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 2020-01-17, 04:58 #1 wreck     "Bo Chen" Oct 2005 Wuhan,China 2·79 Posts Two small factors found by Bommer In the recent cleared report, I found there are two small factors report, both less than 40 bits. The two factors is found by Bommer using ECM with B1 = 25000. The two exponents is 218527 and 219851. 218527 18087479791 Bommer Manual testing 218527 F-ECM 2020-01-15 11:33 36.7 0.0298 Factor: 18087479791 / (ECM curve 1, B1=250000, B2=25000000) ; log(18087479791) / log(2) ~34.07427235371961474669 >> factor(18087479791-1) ans = 2 3 5 31 89 218527 >> 219851 1894675919 Bommer Manual testing 219851 F-ECM 2020-01-15 11:33 42.6 0.0298 Factor: 1894675919 / (ECM curve 1, B1=250000, B2=25000000) ; log(1894675919) / log(2) ~30.81930395302322145371 >> factor(1894675919-1) ans = 2 31 139 219851 >> These two factors should could be found by p-1 using B1 = 200, that will save some hours , I'm not sure where is the problem why this factor is not P-1'ed. Also notice that these two factors also missed by TJAOI using his factoring method. I would propose finish B1 = 1000 using P-1 for exponent less than 1 million.
 2020-01-17, 05:09 #2 axn     Jun 2003 3·1,511 Posts These factors have been known for ages. They are trivially found by TF (35 and 31 bits respectively). Looks like Bommer did some improper ECM without using known factors (or maybe there was some glitch). See the history of the exponents: https://www.mersenne.org/report_expo...ll=1&ecmhist=1 https://www.mersenne.org/report_expo...ll=1&ecmhist=1
 2020-01-19, 10:46 #3 wreck     "Bo Chen" Oct 2005 Wuhan,China 2×79 Posts Yes, I found this two factors is found before, but I dont know how to delete the post, and it is still a little strange to mark this factor found at 2020, so this post perhaps has some useful information.
2020-01-19, 13:55   #4
axn

Jun 2003

3×1,511 Posts

Quote:
 Originally Posted by wreck and it is still a little strange to mark this factor found at 2020, so this post perhaps has some useful information.
Agreed, definitely the server should not have accepted the factor or done a cofactor PRP test.

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