20210601, 01:31  #1 
Jan 2020
3^{3}×13 Posts 
This PRP Cofactor Assignment (why factor is similar to p)
I got this PRP Cofactor assignment from the server today 
https://www.mersenne.org/report_expo...1180011&full=1 Why is the factor so similar to the exponent itself? 
20210601, 02:15  #2 
Jan 2021
California
3^{2}×17 Posts 
All factors will be "similar" to the exponent. They will be of the form 2kp+1. In this particular case, k is 5, yielding 10p+1.
The very first nonprime Mersenne number M11=2047 has factors 23 and 89 (2*11+1 and 8*11+1). Last fiddled with by slandrum on 20210601 at 02:36 
20210604, 00:23  #3 
Jan 2020
3^{3}×13 Posts 
The other question I have is the ceiling limit of the exponent for the PRP cofactor.
Will it be possible to run a PRP cofactor test for M168,713,323/12,028,146,460,379,499,674,057 on a PC with Threadripper 5970X and Geforce 3080 Ti? 
20210604, 04:04  #4 
Einyen
Dec 2003
Denmark
2×1,579 Posts 
There is no software to do it on the 3080 Ti, but you can do it with Prime95/mprime. It can run PRPCF test as high as normal PRP tests, but the test will take as long as a normal PRP test in the 168M range, so it is a lot of work "just" to test the cofactor, which will be composite with >99.99% probability (just guessing that number).

20210604, 13:24  #5  
Feb 2017
Nowhere
7·23·29 Posts 
Quote:
According to the detailed status report for exponent 168713323, TF was working the range from 2^73 and 2^74 when it found the factor. It might be worthwhile doing more TF of the cofactor before embarking on a PRP test. 

20210604, 14:45  #6  
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
5424_{10} Posts 
Quote:
For 168713323 Code:
Date User Type Result 20210423 Tucker Kao F Factor: 12028146460379499674057 / TF: 7374* The need for restarting can be avoided in mfaktx by changing mfaktx.ini entry StopAfterFactor back to the default value 1: # possible values for StopAfterFactor: # 0: Do not stop the current assignment after a factor was found. # 1: When a factor was found for the current assignment stop after the # current bitlevel. This makes only sense when Stages is enabled. # 2: When a factor was found for the current assignment stop after the # current class. # # Default: StopAfterFactor=1 StopAfterFactor=1 

20210604, 18:48  #7  
Jan 2020
3^{3}×13 Posts 
David Kirkby wants to find a prime using the least amount of time. So, if PRP Cofactor takes around the same time as the regular PRP for the similar exponents, then any cofactor PRP on M82,589,939 or above still has the chance to find a world record prime while not a Mersenne Prime, but a 1/100,000 chance is still worth the try for him.
Quote:
What will the code be for worktodo.txt when PRP Cofactor with multiple existing factors? Quote:
Last fiddled with by tuckerkao on 20210604 at 19:14 

20210604, 19:02  #8 
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
2^{4}·3·113 Posts 
Mfaktc supports any reasonably modern NVIDIA gpu supporting CUDA, although for the bleeding edge it can sometimes be a challenge to locate executables or build it yourself for the latest CUDA level and OS of your choice. Mfaktc does TF for Mersenne numbers for exponent <2^{32}, factor less than 95 bits. It does not do cofactor TF.
More mfaktc info here, here, and here. The OpenCL equivalent for AMD GPUs, and some CPUs' integrated graphics processors is mfakto which can factor up to 92 bits. Worktodo entry formats are described here with examples included; organized by application name first, then available computation type for each application. Bookmark this and use your web browser's search function to find keywords, & answer your own questions. Last fiddled with by kriesel on 20210604 at 19:10 
20210604, 19:38  #9 
Jan 2020
3^{3}·13 Posts 
I got this PRP Cofactor assignment a while ago, this exponent only has 1 known factor.
PRP=1,2,11180011,1,99,0,3,1,"111800111" M103347143 has 2 known factors. How do you write the Cofactor PRP line in this case? I understand it's important to finish the TFs to the GPU72 recommended bit levels or higher before running a PRP Cofactor test. Last fiddled with by tuckerkao on 20210604 at 19:38 
20210604, 19:51  #10  
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
10011001100000_{2} Posts 
I don't think that you know what you are doing.
Do you have any clue what you are talking about? Why do you want to focus on that number? Do you understand the difference between TF work (and the goals and reasons for using it) and running a PRP on a cofactor? Quote:
Last fiddled with by Uncwilly on 20210604 at 19:51 

20210604, 19:54  #11  
Jan 2020
351_{10} Posts 
Quote:
The remaining cofactor has the slim chance to be a very large probable prime, thus worth the PRP Cofactor to test and fully factor the entire Mersenne number. CPRP, the remaining cofactor is not a probably prime, so more than 1 unknown prime cofactor. PPRP, the remaining cofactor is a probable prime, so time to run the LL test on the cofactor. Last fiddled with by tuckerkao on 20210604 at 19:59 

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