Wieferich primes

Wieferich primes is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

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In number theory, a Wieferich prime is a prime number p such that p² evenly divides 2^{(p − 1)} − 1 .

It is conjectured that there are infinitely many Wieferich primes, but as of March 2021,only two have been identified.

Task

• Write a routine (function procedure, whatever) to find Wieferich primes.

• Use that routine to identify and display all of the Wieferich primes less than 5000.

See also

• OEIS A001220 - Wieferich primes

Raku

<lang perl6>put "Weiferich primes less than 5000: ", join ', ', ^5000 .grep: { .is-prime and not ( exp($_-1, 2) - 1 ) % .² };</lang>

Output:

Weiferich primes less than 5000: 1093, 3511