These are the prime numbers of the form Mn
Not every value of n gives a prime Mn
, for instance 24
-1 = 15 is obviously not prime.
n must be a prime number, but it is not sufficient : 211
-1 = 2047 = 23 x 89
Mn=3, 7, 31, 127, 8191, ...
We don't know if there are infinitely many.
The Mersenne primes are related with even perfect numbers.