> 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 conditions
> (subject to the ALERT above).
Remember that the smallest factor of M_p (p prime) is 2*p+1. This is
the smallest factor in a fair number of cases. This means, however,
that the smallest M_p which has a factor around 2^10 must have p~=2^9.
I think we're well past that point.
If I understand you correctly, you suggest making a massive table
of primes, and what M_p they divide. This would be very inefficient!!
Since I doubt that you could Store such a table in memory, the lookup
time would be enormous compared to the time spent to actually testing
the factor. Even if you could store it in memory, I think that the
lookup time would still be greater than the time spent testing the
factor.
If you mean to create a range (eg: <2^32) and test for which M_p divide
primes in that range one by testing the potential factors, this might
work, though Chris Nash did this on smaller ranges, and most of
the results weren't worth much. I think it is much faster to test exponents
for factors rather than the other way around, when dealing only with
prime exponents.
-Lucas Wiman
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