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

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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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Jun 2003

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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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Old 2021-06-21, 19:02   #5
MattcAnderson
 
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"Matthew Anderson"
Dec 2010
Oregon, USA

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Default 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.
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Old 2021-06-21, 19:21   #6
Uncwilly
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Quote:
Originally Posted by MattcAnderson View Post
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.
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Old 2021-06-27, 09:28   #7
Mark Rose
 
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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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