We have seen the LL test error rate climb with time as we move to higher exponents and can expect it to continue to do so.
Long ago when smaller exponents were being tested the rate was ~0.5% as I recall. (An error rate very much smaller than this would still justify double checking; 0.01% would still yield erroneous results on 100 exponents already done.) The error rate found upon double checking is likely to continue to increase. For a hypothetical pool of machines of constant reliability, the error rate per trillion operations (or should that be per hour of 100% cpu utilization?) would be about constant. The number of operations goes up slightly faster than the square of the exponent, so twice the exponent means more than 4 times the error rate per exponent. (More iterations, performed in more pieces, of slightly lower precision) Machine reliability generally declines with machine age, overclocking, environmental temperature extremes, decreasing power quality, addition of low quality components (watch out for bad RAM). Other factors usually beyond our control such as cosmic rays have an influence. To counter these effects, increasing reliability of the machine pool would be needed. Note, not all errors are in the first LL test. It's possible to have a mismatch between first & second test that is not resolved by a third LL test. It's also possible to have an error in factoring attempts yield a false positive for a factor that fails verification. If I recall correctly, verification of a Mersenne prime is run on different software on a different computer architecture to maximize the chance of a software bug or computer hardware design error from yielding a false positive. During the QA effort, comparisons of interim LL test residues were made among differing software run on differing computer architectures. Ken At 04:21 PM 6/22/2008 +0200, [EMAIL PROTECTED] wrote: >The error rate is around 3,2 % (From the last statistic files : 32404 bad >results and 1001016 verified results.) > >In other words one test in 31 is bad. Enough to justify double-checking >in George Woltman's and many others opinion. > >Jacob Ken Kriesel, PE <[EMAIL PROTECTED]> _______________________________________________ Prime mailing list [email protected] http://hogranch.com/mailman/listinfo/prime
