number)|1524181]], [[2017963 (number)|2017963]], [[2474431 (number)|2474431]], [[2690201 (number)|2690201]], [[3085553 (number)|3085553]], [[3326489 (number)|3326489]], [[4393139 (number)|4393139]] ({{OEIS2C|A050249}})
 
=== [[Wieferich prime]]s ===
Primes ''p'' such that {{nowrap|''a''<sup>''p'' − 1</sup> &equiv; 1 (mod ''p''<sup>2</sup>)}} where ''a'' is not a [[perfect power]].
 
2<sup>''p'' − 1</sup> &equiv; 1 (mod ''p''<sup>2</sup>): [[1093 (number)|1093]], [[3511 (number)|3511]] ({{OEIS2C|A001220}})<br>
3<sup>''p'' − 1</sup> &equiv; 1 (mod ''p''<sup>2</sup>): [[11 (number)|11]], [[1006003 (number)|1006003]] ({{OEIS2C|A014127}})<ref>{{cite book | last = Ribenboim | first = P. | authorlink = Paulo Ribenboim | title = The new book of prime number records | publisher = Springer-Verlag | location = New York | page = 347 | url = http://books.google.de/books?id=72eg8bFw40kC&printsec=frontcover&dq=ribenboim&hl=de&ei=PoJATZvqO4WU4Qamg-n-Ag&sa=X&oi=book_result&ct=result&resnum=1&ved=0CDEQ6AEwAA#v=onepage&q&f=false | isbn = 0-387-94457-5}}</ref><ref>{{cite web | title = Mirimanoff's Congruence: Other Congruences | url = http://www.museumstuff.com/learn/topics/Mirimanoff%27s_congruence::sub::Other_Congruences | accessdate = 26 January 2011}}</ref><ref>{{cite journal | last1 = Gallot | first1 = Y. | last2 = Moree | first2 = P. | last3 = Zudilin | first3 = W. | title = The Erdös-Moser equation 1{{sup|''k''}} + 2{{sup|''k''}} +...+ (m−1){{sup|''k''}} = m{{sup|''k''}} revisited using continued fractions | journal = Mathematics of Computation | volume = 80 | pages = 1221–1237 | publisher = American Mathematical Society | year = 2011 | url = http://www.mpim-bonn.mpg.de/preprints/send?bid=4053 | doi = 10.1090/S0025-5718-2010-02439-1 | id =  | arxiv=0907.1356}}</ref><br>
5<sup>''p'' − 1</sup> &equiv; 1 (mod ''p''<sup>2</sup>): [[2 (number)|2]], [[20771 (number)|20771]], [[40487 (number)|40487]], [[53471161 (number)|53471161]], [[1645333507 (number)|1645333507]], [[6692367337 (number)|6692367337]], [[188748146801 (number)|188748146801]] ({{OEIS2C|A123692}})<br>
6<sup>''p'' − 1</sup> &equiv; 1 (mod ''p''<sup>2</sup>): [[66161 (number)|66161]], [[534851 (number)|534851]], [[3152573 (number)|3152573]] ({{OEIS2C|A212583}})<br>
7<sup>''p'' − 1</sup> &equiv; 1 (mod ''p''<sup>2</sup>): [[5 (number)|5]], [[491531 (number)|491531]] ({{OEIS2C|A123693}})<br>
10<sup>''p'' − 1</sup> &equiv; 1 (mod ''p''<sup>2</sup>): [[3 (number)|3]], [[487 (number)|487]], [[56598313 (number)|56598313]] ({{OEIS2C|A045616}})<br>
11<sup>''p'' − 1</sup> &equiv; 1 (mod ''p''<sup>2</sup>): [[71 (number)|71]]<ref name="RibenboimWelt">{{Cite book | last = Ribenboim | first = P. | authorlink = Paulo Ribenboim | title = Die Welt der Primzahlen | publisher = Springer | year = 2006 | location = Berlin | page = 240 | url = http://www.scribd.com/doc/35180646/Ribenboim-Die-Welt-der-Primzahlen  | isbn = 3-540-34283-4}}</ref><br>
12<sup>''p'' − 1</sup> &equiv; 1 (mod ''p''<sup>2</sup>): [[2693 (number)|2693]], [[123653 (number)|123653]] ({{OEIS2C|A111027}})<br>
13<sup>''p'' − 1</sup> &equiv; 1 (mod ''p''<sup>2</sup>): [[863 (number)|863]], [[1747591 (number)|1747591]] ({{OEIS2C|A128667}})<ref name="RibenboimWelt"/><br>
17<sup>''p'' − 1</sup> &equiv; 1 (mod ''p''<sup>2</sup>): [[3 (number)|3]], [[46021 (number)|46021]], [[48947 (number)|48947]]<ref name="RibenboimWelt"/><br>
19<sup>''p'' − 1</sup> &equiv; 1 (mod ''p''<sup>2</sup>): [[3 (number)|3]], [[7 (number)|7]], [[13 (number)|13]], [[43 (number)|43]], [[137 (number)|137]], [[63061489 (number)|63061489]] ({{OEIS2C|A090968}})<ref name="RibenboimWelt"/>
 
=== [[Wilson prime]]s ===
Primes ''p'' for which ''p''{{sup|2}} divides (''p''−1)! + 1.
 
[[5 (number)|5]], [[13 (number)|13]], [[563 (number)|563]] ({{OEIS2C|A007540}})
 
{{As of|2011}}, these are the only known Wilson primes.
 
=== [[Wolstenholme prime]]s ===
Primes ''p'' for which the [[binomial coefficient]] <math>{{2p-1}\choose{p-1}} \equiv 1 \pmod{p^4}.</math>
 
[[16843 (number)|16843]], [[2124679 (number)|2124679]] ({{OEIS2C|A088164}})
 
{{As of|2011}}, these are the only known Wolstenholme primes.
 
=== [[Woodall number|Woodall]] primes ===
Of the form ''n''×2{{sup|''n''}} − 1.
 
[[7 (number)|7]], [[23 (number)|23]], [[383 (number)|383]], [[32212254719 (number)|32212254719]], [[2833419889721787128217599 (number)|2833419889721787128217599]], [[195845982777569926302400511 (number)|195845982777569926302400511]], [[4776913109852041418248056622882488319 (number)|4776913109852041418248056622882488319]] ({{OEIS2C|A050918}})
 
== See also ==
* [[Illegal prime]]
* [[Largest known prime]]
* [[List of numbers]]
* [[Prime gap]]
* [[Prime number theorem]]
* [[Probable prime]]
* [[Pseudoprime]]
* [[Strobogrammatic prime]]
* [[Strong prime]]
* [[Wieferich pair]]
 
== Notes ==
{{reflist}}
 
== External links ==
* [http://primes.utm.edu/lists/ Lists of Primes] at the Prime Pages.
* [http://primes.utm.edu/nthprime/ The Nth Prime Page] Nth prime through n=10^12, pi(x) through x=3*10^13, Random prime in same range.
* [http://www.prime-numbers.org/ Prime Numbers List] Full list for prime numbers below 10,000,000,000, partial list for up to 400 digits.
* [http://www.primos.mat.br/indexen.html Prime Numbers up to  1,000,000,000,000]
* [http://www.rsok.com/~jrm/printprimes.html Interface to a list of the first 98 million primes] (primes less than 2,000,000,000)
* {{MathWorld|title=Prime Number Sequences|urlname=topics/PrimeNumberSequences}}
* [http://oeis.org/wiki/Index_to_OEIS:_Section_Pri Selected prime related sequences] in [[On-Line Encyclopedia of Integer Sequences|OEIS]].
* Fischer, R. [http://www.fermatquotient.com/FermatQuotienten/FermQ_Sort Thema: Fermatquotient B^(P−1) == 1 (mod P^2)] {{de icon}} (Lists Wieferich primes in all bases up to 1052)
* {{cite web|last=Padilla|first=Tony|title=New Largest Known Prime Number|url=http://www.numberphile.com/videos/largest_prime.html|work=Numberphile|publisher=[[Brady Haran]]}}
 
{{Use dmy dates|date=May 2011}}
 
{{Prime number classes}}
 
[[Category:Prime numbers|*]]
[[Category:Classes of prime numbers|*]]
[[Category:Mathematics-related lists|Prime numbers]]

Latest revision as of 23:23, 27 November 2014

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