# Does there exist a prime number $p$ such that $p^2 \mid 2^{p-1}-1$?

Does there exist a prime number $p$ such that $p^2 \mid 2^{p-1}-1$ ?

I tried for some small number $p$ and I think that it does, but I don't know how to prove this.

• – lab bhattacharjee Jan 14 '16 at 7:50
• +1 for an interesting question, though I bet that somebody has already asked it here before. – barak manos Jan 14 '16 at 7:51
• $3511$ also works. – fosho Jan 14 '16 at 7:53
• See OEIS sequence A001220. – Jose Arnaldo Bebita-Dris Jan 14 '16 at 8:10
• See also here. – Dietrich Burde Jan 14 '16 at 12:08

## 1 Answer

Actually there is.

$1093$ does the job.

These primes are named Wieferich primes but we don't know if there are infinitely many.
For more see here