I may be a little obtuse here (and spelling, expression of ideas may be
inadequate) but
A Mersenne number's prime divisors are unique to that number. Letting a and
b be primes, 2^a - 1 and 2^b - 1 have completely different factors. So we
can make a table (database) with
p1 divides M(q1)
p2
Why test factor for primes in the range 2^1 to 2^10? If someone made the
table I described, it is possible that all primes less than 2^10 are in the
table I have described because they are known divisors of a Mersenne number
OR are not candidates for dividing any Mersenne number by other
