Unsolved problems in number theory | Classes of prime numbers

Wolstenholme prime

In number theory, a Wolstenholme prime is a special type of prime number satisfying a stronger version of Wolstenholme's theorem. Wolstenholme's theorem is a congruence relation satisfied by all prime numbers greater than 3. Wolstenholme primes are named after mathematician Joseph Wolstenholme, who first described this theorem in the 19th century. Interest in these primes first arose due to their connection with Fermat's Last Theorem. Wolstenholme primes are also related to other special classes of numbers, studied in the hope to be able to generalize a proof for the truth of the theorem to all positive integers greater than two. The only two known Wolstenholme primes are 16843 and 2124679 (sequence in the OEIS). There are no other Wolstenholme primes less than 109. (Wikipedia).

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Related pages

Fermat's Last Theorem | Irregular prime | Prime number | Wall–Sun–Sun prime | Congruence relation | Bernoulli number | Binomial coefficient | Natural logarithm | Table of congruences | Wieferich prime | Harmonic number | Wolstenholme's theorem | Regular prime | Wilson prime | Joseph Wolstenholme | Number theory