For the factor to be about 6300000, the exponent could be at most about
3150000, since the factors of mersenne numbers are of the form q=2kp+1.
(if q=6300000, for k=1, p=~3150000, and for larger k, p is smaller)
But nearly all numbers below 3310000 have already been not only tested
for factors to at least 2^50 (with most exponents factored up to 2^55
or more), but Lucas-Lehmer tested also already (except for 72).
I think it is much more likely that the exponent tested is p=~6300000,
and the factor found for it is somewhere between 2^55 and 2^62 or so.
Ken
At 09:03 AM 1998/09/17 -0400, you wrote:
>> >Computer running prime95 ver 16.4 intel 486 today found a
>> >factor of the number it was processing, contacted primenet,
>> >sent the result, obtained a new number to factor, and then
>> >continued to factor the same number it had just found a factor
>> >for. I do not have the files immediately to hand but the
>> >number was in the 6300000 range and the factorization had
>> >reached the 6th or 7th iteration of 16. Can someone tell me,
>>
>> The factoring test will continue on the chance that a smaller factor
>> may be found. I believe this is in the interest of doing some kind
>> of analysis on the smallest factors of composite Mersenne numbers.
>
>Well, is it aware enough not to try any factors larger than those
>already found? In the case above, iterations 7-16 should go _very_
>fast if the iteration 6 factor found was only 6300000.
>
>-- Tim
>
