Definition:Wolstenholme Prime
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Definition
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.
Sources
- Weisstein, Eric W. "Wolstenholme Prime." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/WolstenholmePrime.html