Wolstenholme prime

This article defines a property that can be evaluated for a prime number. In other words, every prime number either satisfies this property or does not satisfy this property.
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Definition

A Wolstenholme prime is a prime number $p$ such that:

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

In other words, it satisfies a stronger version of Wolstenholme's theorem, which is true for all primes greter than 3.

Occurrence

Initial examples

Currently there are only two known Wolstenholme primes: 16843 and 2124679.