Definition:Wieferich Prime

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Definition

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

$p^2 \divides 2^{p − 1} − 1$

where $\divides$ denotes divisibility.


Sequence of Wieferich Primes

The sequence of Wieferich primes begins:

$1093, 3511 \ldots$

No other Wieferich primes exist below $4 \cdotp 968543 \times 10^{17}$.


Also see

  • Results about Wieferich primes can be found here.


Source of Name

This entry was named for Arthur Josef Alwin Wieferich.


Sources