Stefan Struiker writes:
When a requested factoring assignment is listed with, say, 52 in an
account log, does this mean it has been factored to 52 bits, but
_without_ success?
Yes, the number should have no factors less than 2^52.
Or could a factor have already been found in some cases, but less
than 52 bits long?
Nope, unless the factor was not reported for some reason (bug, disk
crash, etc.).
My strategy in factoring 13.3 mill exponents and up, is to save L-L
testing and DCing time by knocking some out early. Seem to be on a
roll, too, with factors found 40% of the time, with a turnaround of
40 hours per.
That's a very high rate of factors, I'd've thought, but that happens
sometimes.
In any case, Prime95 "knows" how much factoring work should be done
for a particular Mersenne number before starting an LL test (first or
double-check) on it and will do more factoring if the data it gets
from Primenet (or other source) indicates the number has not been
factored "enough". The predicated chances of finding a factor during
trial and P-1 factoring is taken into account, along with how long the
factoring takes to do and how long the two LL tests will take.
So your phrase "knocking some out early" is exactly correct: if noone
tries to factor a particular Mersenne number before it is given to a
Prime95 that wants to run an LL test, that Prime95 will do some
factoring first, usually before it even finishes the prior Mersenne
number's LL test (to make sure it has "enough" work in worktodo.ini).
Eric Hahn writes:
If it's listed as 52 in the fact-bits column of the report, it
means that it's been trial-factored thru 2^52 without any factors
being found. Currently, all exponents thru Prime95's limit of
79.3M have been factored to at least 2^50... If a factor is
found for an exponent, it's eliminated from further testing
of any kind.
Yup. Here's a short summary of my current data. For Mersenne numbers
with prime exponent that have no LL test nor a factor, here are the
smallest exponents trial factored only as far as the last column:
M( 5178743 )U: 2^62
M( 8896813 )U: 2^61
M( 9993539 )U: 2^60
M( 10078559 )U: 2^55
M( 11300657 )U: 2^54
M( 11505331 )U: 2^53
M( 11521879 )U: 2^52
M( 20500019 )U: 2^51
M( 30100181 )U: 2^50
M( 79300037 )U: 2^45
M( 79306169 )U: 2^43
The exponents above 79.3 million have probably only been worked on by
me, personally, since they're above Prime95's limit, but I'm still a
bit surprised they haven't been factored further; trial factoring to
the same depth is _easier_ for larger exponents, not harder.
Jeff Woods writes:
Isn't the factor itself verified?
Yes, if only by me, as I noted in another thread in the last couple of
weeks.
Will
http://www.garlic.com/~wedgingt/mersenne.html
_________________________________________________________________
Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm
Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
