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Old 2021-06-01, 01:31   #1
tuckerkao
 
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Default 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?
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Old 2021-06-01, 02:15   #2
slandrum
 
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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 non-prime Mersenne number M11=2047 has factors 23 and 89 (2*11+1 and 8*11+1).

Last fiddled with by slandrum on 2021-06-01 at 02:36
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Old 2021-06-04, 00:23   #3
tuckerkao
 
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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?
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Old 2021-06-04, 04:04   #4
ATH
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Quote:
Originally Posted by tuckerkao View Post
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?
There is no software to do it on the 3080 Ti, but you can do it with Prime95/mprime. It can run PRP-CF 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).
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Old 2021-06-04, 13:24   #5
Dr Sardonicus
 
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Quote:
Originally Posted by tuckerkao View Post
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?
Congratulations on finding a factor!

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.
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Old 2021-06-04, 14:45   #6
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Quote:
Originally Posted by Dr Sardonicus View Post
It might be worthwhile doing more TF of the cofactor before embarking on a PRP test.
Or TF of the Mersenne number.
For 168713323
Code:
Date          User     Type    Result
2021-04-23   Tucker Kao  F   Factor: 12028146460379499674057 / TF: 73-74*
That * indicates 73-74 was not finished, so start again from 73.
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
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Old 2021-06-04, 18:48   #7
tuckerkao
 
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David Kirkby wants to find a prime using the least amount of time. So, if PRP Co-factor takes around the same time as the regular PRP for the similar exponents, then any co-factor 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:
Originally Posted by ATH View Post
There is no software to do it on the 3080 Ti, but you can do it with Prime95/mprime.
Glad I hadn't purchased my new computer yet, always better to ask first. What graphic cards are supported by mfaktc at this time? What about AMD Radeon 6900 XT or Geforce RTX 3090?

What will the code be for worktodo.txt when PRP Co-factor with multiple existing factors?

Quote:
Originally Posted by kriesel View Post
Or TF of the Mersenne number.
For 168713323
Code:
Date          User     Type    Result
2021-04-23   Tucker Kao  F   Factor: 12028146460379499674057 / TF: 73-74*
That * indicates 73-74 was not finished, so start again from 73.
The need for restarting can be avoided in mfaktx by changing mfaktx.ini entry StopAfterFactor back to the default value 1:
StopAfterFactor=1
There are plenty of regular PRPs I can perform in the M168M range at this time. I'll try to finish all the unfactored M168,xxx,323 to 2^78 first.

Last fiddled with by tuckerkao on 2021-06-04 at 19:14
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Old 2021-06-04, 19:02   #8
kriesel
 
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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 <232, 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 2021-06-04 at 19:10
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Old 2021-06-04, 19:38   #9
tuckerkao
 
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I got this PRP Co-factor 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 Co-factor 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 Co-factor test.

Last fiddled with by tuckerkao on 2021-06-04 at 19:38
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Old 2021-06-04, 19:51   #10
Uncwilly
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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:
I got this PRP Co-factor assignment a while ago, this exponent only has 1 known factor.
M103347143 has 2 known factors.
Those 2 statements are both false.

Last fiddled with by Uncwilly on 2021-06-04 at 19:51
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Old 2021-06-04, 19:54   #11
tuckerkao
 
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Quote:
Originally Posted by Uncwilly View Post
Do you understand the difference between TF work (and the goals and reasons for using it) and running a PRP on a cofactor?

Those 2 statements are both false.
I already finished the PRP Co-factor assignment on M11180011

The remaining co-factor has the slim chance to be a very large probable prime, thus worth the PRP Co-factor to test and fully factor the entire Mersenne number.

C-PRP, the remaining co-factor is not a probably prime, so more than 1 unknown prime co-factor.
P-PRP, the remaining co-factor is a probable prime, so time to run the LL test on the co-factor.

Last fiddled with by tuckerkao on 2021-06-04 at 19:59
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