Wolstenholme prime

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• Wolstenholme-Primzahl
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• Número_de_Wolstenholme
• Nombre_de_Wolstenholme
• Numero_primo_di_Wolstenholme

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In number theory, a Wolstenholme prime is a certain kind of prime number. A prime p is called a Wolstenholme prime iff the following condition holds:

Wolstenholme primes are named after 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 10⁹.[1] This data is consistent with the heuristic that the residue modulo p⁴ is a pseudo-random multiple of p³. This heuristic predicts that the number of Wolstenholme primes between K and N is roughly ln ln N - ln ln K. The Wolstenholme condition has been checked up to 10⁹, and the heuristic says that there should be roughly one Wolstenholme prime between 10⁹ and 10²⁴.

See also

• Wieferich prime
• Wilson prime
• Wall-Sun-Sun prime
• List of special classes of prime numbers

References

J. Wolstenholme (1862). "On certain properties of prime numbers". Quarterly Journal of Mathematics 5: 35–39. 

External links

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