Wolstenholme prime

Encyclopedia : W : WO : WOL : Wolstenholme prime

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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:

[ \equiv 1 \pmod]

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 in OEIS); any other Wolstenholme prime must be greater than 10⁹.

See also

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

External links

• [The Prime Glossary: Wolstenholme prime]
• [Status of the search for Wolstenholme primes]

 

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