Definition:Wolstenholme Prime

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A Wolstenholme prime is a prime number $p$ such that $p > 7$ which satisfies the congruence:

$\dbinom {2 p - 1} {p - 1} \equiv 1 \pmod {p^4}$

where $\dbinom {2 p - 1} {p - 1}$ denotes a binomial coefficient.

Known Instances of Wolstenholme Primes

At time of writing, there are only $2$ known instances of Wolstenholme Primes:

$16843, 2124679$

Also see

  • Results about Wolstenholme primes can be found here.

Source of Name

This entry was named for Joseph Wolstenholme.