Hi,
At 03:30 PM 10/12/99 +0300, Jukka Santala wrote:
>Is it just me, or does factoring smaller Mersenne numbers take
>propotionally much longer? I would expect M727 to be much faster than
>the 33M range to a fixed depth, yet the opposite _seems_ to be true.
Since factors are of the form 2kp+1 there are many more factors to test
when you factoring M727. Yes each factor can be tested in less time,
but this is overwhelmed by extra factors to test.
>the real complaint I have
>is that factoring numbers to depths beyond the "default" seems nearly
>impossible.
Yes, the only way to trial factor to a greater depth is with
the Advanced/Factor menu choice - and it is difficult to use.
Improving this is in the wish list, but didn't make the cut for v19.
The biggest reason is: More trial factoring is likely a waste of time.
You will find more factors using ECM. Compare the cost of running
700 curves at B1=250000 (this will find most 30-digit factors) against
trial factoring to 99 bits! It is true that ECM can miss a factor,
but for M727 which has had thousands of curves run at bounds as high
as 50,000,000 - the chance of finding a factor smaller than 30 digits
is.....well, zero.
Regards,
George
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