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
Factor
<lang factor>USING: io kernel math math.functions math.primes prettyprint sequences ;
"Weiferich primes less than 5000:" print 5000 primes-upto [ [ 1 - 2^ 1 - ] [ sq divisor? ] bi ] filter .</lang>
- Output:
Weiferich primes less than 5000:
V{ 1093 3511 }
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