Factor of Mersenne Number Mp is of form 2kp + 1/Historical Note

Historical Note on Factor of Mersenne Number $M_p$ is of form $2 k p + 1$

This result was known to Pierre de Fermat by $1640$, and it has been suggested that Marin Mersenne made use of it when providing his famous list of Mersenne primes in his Cogitata Physico-Mathematica of $1644$.

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $127$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $127$