Find all primes p in the interval $[1, 4000]$, such that $2^{(p-1)}$ is congruent with $1\,\,(\mathrm{mod} \,\, p ^ 2)$.

Question

I was checking the following number theory exercise:

Find all primes $p$ in the interval $[1, 4000]$, such that $2^{(p-1)}$ is congruent with $1\,\,(\mathrm{mod} \,\, p^2)$.

Any clue or help will be really appreciated.

Answer 1

Such primes are called Wieferich primes.

The only known Wieferich primes are $1093$ and $3511$ (OEIS/A001220).