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[[File:Legendre's constant.svg|thumb|right|250px|The first 100,000 elements of the sequence ''a<sub>n</sub>'' =&nbsp;ln(''n'')&nbsp;&minus;&nbsp;''n''/''&pi;''(''n'') (red line) appear to converge to a value around 1.08366 (blue line).]]
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'''Legendre's constant''' is a [[mathematical constant]] occurring in a formula conjectured by [[Adrien-Marie Legendre]] to capture the [[asymptotic behavior]] of the [[prime-counting function]] <math>\scriptstyle\pi(x)</math>. Its value is now known to be exactly&nbsp;[[1 (number)|1]].


Examination of available numerical evidence for known [[prime number|primes]] led Legendre to suspect that <math>\scriptstyle\pi(x)</math> satisfies:
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:<math>\lim_{n \to \infty } \left( \ln(n) - {n \over \pi(n)} \right)= B</math>
  <li>[http://observatoiredesreligions.fr/spip.php?article9 http://observatoiredesreligions.fr/spip.php?article9]</li>
 
 
where ''B'' is Legendre's constant. He guessed ''B'' to be about 1.08366, but regardless of its exact value, the existence of ''B'' implies the [[prime number theorem]].
  <li>[http://forum.tag-knowledge.com/default.aspx?g=posts&t=794055 http://forum.tag-knowledge.com/default.aspx?g=posts&t=794055]</li>
 
 
Later [[Carl Friedrich Gauss]] also examined the numerical evidence and concluded that the limit might be lower.
  <li>[http://jennrubin.ascportfolios.org/forum/profile.php?id=1201526 http://jennrubin.ascportfolios.org/forum/profile.php?id=1201526]</li>
 
 
[[Charles Jean de la Vallée-Poussin]], who proved the prime number theorem (independently from [[Jacques Hadamard]]), finally showed that ''B'' is&nbsp;1.
  <li>[http://f1sqg2003.free.fr/forum.php?mod=viewthread&tid=476898 http://f1sqg2003.free.fr/forum.php?mod=viewthread&tid=476898]</li>
 
 
Being evaluated to such a simple number has made the term Legendre's constant mostly only of historical value, with it often (technically incorrectly) being used to refer to Legendre's first guess 1.08366... instead.
</ul>
 
==External links==
*{{mathworld|urlname=LegendresConstant|title=Legendre's constant}}
 
[[Category:Conjectures about prime numbers]]
[[Category:Mathematical constants]]

Latest revision as of 19:29, 11 January 2015

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The mass of the proton or neutron increases when the particle attains extreme speed, for instance in a cyclotron or linear accelerator.An early model of the atom was developed through the physicist ErnestRutherford in 1912. He was the first one to suggest that atoms are like miniature solar systems, except that the attractive force is not caused by gravity, but by opposing electrical charges. Within the socalled Rutherford atom, electrons orbit the nucleus in circular paths.

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The cold snap gripping much of the country is surely prodding many to imagine owning a second home someplace warm, or of moving there permanently. Data show that Florida's housing market may be in a sweet spot. Prices remain low, as Florida was among the states hit hardest through the collapse of the housing bubble, but costs are on the rise, so a purchase now would seem less risky than it might have a year ago..

OK, but first let's hear how he wooed Tana. "I took her for some time motorcycle ride, then out to lunch, and then I said, 'Can I cook for you tonight?' She was my mate's girlfriend" he claims she was his mate's exgirlfriend, though many reports suggest these were still together "and she was gorgeous, and I knew I could cook much better Replica Oakley Australia than him. I put together the most wonderful langoustine salad, and I made this amazing fragrant lemongrass mayonnaise to put over the prawns, these beautiful, thick, number one langoustines, which were poached in bouillon and served over a nice fresh greenbean salad with slightly toasted hazelnuts, and it was fucking amazing.

If you want great color, weave, cut, fly out. I can speak personally for Diane, Jose, Vanessa Karen. All of them are 5 stars; real pros. Based on Ian Jarman, now manager of Power Systems software and formerly the machine i product manager, the consumer group, software vendors, end user, and other people polled by IBM as research behind the branding moves overwhelmingly were behind the name change for that operating system. When asked if IBM must have changed the name of the operating system on Power6 iron, 83 percent of these polled said yes. What IBM didn't share with me is any data about what they thought the name ought to be.