On Fermat’s quotient, base two

Abstract:

This paper extends the search for solutions of the congruence \[ {2^{p - 1}} - 1 \equiv 0\quad \pmod {p^2}\] to the limit $p < 6 \cdot {10^9}$. No solution, except the well-known $p = 1093$ and $p = 3511$, was found.