p59 factor of 6, 334+ by ecm

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p59 factor of 6, 334+ by ecm

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Send message Joined: 2 Oct 09 Posts: 50 Credit: 111,128,218 RAC: 0 |
The early NFS@Home numbers were all tested extensively by ECM (the Elliptic Curve Method) for small and medium sized prime factors, past 55-digits. The three most recent numbers were less tested, and of these 6, 334+ was hardly tested at all before selection (due to rapid NFS@Home progress!). We had expected 50-digit prime factors to have been removed, and planned on removing prime factors up to 55-digits, with a chance of finding larger factors, before starting sieving. So I'm happy to report that the 59-digit prime p59 = 37597376323754357344197406664995834047249702145969970498293 divides the 239-digit composite factor of 6,334+ we had intended to factor. Unfortunately, there remains a composite cofactor of 181-digits; and sieving by snfs (with difficulty 259) is still easier than using gnfs (with gnfs on a 181-digit number perhaps comparable in difficulty to snfs on a number with difficulty of 270-digits). I'm not done testing yet, but there's most likely not another factor in ECM range (up to 70-digit primes). This factor was found by GMP-ECM, under the ECMNET project, Dodson/ECMNET; which is also the software used by the boinc project yoyo (for which Beyond of Team Ars Technica found a recent large prime factor). The machine used was one of 300+ 32-bit linux/xeons, along with c. 500 pcs (1050 pcs used during 8pm to 8am) distributed under condor. The first step limit B1 was 260,000,000 (with default B2), optimal for finding 60-digit primes. This p59 is the 4th largest prime found this year by ECMNET, just below the 59-digit prime in 3rd place found by yoyo@home earlier this year. It's nowhere near the Top 10 on Brent's list, for which the three smallest primes all have 62-digits. At the risk of trying the patience of NFS@home readers, I can report that four of those Top 10 are Dodson/ECMNET factors, including the two largest at 67-digits and 66-digits (just a bit larger than the 66-digit prime found by the ECMNET founder, Paul Zimmermann). -bdodson |

Send message Joined: 26 Jun 08 Posts: 623 Credit: 357,639,476 RAC: 203,381 |
Thanks Bruce for doing the ECM pretesting of the numbers. It is unfortunate that the cofactor remains composite. Had it been prime, then 6,334+ would be complete. |