Factoring details

[mturpin]

I am wondering what the following means:

"Trial factoring M82611773 to 2^68 is 82.77% complete. Time:374.213 sec."

M82611773 must be 2^82611773-1, the number being tested for primality? Is the program checking all factors n < 2^68? Is the time a cumulative time, or since the last message?

Thanks for any help.

[firejuggler]

primality?
no, just factors (at this point).

fator n<2^68?
not exactly..
All mersenne factor are of the form 2*k*p+1 where p is 82611773 in your case.
what is tested is the value of k wich make 2*k*p+1 <2^68... k being an integer, equal or above 1.

as for the time it is since the last message.

[Mr. P-1]

Originally Posted by firejuggler

primality?
no, just factors (at this point).

To clarify, the number will eventually be tested for primality (by you or someone else), if no factor is found.

To find out whether the person who will do the primality test will be you or someone else, look in your worktodo.txt file. If the line with that exponent begins with "Test=" or "Doublecheck=", they you will do the primality test. If it begins with "Factor=", then you're only doing the factoring stage.

[Uncwilly]

Originally Posted by mturpin

"Trial factoring M82611773 to 2^68 is 82.77% complete. Time:374.213 sec."

M82611773 must be 2^82611773-1, the number being tested for primality? Is the program checking all factors n < 2^68? Is the time a cumulative time, or since the last message?

As explained above, yes M82611773 is 2^82611773-1
The factors of Mersenne numbers can only be in the form 2*k*p+1
Your machine is testing for numbers in the range between 2^67 and 2^68. The report is stating that you are 82.77% of the way through that. 374.213 seconds (wall clock time) have elapsed since the last status update.

The trial factoring that you are doing is the fastest way to eliminate as many candidates as possible. The starting list of candidates is all prime numbers for the exponent. About 50% are quickly eliminated by trial factoring to low bit levels. Then about 10-15% more are eliminated by more trial factoring and 'P-1' testing. Those numbers that remain are then tested for primality. This test takes much longer, but will not find any factors.

[LaurV]

For more details, please see the math page on GIMPS server.