On 1 Oct 2001, at 22:23, Jean-Yves Canart wrote: > I have browsed some logs I archived long time ago and I have found > this: > > In may 1998, one user, "tomfakes", cleared around 80 exponents with > factor found = "1" It was in the range 7013000-7055000.
Well, (s)he's not lying - 0 = n (mod 1) is a property of integers ;-) In any event: (a) this is the _opposite_ of the reported problem - what seems to have happened is that "no factor found" was being reported, sometimes erroneously; (b) this won't get through now PrimeNet validates submitted factors; the code I wrote for this purpose rejects as garbage any single-digit factor, after stripping off any leading zeroes as well as white space. (Obviously a Mersenne number with a prime exponent p > 5 cannot have any factors less than 10, and we know pretty much all there is to know about exponents up to and including 5, so excluding these is not a practical problem). > > At 04:07 PM 9/30/2001 -0700, Daniel Swanson wrote: > > >I went through the Cleared Exponents > > >report looking for other examples of factors found during > > double-checks that > > >should have been found during the initial factorization. > > > 5977297 53 DF 6726544627832489 > > > 6019603 57 DF 137024179940485697 > > > 7019297 57 DF 160100125459121849 > > > 7020641 58 DF 226230108157229263 > > > 7025987 56 DF 74052063365823791 > > > 7027303 55 DF 31090234297428433 > > >10159613 56 DF 68279769831982367 > > >Were numbers in this range all originally factored by the same user > > >or computer? > > > > My logfiles from that long ago have been zipped and stored on CDROM. > > It is possible that 7,010,000 - 7,030,000 were all factored by one > > person. It was not uncommon for me to hand out large blocks for > > factoring to users without Internet connections. While I no longer > > do this, there are a handful of users pre-factoring the 20,000,000 - > > 80,000,000 area. I hope their machines are reliable!! They > > probably are as they are finding the expected number of factors. The primes from that block of 20,000 numbers represents quite a bit of work and maps poorly onto the "missed" factors reported. A few mistakes are inevitable but, since testing a factor takes of the order of a microsecond on current systems, hardware glitches shouldn't be much of a risk. (? Unless they get into the code stream used to generate potential factors?) Reports of two "missed" factors of exponents within spitting distance of 6,000,000 and no less than four just over 7,000,000 looks high for random glitches to be responsible, even on really ropy hardware. Remember that P-1 (which found the factors missed by trial factoring) can only find a small proportion of the "small" factors, especially when it's being run with "double checking" limits. > > > > Anyway, it doesn't appear to be a program bug as you were able to > > find the factor with trial factoring. I'm guessing either bad > > hardware or an older prime95 version had a bug. If it _was_ Prime95. There are other factoring programs out there; maybe there was a higher incidence of use about 3.5 years ago when these exponents would have been the subject of factoring assignments. > > Either way, GIMPS > > has never considered missing a factor as a big deal. It only means > > some wasted effort running a LL test that could have been avoided. True enough - though I'm concerned that the "no factors below 2^N" database may be seriously flawed, from the point of view of GIMPS it would seem to be a waste of time to go round redoing trial factoring just to fix this problem. However if it could be established that all the "missed" factors reported were the work of one user, perhaps it would be worth fixing the database to force rerunning of trial factoring for those factoring assignments run by that user when the exponents are reassigned for double checking (or LL testing). Regards Brian Beesley _________________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
