Here is an exemple with M67
take M67  1 (2^672)
all factors of this are: (2,3,3,7,23,67,89,683,20857,599479)
so it contains 67
and it`s the same for all mersenne.
It`s also the case with any prime numbers.
take 193707721 the numbers that divides M67
the factors of 1937077211 are (2,2,2,3,3,3,5,67,2677)
so you know you only have to test M67 and M2677.
and since we are only concerned with numbers less then 79.3M
there no need to search all factors of the number.
You can also include the properties of mersenne numbers to speed up the process.
Can a prime numbers be the factor of more than one Mersenne?
