> However, a semi-reasonable task would be to test numbers for factors up to
> 2^16.
Done.
> Pitiful, I know, but a TI could test a single number in 12 hours.
An optimized algorithm will do it in about zero seconds.
> B) To Mr. Woltman or Mr. Kurowski - how "useful" would factoring (most
likely
> very large) exponents to only 2^16 be? Or have "real" computers already
> quickly scanned very high for such small factors?
The smallest factor of 2^p-1, p a prime, is at least as big as 2p+1. All
factors of a Mersenne number of prime exponent are of the form 2kp+1 -
similarly for all 'new' factors of a composite exponent (ie that haven't
appeared in any Mersenne number with an exponent that is a factor of the
original one).
Chris Nash
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