Here are some details on my search for PRP repunits. Some years ago I wrote a C program using the MIRACL library to do the search. The program considered only Rp with p prime, and trial divided using 2kp+1 up to about 11 digits (e.g. 100647575569 divides R84751). I tried to beat the record of 1031 but Harvey Dubner beat me with R49081. I continued the search off & on for the last year. I assumed that Harvey would continue from 49081, so my strategy was to start at 75000 and work around there (76000, 74000, 77000, ...). My C program was not as efficient as PrimeForm so I only used my program to trial divide by 2kp+1 (as PrimeFrom did not do this up to 10^11, or for this type of factor). I then started using PrimeForm, and later switched to pfgw after discovering the inefficiency "wall" (78941 took about 4.7 hours, but 78977 took 11 hours! on a Pentium II /400Mhz). pfgw reported R86453 on Oct 26, which coincided with the announcement of the winner of the Eternity (1 million UK pound prize) puzzle, which I had been actively following: I placed 206 out of 209 pieces. [Go to www.mathpuzzle.com for details]. --- In primeform@egroups.com, "Michael Bell" <mdb36@c...> wrote: > Hi, > > Congratulations on the find, is this part of a project, or are you working > on Repunits alone? ==>> THIS IS NOT PART OF A PROJECT, I DABBLE IN REPUNITS. > Did you use any kind of sieve in the search? (I'm > certain one could be written that would be about as fast as the factorial > sieve, I'm guessing you couldn't go better than that though) ==>> I ONLY TRIAL DIVIDED USING 2KP+1. ==>> WHAT IS THE FACTORIAL SIEVE? > > I assume there is no chance of a proof of primality, a shame really - even > if the Generalised Riemann Hypothesis was proved it would take a very long > time to run all those SPRP tests! ==>> I DON'T HAVE EXPERTISE IN THAT AREA. ALSO, R49081 HAS NOT BEEN CRACKED YET. > > Are you going to continue searching for higher repunits? Maybe a search > could be organised (although it might be hard to get people to search for > non-archivable primes). ==>> MY PROGRAM ONLY WENT AS LOW AS 63000. HARVEY TOLD ME THAT HE HAD SEARCHED UP TO 62000 (CONFIRMING MY ASSUMPTION!), SO I ONLY PLAN TO TEST THE GAP BETWEEN 62000 AND 63000. I AM CURRENTLY TESTING 42 CASES IN THAT RANGE, AND I EXPECT IT TO FINISH SOON. > > Sorry if that sounded like 20 questions, I was surprised by the lack of > response to this find (maybe everyone is in shock from Conrad Curry's > announcement that he'd found the remaining factors to prove (402^2521-1)/401 > prime). > > Michael.

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