en>Hyacinth: /* References */ {{Disproved conjectures}}

2014-09-30T22:23:11Z

References: {{Disproved conjectures}}

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	~~In [[computational number theory]]~~, ~~the '''Adleman–Pomerance–Rumely primality test'~~'' ~~is an [[algorithm]] for determining whether a number is [[prime number\|prime]]. Unlike other, more efficient algorithms for this purpose,~~ it ~~avoids the use of random numbers, so it is a [[deterministic algorithm\|deterministic]] [[primality test]]~~. ~~It is named after its discoverers, [[Leonard Adleman]], [[Carl Pomerance]],~~ and ~~[[Robert Rumely]]. The test involves arithmetic in [[cyclotomic field]]s.~~		Hi there, I am Felicidad Oquendo. Meter reading is exactly where my primary income arrives from but quickly I'll be on my own. The thing she adores most is to perform handball but she can't make it her profession. Delaware has usually been my residing location and will by no means transfer.<br><br>Also visit my homepage; [http://Crossroad-Rto.ca/ActivityFeed/MyProfile/tabid/55470/userId/428152/Default.aspx http://Crossroad-Rto.ca/]

	~~It was later improved~~ by ~~[[Henri Cohen (number theorist)\|Henri Cohen]] and [[Hendrik Willem Lenstra]] and called APRT-CL (or APRCL)~~. ~~It is often used with [[UBASIC]] under the name APRT-CLE (APRT-CL extended) and can test primality of an integer ''n'' in time:~~

	: <~~math~~>~~O((\ln n)^{c\,\ln\,\ln\,\ln n}).~~<~~/math~~>

	~~== External links ==~~
	*[http://~~primes~~.~~utm.edu~~/~~prove~~/~~prove4_1.html APR and APR-CL]~~
	*A [http://~~www.alpertron.com.ar~~/~~ECM~~.~~HTM factoring applet] that uses APR-CL on certain conditions (source code included)~~
	*[http://~~pari.math.u~~-~~bordeaux~~.~~fr/ Pari~~/GP] ~~uses APR-CL conditionally in its implementation of isprime().~~

	~~==References==~~
	* {{cite journal \| last1=Adleman \| first1=Leonard M. \| author1-link=Leonard Adleman \| last2=Pomerance \| first2=Carl \| author2-link=Carl Pomerance \| last3=Rumely \| first3=Robert S. \| author3-link=Robert Rumely \| title=On distinguishing prime numbers from composite numbers \| journal=[[Annals of Mathematics]] \|volume=117 \| issue=1 \| year=1983 \| pages=173–206 \| doi=10.2307/2006975 }}
	* {{cite journal \| last1=Cohen \| first1=Henri \| author1-link=Henri Cohen (number theorist)\|
	last2=Lenstra \| first2=Hendrik W., Jr. \| author2-link=Hendrik Lenstra \| title=Primality testing and Jacobi sums \| journal=[[Mathematics of Computation]] \| volume=42 \| year=1984 \| pages=297–330 \| issue=165 \| doi=10.2307/2007581 }}
	* {{cite book \| last=Riesel \| first = Hans \| authorlink=Hans Riesel \| title=Prime Numbers and Computer Methods for Factorization \| publisher=Birkhauser \| year=1994 \| isbn=0-8176-3743-5 \| pages=131–136 }}

	~~{{number theoretic algorithms}}~~

	~~{{DEFAULTSORT:Adleman-Pomerance-Rumely primality test}}~~
	~~[[Category:Primality tests]]~~


	~~{{algorithm-stub}}~~
	~~{{numtheory-stub}}~~

en>Bender235: /* References */ fix, see WP:ENDASH

2011-07-19T13:13:04Z

References: fix, see WP:ENDASH

New page

In [[computational number theory]], the '''Adleman–Pomerance–Rumely primality test''' is an [[algorithm]] for determining whether a number is [[prime number|prime]]. Unlike other, more efficient algorithms for this purpose, it avoids the use of random numbers, so it is a [[deterministic algorithm|deterministic]] [[primality test]]. It is named after its discoverers, [[Leonard Adleman]], [[Carl Pomerance]], and [[Robert Rumely]]. The test involves arithmetic in [[cyclotomic field]]s.

It was later improved by [[Henri Cohen (number theorist)|Henri Cohen]] and [[Hendrik Willem Lenstra]] and called APRT-CL (or APRCL). It is often used with [[UBASIC]] under the name APRT-CLE (APRT-CL extended) and can test primality of an integer ''n'' in time:

: <math>O((\ln n)^{c\,\ln\,\ln\,\ln n}).</math>

== External links ==
*[http://primes.utm.edu/prove/prove4_1.html APR and APR-CL]
*A [http://www.alpertron.com.ar/ECM.HTM factoring applet] that uses APR-CL on certain conditions (source code included)
*[http://pari.math.u-bordeaux.fr/ Pari/GP] uses APR-CL conditionally in its implementation of isprime().

==References==
* {{cite journal | last1=Adleman | first1=Leonard M. | author1-link=Leonard Adleman | last2=Pomerance | first2=Carl | author2-link=Carl Pomerance | last3=Rumely | first3=Robert S. | author3-link=Robert Rumely | title=On distinguishing prime numbers from composite numbers | journal=[[Annals of Mathematics]] |volume=117 | issue=1 | year=1983 | pages=173–206 | doi=10.2307/2006975 }}
* {{cite journal | last1=Cohen | first1=Henri | author1-link=Henri Cohen (number theorist)|
last2=Lenstra | first2=Hendrik W., Jr. | author2-link=Hendrik Lenstra | title=Primality testing and Jacobi sums | journal=[[Mathematics of Computation]] | volume=42 | year=1984 | pages=297–330 | issue=165 | doi=10.2307/2007581 }}
* {{cite book | last=Riesel | first = Hans | authorlink=Hans Riesel | title=Prime Numbers and Computer Methods for Factorization | publisher=Birkhauser | year=1994 | isbn=0-8176-3743-5 | pages=131–136 }}

{{number theoretic algorithms}}

{{DEFAULTSORT:Adleman-Pomerance-Rumely primality test}}
[[Category:Primality tests]]

{{algorithm-stub}}
{{numtheory-stub}}

Ganea conjecture - Revision history

en>Hyacinth: /* References */ {{Disproved conjectures}}

en>Bender235: /* References */ fix, see WP:ENDASH