ECM on numbers with known factors
 

Hello,

at the moment I want to run some Elliptic Curves on M-numbers with known factors. Is there a possibility to tell prime95 about the already known factors? With GMP-ECM I simply divide out already known factors in the input file, f.e.
(2^1051-1)/3575503
but I don't see a similary way for prime95.
Thank You for every help,

Matthias

Create a file "lowm.txt" for 2^n-1 numbers with content like e.g.
M( 123 )C: 456

if the number 2^123-1 had the factor 456. For 2^n+1 numbers, make a file "lowp.txt" and start the line with P instead of M. If the files are in the Prime95 working directory, it scans them for known factors when it starts P-1 or ECM.

Alex

Thank you Alex, very appreciatet. I will test it immediately.

best regards (and Merry Christmas to all),

Matthias

lowm.txt is no longer the preferred way of doing this.

Put in worktodo.txt:

ECM2=k,b,n,c,B1,B2,curves_to_do[,specific_sigma,B2_start][,"factors"]

where factors is a comma separated list of known factors

I confirm the lowm.txt file works with mprime 25.6 and earlier versions at least. I haven't used newer versions yet (is it being dropped?). Monday I found this 38 digit ECM factor:

[quote]ECM found a factor in curve #746, stage #2
Sigma=2718571677409511, B1=3000000, B2=300000000.
UID: jaysonking/atlas, M2833 has a factor: 23566472916933362899116269461226511839[/quote]:smile:

Good luck on your search.

Hello again,

[quote=Prime95;155088]lowm.txt is no longer the preferred way of doing this.

Put in worktodo.txt:

ECM2=k,b,n,c,B1,B2,curves_to_do[,specific_sigma,B2_start][,"factors"]

where factors is a comma separated list of known factors[/quote]

thank you for pointing this out. I already tried it with lowm.txt, it works fine for me. But it seems easier to do it with command line in worktodo.txt. I will test it the next time.

@ Jayson King
I saw this factor in the 'recent cleared' list on monday, what a monster, congratulations:wblipp:
If I remember right you already found a 41-digit factor some days before (exponent range ~ 10000)... could you play lotto for me next week? :whistle:

best regards,

Matthias

[QUOTE=jrk;155095]I confirm the lowm.txt file works with mprime 25.6 and earlier versions at least. I haven't used newer versions yet (is it being dropped?)[/QUOTE]

It is not being dropped. However, when ECMing k*b^n+c it only works if k=1, b=2, and c=-1. The worktodo.txt approach can handle all cases.

I should add: if you use the low[mp].txt file, you can have several lines for the same input number. So when you find another factor and want to continue factoring the cofactor, you don't need to multiply the known factors up to put them in a single line - just add another line with the new factor. Plus, iirc, the exponents must be in non-decreasing order; i.e., i think Prime95 stops scanning lowm.txt for factors once it reads an exponent greater than the one it's trying to factor.

Alex

[QUOTE=Prime95;155088]lowm.txt is no longer the preferred way of doing this.

Put in worktodo.txt:

ECM2=k,b,n,c,B1,B2,curves_to_do[,specific_sigma,B2_start][,"factors"]

where factors is a comma separated list of known factors[/QUOTE]

Composite factors too?
For example M118297 has known factors: 1892753, 3568547303, 404339666506801 and composite factors: 6754378613395159, 765315116799747113153, 1442905226408764139707703 and 2731063196000867551724173976359
Which to put in "factors"?

Just the prime factors: "1892753,3568547303,404339666506801"
[I]Or[/I] their product - this will work too: "2731063196000867551724173976359"

[QUOTE=Batalov;371926]Just the prime factors: "1892753,3568547303,404339666506801"
[I]Or[/I] their product - this will work too: "2731063196000867551724173976359"[/QUOTE]

I done
ECM2=1,2,119923,-1,50000,5000000,27,"1918769,[B]8047312993[/B],[B]5783659875377[/B]"

result
"M119923 has a factor: 46542921262214092873361, AID: 9D7EF7410F11BDE1323E8C229717E099

PrimeNet success code with additional info:
Composite factor 46542921262214092873361 = [B]8047312993[/B] * [B]5783659875377[/B]
Already have factor [B]8047312993[/B] for M119923
Already have factor [B]5783659875377[/B] for M119923"

What is wrong?

Have you modified the line already [I]after [/I]you started the test?
If so, this would be the reason.

A running P95 process:
1) does not re-read the worktodo.txt file (if it is modified while the program is running). In fact, if you modify the worktodo.txt, save it, [I]then[/I] stop P95 and then check [I]what[/I] is in the worktodo.txt file, you will find that it will be [I]restored[/I] to what it was before, when P95 was started. This is done from P95 memory at the moment when it is stopped. This is unusual for new users, but once you learn this feature, you can live with it.
2) can use the intermediate save files (the "m" and "e" files) from the run before this one (and the save file doesn't know that you changed the worktodo line, and will continue from the earlier state, i.e. without the listed factors). Solution: remove these files (or move them to another directory).

I have just run your line as is in P95 several times. The known factors were not found even once (which is just what one would expect).

P.S. In fact,
ECM found a factor in curve #22, stage #2
Sigma=3698465552502853, B1=50000, B2=5000000.
M119923 has a factor: 68966518357695541070447 (ECM curve 22, B1=50000, B2=5000000)

Why running ECM on numbers with [U]already known[/U] factors if we still have so many numbers without any known factors? Wouldn´t it make more sense to run ECM on those?

Maybe he wants to beat [URL="http://www.primenumbers.net/prptop/searchform.php?form=%282%5Ex-1%29%2F%3F&action=Search"]NOOE's PRP records[/URL]? Who knows?

Just in case,
[code][Thu Apr 24 18:11:39 2014]
M119923/known_factors is not prime. RES64: 3977ECB8E69C84AE. We4: F49D9B33,00000000
Known factors used for PRP test were: 1918769,8047312993,5783659875377,68966518357695541070447[/code]

[QUOTE=Batalov;371939]Have you modified the line already [I]after [/I]you started the test?
If so, this would be the reason.
[/QUOTE]
No, absolutely no

[QUOTE=Batalov;371939]
ECM found a factor in curve #22, stage #2
Sigma=3698465552502853, B1=50000, B2=5000000.
M119923 has a factor: 68966518357695541070447 (ECM curve 22, B1=50000, B2=5000000)[/QUOTE]
My congratulations!
It was not successful me :confused:

It was simply a free by-product of the test that I ran for you.

I agree with lycorn about ECMing numbers without known factors, if ECM is what one likes to run.