Wolstenholme prime - Definition and Overview

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 p³ in 1862, following Charles Babbage who showed the equivalent for p² in 1819.

The only known Wolstenholme primes so far are 16843 and 2124679 (sequence A088164 in OEIS); any other Wolstenholme prime must be greater than 6.4 · 10⁸.

Also see

• Wieferich prime
• Wilson prime
• Wall-Sun-Sun prime

External links

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