20200117, 04:58  #1 
"Bo Chen"
Oct 2005
Wuhan,China
173 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}·673 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
173_{10} 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
12410_{8} Posts 

20210621, 19:02  #5 
"Matthew Anderson"
Dec 2010
Oregon, USA
1165_{10} Posts 
factordb data
Hi all,
An integer factorization database exists at factordb.com In my humble opinion, this database will be more useful if it has more data in it. Feel free to donate computer power to this effort. I do. Currently, it can do prime factorization of most numbers up to about 50 digits. Examples  23504957230957830295783029578302495782039857324521<50> = 19 · 41 · 887 · 1580053 · 21529142531645108721618396168821641609<38> also, a fully factored (into prime numbers) integer, 23504957230957830295793029578302495782039857324521<50> = 1229 · 19125270326247217490474393472988198358047076749<47> When I put a 70 or 80 digit input, I usually receive an unfactored composite in the factorization provided by factordb. Good fun. 
20210621, 19:21  #6 
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
7×1,523 Posts 

20210627, 09:28  #7 
"/X\(‘‘)/X\"
Jan 2013
5611_{8} Posts 
For reasonably small numbers, like 23504957230957830295783029578302495782 (38), you can factor it in a fraction of a second
$ time factor 23504957230957830295783029578302495782 23504957230957830295783029578302495782: 2 3 241 119829401 33842479193 4008349790106769 real 0m0.013s user 0m0.010s sys 0m0.003s 
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