Need help factoring Cunningham numbers

[jasong]

I know I'm supposed to do Stage 1 with Prime95 and Stage 2 with GMP-ECM, but I can't for the life of me find the instructions.

I'll have finished up my SOB sieving by early Wednesday morning GMT, so I think I've got plenty of time to learn, but I'd really appreciate some help.

Thanks in advance!

[Mystwalker]

You'll probably find this thread interesting, especially #23.

Basically, you have to:

1. Add GmpEcmHook=1 to your prime.ini

2. Enter the number you want to factor into worktodo.ini (the syntax for ECM2 can be found in whatsnew.txt - important: set B2 value to 1)

3. ecm -resume [resultsFile] 1 [B1]-[wantedB2] > [outputFile]
You have to replace the [xyz] with the resp. content. And maybe you want to add the "-n" parameter to the start to lower the priority of gmp-ecm.

[jasong]

Originally Posted by Mystwalker

You'll probably find this thread interesting, especially #23.

Basically, you have to:

1. Add GmpEcmHook=1 to your prime.ini

2. Enter the number you want to factor into worktodo.ini (the syntax for ECM2 can be found in whatsnew.txt - important: set B2 value to 1)

3. ecm -resume [resultsFile] 1 [B1]-[wantedB2] > [outputFile]
You have to replace the [xyz] with the resp. content. And maybe you want to add the "-n" parameter to the start to lower the priority of gmp-ecm.

Thanks Mystwalker, I'll get right on it.

Edit(question):

Change the input to
ECM=16384,11000000,1,100,0,0,1,0

My Prime95 program has never run, do I need to create an input file?

Also, I need to know how to reserve numbers.(I'm just now reading the other threads, so I apologize if it's easily answered)

[Andi47]

Originally Posted by jasong

My Prime95 program has never run, do I need to create an input file?

Also, I need to know how to reserve numbers.(I'm just now reading the other threads, so I apologize if it's easily answered)

If no worktodo.ini file exists in your Prime95 directory, you need to create it. (enter the ECM=... line into this file)

Edit: The seventh value (here in bold font) the line ECM=16384,11000000,1,100,0,0,1,0 determines if you want to ecm a number of the form 2^n-1 or 2^n+1. 0 stands for 2^n-1 and 1 for 2^n+1.

[T.Rex]

What are the differences between:
ECM=16384,11000000,1,100,0,0,1,0
and:
ECM2=1,2,16384,1,44000000,0,20,0,0
?
Last one (ECM2) provides the following results in results file:
2^16384+1 completed 10 ECM curves, B1=44000000, B2=4290000000

T.

[jasong]

I apologize in advance if a search could've solved this problem, but I'm hoping the answer will be easy for you, although not obvious to me.

I've been told ecm is a basically random process. In the case of first running Prime95 and then ecm is it still that same random process?

Basically, what I'm asking is: Should I just randomly pick a number from the Cunningham tables and run it for, say, 24 hours, then report the number of curves? Or is there something else I need to be aware of? (Obviously, if I find a factor, I'll report it. )

[Mystwalker]

Originally Posted by T.Rex

What are the differences between:
ECM=16384,11000000,1,100,0,0,1,0
and:
ECM2=1,2,16384,1,44000000,0,20,0,0
?

Do you want to know the difference between ECM and ECM2 or between those two specific lines?
If it's the first:
ECM2 can be used in a much more general way, as base, exponent and constant can be chosen "arbitrarily".

[Andi47]

Originally Posted by Mystwalker

Do you want to know the difference between ECM and ECM2 or between those two specific lines?
If it's the first:
ECM2 can be used in a much more general way, as base, exponent and constant can be chosen "arbitrarily".

Am I right, does ECM2=1,2,16384,1,44000000,0,20,0,0 mean:

"Do 20 curves at B1=44M on 1*2^16384+1", and if the bold value is 0, it would do curves on 1*2^16384-1 ?

What are the other values, being zero in this example?

[Mystwalker]

Originally Posted by jasong

I've been told ecm is a basically random process. In the case of first running Prime95 and then ecm is it still that same random process?

In this case (doing stage1 with Prime95 - opposed to P-1, TF or LL testing), you also do ECM factorization with Prime95. It's just that you share the computation between Prime95 and gmp-ecm to assign each program the part it's good at.

Basically, what I'm asking is: Should I just randomly pick a number from the Cunningham tables and run it for, say, 24 hours, then report the number of curves? Or is there something else I need to be aware of? (Obviously, if I find a factor, I'll report it. )

All in all, that's the way. But of course, you don't have to pick a number at random. It's all based on your personal preferences.

By the way:
In certain circumstances, it could be better to also use gmp-ecm for stage1. This is especially the case when:

1. the remaining composite is much smaller than the original number and/or
2. the base is greater than 2.

In such cases, you should do a speed comparison of stage1 before fully getting into the factorization of that number.

Be aware that most numbers of the Cunningham Tables already sustained quite some factorization effort. I wouldn't start below the 45 digit range (--> B1=11M).

[Mystwalker]

Originally Posted by Andreas Schinde

Am I right, does ECM2=1,2,16384,1,44000000,0,20,0,0 mean:

"Do 20 curves at B1=44M on 1*2^16384+1"

Basically yes, plus you say that the default B2 bound (100*B1, but at most 4290000000) should be used. But I wouldn't add the last two zeros. The first one seems to be a specific sigma value (which means that the 19 curves after the first one are basically wasted, as they all have the same sigma value), the second seems not to be specified. The syntax is in whatsnew.txt:

Originally Posted by wahtsnew.txt

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

and if the bold value is 0, it would do curves on 1*2^16384-1 ?

The old variant ("ECM") did it that way, but with ECM2, you have to add the constant here. "0" would mean "no constant", which it pretty useless. For "-1", you also have to enter "-1"...

What are the other values, being zero in this example?

see above

[Andi47]

Originally Posted by Mystwalker

The old variant ("ECM") did it that way, but with ECM2, you have to add the constant here. "0" would mean "no constant", which it pretty useless. For "-1", you also have to enter "-1"...

So, if I want to do 20 curves on M16384, I would have to enter ECM2=1,2,16384,-1,44000000,0,20,0,0 ?