Wolstenholme prime
From Wikipedia, the free encyclopedia
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.
[edit] See also
[edit] References
J. Wolstenholme, "On certain properties of prime numbers", Quarterly Journal of Mathematics 5 (1862), pp. 35–39.
