mersenneforum.org > Math How do I test if it is a mersenne prime on GIMPS?
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 2014-11-08, 01:09 #1 spkarra   "Sastry Karra" Jul 2009 Bridgewater, NJ (USA) 33 Posts How do I test if it is a mersenne prime on GIMPS? Hi, I have a prime number (93886421). I cannot test if it is a Mersenne Prime or not on my computer. I want to submit as a manual assignment on GIMPS website. I made sure that the above number is prime before checking on GIMPS Starting calculation... NUMBER: 93886421 4845 iterations Checked range: 3 -> 9691 of 9691 ************************* * This number IS prime! * ************************* I tried to give the range and it is giving me this error: Error code: 40 Error text: No assignment available meeting CPU, program code and work preference requirements, cpu_id: 125173, cpu # = 0, user_id = 19502 ------------------------------------------------------------------- Will someone tell me where my mistake was? Thanks, Sastry Karra Last fiddled with by spkarra on 2014-11-08 at 01:12 Reason: adding more information
 2014-11-08, 01:19 #2 sdbardwick     Aug 2002 North San Diego County 2·34·5 Posts Factor found for that exponent PrimeNet entry here. Last fiddled with by sdbardwick on 2014-11-08 at 01:21
2014-11-08, 01:51   #3
Batalov

"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

23×439 Posts

Quote:
 Originally Posted by spkarra I have a prime number (93886421). I made sure that the above number is prime before checking on GIMPS Starting calculation... NUMBER: 93886421 4845 iterations Checked range: 3 -> 9691 of 9691 ************************* * This number IS prime! * *************************
So far so good. You have checked that 93886421 is prime. (If it was not prime, then 2^93886421-1 could not be prime.)

However, this is only one prerequisite for even thinking about testing 2^93886421-1 for primality. The second step is this: does it have small factors? This can be checked in much shorter time than running the primality test, and is always done. GIMPS database stores the old results so that you would not have to repeat them. In this particular case, some one found a factor. 7911153228307378607 divides 2^93886421-1. Ok? Then the rest is unnecessary to test Steps 3 (a P-1 test) and 4 (L-L test). It is not prime.

Compare your story with small toy stories below:

Example 1:
I want to test if 2^9999999999-1 is prime. Step 1. Is 9999999999 prime? No, it is not. 3 divides 9999999999, and because of that 2^3-1 divides 2^9999999999-1. End of story. 2^9999999999-1 is not prime.

Example 2:
I want to test if 2^11-1 is prime. Step 1. Is 11 prime? Yes it is. Good, now on to Step 2.
Do small numbers (and we know that they must be of type 2*11*k+1, e.g. 23, 67, 89...) divide 2^11-1?
Does 23 divide 2^11-1? Yes it does. End of story. 2^11-1 is not prime.

 2014-11-08, 19:51 #4 TheMawn     May 2013 East. Always East. 11×157 Posts I have always wondered if the residue at the end of a test could give any insight into the number itself. Does it hold any value or is it random gibberish? Only if the residue was worth anything would there be any reason at all to run the primality test on a known composite. As for the specific question: You cannot get Primenet to assign that number to you, but if you REALLY want to waste your time testing a known composite, I think you can force Prime95 to run the test anyway without an assignment by manually putting it into your worktodo.txt. Seriously though, don't do it.
2014-11-08, 22:02   #5
spkarra

"Sastry Karra"
Jul 2009
Bridgewater, NJ (USA)

33 Posts

Quote:
 Originally Posted by sdbardwick Factor found for that exponent PrimeNet entry here.

Thanks a lot.

 2014-11-08, 22:04 #6 spkarra   "Sastry Karra" Jul 2009 Bridgewater, NJ (USA) 33 Posts Thanks a lot Batalov. I tried for 93887011. -------------------- 93887011 is a prime number! ---------------- Then I tried for 2^93887011-1 for primality. I got this: ------------------------------------------------- PrimeNet Exponent Status Exponent Range: to Output results in text-only format Show full details (current assignment, history, LL residues) 93,887,011No factors below270 Assigned2014-03-11ahmeraliTFexpired on 2014-05-102014-05-10ANONYMOUSTFexpired on 2014-07-09 HistoryDateUserResult2010-12-28For ResearchNFno factor from 2^64 to 2^652013-12-26sasakiNFno factor from 2^65 to 2^662014-02-16SMoffatNFno factor from 2^66 to 2^672014-02-19SMoffatNFno factor from 2^67 to 2^682014-08-10SMoffatNFno factor from 2^68 to 2^692014-09-14Ryan PropperNFno factor from 2^69 to 2^70 ---------------------------------------------------- Thanks, Sastry Karra Last fiddled with by spkarra on 2014-11-08 at 22:12
 2014-11-08, 22:42 #7 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 1009710 Posts This one is fine to test, but you still have steps 2, 3 and 4 to do. Step 2. Small factors are not tested deep enough. (wanted level is 2^74. Makes sense to do all factoring de novo.) Step 3. P-1 test has not been run Step 4. L-L test has not been run Why are they done in this order? (and why do you not want to skip steps?) Because each step takes more time than the previous. You can reserve this number by starting running it in your own copy of Prime95 that is configured to communicate to the GIMPS server. Your program will communicate and will have it reserved. then you can pause your Prime95 (or you can run it on and off) but start factoring in mfaktc in parallel. If you don't have a graphics card, take some other exponent that already has steps 2 and 3 done. Read the instructions at http://www.mersenne.org/gettingstarted/ and optionally here on the forum (use the search function).
 2014-11-08, 22:43 #8 TheMawn     May 2013 East. Always East. 110101111112 Posts You can manually reserve this exponent if you wish. First, however, you want to trial factor it. Probably to 74 - 76 bits. That will take some time, but not nearly as much as running the LL test in its entirety. A modern computer could take several weeks. A not-so-modern computer maybe a few months. Last fiddled with by TheMawn on 2014-11-08 at 22:44
2014-11-10, 18:22   #9
henryzz
Just call me Henry

"David"
Sep 2007
Liverpool (GMT/BST)

10111101001112 Posts

Quote:
 Originally Posted by TheMawn I have always wondered if the residue at the end of a test could give any insight into the number itself. Does it hold any value or is it random gibberish? Only if the residue was worth anything would there be any reason at all to run the primality test on a known composite. As for the specific question: You cannot get Primenet to assign that number to you, but if you REALLY want to waste your time testing a known composite, I think you can force Prime95 to run the test anyway without an assignment by manually putting it into your worktodo.txt. Seriously though, don't do it.
It doesn't for LL tests. For the prp test based on femat's little theorem i.e. $b^{p-1}\equiv1 mod p$ the residue if p has a small factor f is I think $b^{f-1}$. This doesn't work if $b^{f-1}$ > p though so it isn't very useful as those factors should probably have been removed by trial factoring.

2014-11-11, 12:57   #10
spkarra

"Sastry Karra"
Jul 2009
Bridgewater, NJ (USA)

33 Posts

Quote:
 Originally Posted by Batalov This one is fine to test, but you still have steps 2, 3 and 4 to do. Step 2. Small factors are not tested deep enough. (wanted level is 2^74. Makes sense to do all factoring de novo.) Step 3. P-1 test has not been run Step 4. L-L test has not been run Why are they done in this order? (and why do you not want to skip steps?) Because each step takes more time than the previous. You can reserve this number by starting running it in your own copy of Prime95 that is configured to communicate to the GIMPS server. Your program will communicate and will have it reserved. then you can pause your Prime95 (or you can run it on and off) but start factoring in mfaktc in parallel. If you don't have a graphics card, take some other exponent that already has steps 2 and 3 done. Read the instructions at http://www.mersenne.org/gettingstarted/ and optionally here on the forum (use the search function).

Thanks a lot. I will get Prime95 installed on my computer and will try to reserve it. Will update the status soon....

2014-11-11, 16:48   #11
R.D. Silverman

"Bob Silverman"
Nov 2003
North of Boston

23·3·313 Posts

Quote:
 Originally Posted by spkarra Thanks a lot. I will get Prime95 installed on my computer and will try to reserve it. Will update the status soon....
This is the wrong subforum. I see no mathematics in the current thread............

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