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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 [[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.

(contracted; show full)* [http://www.loria.fr/~zimmerma/records/Wieferich.status Status of the search for Wolstenholme primes]

[[Category:Prime numbers]]
[[Category:Factorial and binomial topics]]

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