mersenneforum.org > Data Two small factors found by Bommer
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 2020-01-17, 04:58 #1 wreck     "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 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 23·673 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
 2020-01-19, 10:46 #3 wreck     "Bo Chen" Oct 2005 Wuhan,China 17310 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

124108 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.

 2021-06-21, 19:02 #5 MattcAnderson     "Matthew Anderson" Dec 2010 Oregon, USA 116510 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.
2021-06-21, 19:21   #6
Uncwilly
6809 > 6502

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Aug 2003
101×103 Posts

7×1,523 Posts

Quote:
 Originally Posted by MattcAnderson Currently, it can do prime factorization of most numbers up to about 50 digits.
Numbers that size are easier to check on your own machine than to look up from a table.

 2021-06-27, 09:28 #7 Mark Rose     "/X\(‘-‘)/X\" Jan 2013 56118 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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