Difference between revisions 16190962 and 19417636 on enwiki

< previous diff
next diff >
Wolstenholme prime
In [[mathematics]], a '''Wolstenholme prime''' is a certain kind of [[prime number]]. A prime ''p'' is called a Wolstenholme prime [[iff]] the following condition holds:

:<math>{{2p-1}\choose{p-1}} \equiv 1 \pmod{p^4}</math>

Wolstenholme primes are named after [[mathematician]] [[Joseph Wolstenholme]], who proved [[Wolstenholme's theorem]], the equivalent statement for ''p''<sup>3</sup> in [[1862]], following [[Charles Babbage]] who showed the equivalent for ''p''<sup>2</sup> in [[1819]].

The only known Wolstenholme primes so far are 16843 and 2124679 {{OEIS|id=A088164}}; any other Wolstenholme prime must be greater than 6.4 &middot; 10<sup>8</sup>.

== Also see ==

* [[Wieferich prime]]
* [[Wilson prime]]
* [[Wall-Sun-Sun prime]]

== External links ==

* [http://primes.utm.edu/glossary/page.php?sort=Wolstenholme The Prime Glossary: Wolstenholme prime]
* [http://www.loria.fr/~zimmerma/records/Wieferich.status Status of the search for Wolstenholme primes]

[[Category:Number theoryPrime numbers]]

[[de:Wolstenholme-Primzahl]]
[[fr:Nombre de Wolstenholme]]