Primes of form Power Less One/Historical Note

Historical Note on Primes of form Power Less One

The proof that if $n$ is composite, then so is $2^n - 1$, is historically attributed to Cataldi, who gave it in $1603$.

Marin Mersenne was aware of this result, but took it further to ask the question as to which numbers of the form $2^p - 1$ are prime when $p$ is prime.

Sources

• 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {A}.12$: Mersenne ($\text {1588}$ – $\text {1648}$)
• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $127$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $127$