On Sunday 09 March 2003 12:24, Daran wrote: > In the hope of more quickly collecting data, I have also redone, to 'first > time test' limits, every entry in pminus1.txt which had previously done to > B1=B2=1000, 2000, and 3000. For these exponents, all in the 1M-3M ranges, > the client was able to choose a plan with E=12. Unfortunately, I found far > fewer factors in either stage 1 or stage 2 than I would expect, which > suggests to me that exponents in this range have had additional factoring > work (possibly ECM) not recorded in the file.
1) What about factors which would be found with your P-1 limits but happened to fall out in trial factoring? (In fact a lot of the smaller exponents - completed before P-1 was incorporated in the client - seem to have been trial factored beyond the "ecomonic" depth.) In any case, if you're using very small values of B1 & B2, I would _expect_ that a very high percentage of the accessible factors will be found during "normal" trial factoring. 2) It would not surprise me at all to find that there is a substantial amount of P-1 work being done which is not recorded in the database file. I've also had "very bad luck" when extending P-1 beyond limits recorded in the database file for exponents under 1 million. Eventually I gave up. 3) ECM stage 2 for exponents over 1 million takes a serious amount of memory (many times what P-1 can usefully employ), whilst running ECM stage 1 only is not very efficient at finding factors - lots of the power of ECM comes from the fact that stage 2 is very efficient (assuming you can find memory!) > Of particular concern is the > possibility that in addition to reducing the number of factors available > for me to find, it may have upset the balance between 'normal' and > 'extended' P-1 factors - the very ratio I am trying to measure. One way to deal with this would be to deliberately forget previously reported work, i.e. take _all_ the prime exponents in the range you're interested in, trial factor to taste then run P-1. This way you can be sure that, though the vast majority of the factors you will find are rediscoveries, the distribution of the factors you find is not distorted by unreported negative results. Regards Brian Beesley _________________________________________________________________________ Unsubscribe & list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
