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Old 2020-01-17, 04:58   #1
wreck
 
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"Bo Chen"
Oct 2005
Wuhan,China

2×79 Posts
Default 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.
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Old 2020-01-17, 05:09   #2
axn
 
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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
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Old 2020-01-19, 10:46   #3
wreck
 
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"Bo Chen"
Oct 2005
Wuhan,China

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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.
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Old 2020-01-19, 13:55   #4
axn
 
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Quote:
Originally Posted by wreck View Post
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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