Recently (before I was subscribed) Robert Baillie mentioned that he'd used Mathematica to search for primes in the leading digits of pi, to 40000 digits. For this size of number, the fastest program for probable primality testing is Chris Nash, Jim Fougeron et al.'s OpenPFGW, which uses George Woltmann's FFT library (as used in GIMPS) for its incredible speed. Similarly the most efficient way to avoid testing is to use some kind of sieving technique to effectively perform trial-division on the candidates and reject the obvious composites. To that end, I've written a trial-division-sieve (not a true sieve, but not naive trial division either, somewhere in between in efficiency), and run it over a range of candidates from 40000 to 100000 digits. I reached a depth approximately 30 times the depth that OpenPFGW's own naive trial division performs. This, using Mertens' theorem, implies that there are about 15% fewer candidates to now test than such trial division. I have no idea how deep Mathematica balances trial-division and PRP testing, but I suspect that it is incomparably less efficient than PFGW at these sizes. I have no spare CPU power to test these numbers myself, but if interested parties want to contact me, I can let them have the presieved ranges, and a PFGW script file that can test the range. Robert can have dibbs, of course. I did some simple back-of-a-fag-packet calculations, and I suspect that the range contains ~0.4 primes, so it will be a stroke of luck if one is found. However, if one is found, I suspect that it will remain the largest such PRP for quite a long time, as the expectation between 100000 and 250000 digits is also only 0.4 (as was the expectation between 16000 and 40000) My TDSieve can be trivially adapted to other constants (e, phi, sqrt2, etc.) and to other bases, so if others are interested in related tasks, please don't hesitate to contact me regarding them (or keep it on-list). Phil ===== When inserting a CD, hold down shift to stop the AutoRun feature In the Device Manager, disable the SbcpHid device. http://www.cs.princeton.edu/~jhalderm/cd3/ __________________________________ Do you Yahoo!? Yahoo! Mail - 50x more storage than other providers! http://promotions.yahoo.com/new_mail