> I was running a double check (assigned by Entropia) and found a factor,
> this is the second time that this has happened. I was just wondering about
> a few things
>
> 1. How often does this happen?
Depends on the bounds, which in turn depends on the exponent and your
memory settings. The estimated probability of finding a factor is
given at the beginning of the run & is typically between 0.02 & 0.05.
> 2. Does the original tester still "lose" the LL-credit they originally
> received. If they do then this doesn't seem fair to me, after all when
> they did the LL-test we didn't have the capability to find that factor.
Yes, in George's tables, but not according to PrimeNet. George's
tables are recalculated each time from the list of exponents without
known factors and take no account of factoring effort. PrimeNet
accumulates all effort contributed "in good faith" by the user for
both LL testing and factoring but does not include any credit for
results submitted manually.
> 3.
> Is it worth going back and performing a P-1 test on all Mersenne
> candidates with no known factor
If we simply want to eliminate exponents as candidates for Mersenne
primes, once we have a pair of matching residuals there seems no
point in searching for factors.
If we are interested in actually finding factors then P-1 will find
factors for _some_ exponents at a lower compuational cost than ECM &
should therefore be tried before ECM. But note that a large fraction
of exponents will fail to succumb to either P-1 or ECM even with very
heavy expenditure of effort.
> 4. Or is it better just to factor them
> deeper towards 2^72
Once we have trial factored to the Prime95 limit there seems lillte
point in going further. For typical exponents, P-1 followed by ECM is
likely (but not guaranteed) to find factors in this range with a
higher frequncy in terms of factors found per CPU year.
>
> Just out of interest I ran P-1 testing on another couple of numbers but no
> factor turned up. It only took about 3 hours for each test though...
>
> [Thu Jun 22 15:19:41 2000]
> UID: nitro/liberator, M3200543 completed P-1, B1=40000, B2=600000, WW1:
> 52E3BFCC [Thu Jun 22 19:00:18 2000] UID: nitro/liberator, M4056419
> completed P-1, B1=45000, B2=652500, WW1: 691E386D
There are a large number of much smaller exponents which have had
very little factoring effort other than trial factoring. See Eric
Hahn's database of P-1 factoring effort ...
http://www.mcn.org/2/ehahn/mersenne/mersenne.html
Personally I think it's more interesting either to eliminate
candidates before LL tests are run, or to try to find a factor for
some of the smaller exponents for which no factors are known.
Over the last 10 days or so I've tested 45 exponents with no known
factors in the range 125,000 - 149,999 using P-1 with B1=1E6,
B2=2.5E7 and have found two factors:
P-1 found a factor in stage #2, B1=1000000, B2=25000000.
UID: beejaybee/Simon2, M143977 has a factor:
1660886238958203449182951
P-1 found a factor in stage #1, B1=1000000, B2=25000000.
UID: beejaybee/Simon2, M125933 has a factor: 1306727074606217680681
The runs take 1.5 - 2.0 hours each on a PIII-450.
Although this success rate is a bit lower than I'd hoped for (just
bad luck, I presume), it's a _lot_ better than trying to find factors
of numbers in the Cunningham tables using ECM.
Regards
Brian Beesley
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