20200117, 04:58  #1 
"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 FECM 20200115 11:33 36.7 0.0298 Factor: 18087479791 / (ECM curve 1, B1=250000, B2=25000000) ; log(18087479791) / log(2) ~34.07427235371961474669 >> factor(180874797911) ans = 2 3 5 31 89 218527 >> 219851 1894675919 Bommer Manual testing 219851 FECM 20200115 11:33 42.6 0.0298 Factor: 1894675919 / (ECM curve 1, B1=250000, B2=25000000) ; log(1894675919) / log(2) ~30.81930395302322145371 >> factor(18946759191) ans = 2 31 139 219851 >> These two factors should could be found by p1 using B1 = 200, that will save some hours , I'm not sure where is the problem why this factor is not P1'ed. Also notice that these two factors also missed by TJAOI using his factoring method. I would propose finish B1 = 1000 using P1 for exponent less than 1 million. 
20200117, 05:09  #2 
Jun 2003
2^{3}×3^{4}×7 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 
20200119, 10:46  #3 
"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. 
20200119, 13:55  #4 
Jun 2003
2^{3}×3^{4}×7 Posts 

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