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
- 1909: Arthur Wieferich: Zum letzten Fermat'schen Theorem (J. reine angew. Math. Vol. 136, no. 3/4: pp. 293 – 302)
- Weisstein, Eric W. "Wieferich Prime." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/WieferichPrime.html