In this page of Caldwell, after the proof of the link with Wieferich primes and pointing out that the two known ones can't be divisors of any Mersenne numbers, in the Comment he asserts «... so $M_q$ is square-free for all primes less than $4 \cdot 10^{12}$». I don't get this latter number, since previously it's said the Wieferich primes are checked up to $6.7\cdot 10^{15}$.
2026-02-23 04:50:07.1771822207
Squarefreeness Mersenne Numbers
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