ECM on numbers with known factors

[MatWur-S530113]

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

[akruppa]

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

[MatWur-S530113]

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

best regards (and Merry Christmas to all),

Matthias

[Prime95]

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

[jrk]

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:

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

Good luck on your search.

[MatWur-S530113]

Hello again,

Originally Posted by Prime95

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

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
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?

best regards,

Matthias

[Prime95]

Originally Posted by jrk

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?)

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.

[akruppa]

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

[Miszka]

Originally Posted by Prime95

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

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"?

[Batalov]

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

[Miszka]

Originally Posted by Batalov

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

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

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

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

What is wrong?