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321 Prime Search :
3*2^7033641+1 is prime!
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JohnHonorary cruncher
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Joined: 21 Feb 06 Posts: 2876 ID: 2449 Credit: 2,681,934 RAC: 0

On 21 Feb 2011 21:45:32 UTC, PrimeGrid’s 321 Prime Search found another Mega Prime: 3*2^7033641+1
The prime is 2,117,338 digits long and will enter Chris Caldwell's The Largest Known Primes Database ranked 14th overall. This is the second mega prime and the largest for the 3*2^n+1 form. It is also the second largest found mega prime using LLR and PrimeGrid's 10th overall mega prime.
The discovery was made by Michael Herder using an Intel Core i7 920 @ 2.67GHz with 6 GB RAM running Windows 7 Ultimate x64. This computer took just over 17 hours and 24 minutes to complete the primality test using LLR. Michael is a member of the BOINCstats team.
For more details, please see the official announcement.
(x)(g)FN testing has already begun. Many of you may recall the previous time we had to conduct this "extra" testing on the prime 3*2^5082306+1. It requires a substantial amount of processing power.
However, this time we are running a "quick" test on the prime which will give us all the potential GF and xGF divisibilities. Once we know these, then we can begin the individual tests on each potential (a,b) divisibility. This frees us up from having to test every (a,b) pair.
The "quick" test will take up to 5 days. It will run the following, each taking the time of one primality test:
GF_sprime_2:
GF_sprime_3:
GF_sprime_5:
GF_sprime_7:
GF_sprime_11:
If you are interested in helping out, please keep tabs on this thread as we'll be doing the testing here. I'll make regular progress updates. Currently we are at:
1 Mar 2011  05:32:10 UTC: GF_sprime_2: 3*2^7033641+1 6922500/7033640
1 Mar 2011  16:35:53 UTC: GF_sprime_3: 3*2^7033641+1 5817500/7033640
2 Mar 2011  00:20:45 UTC: GF_sprime_5: 3*2^7033641+1 2762500/7033640
2 Mar 2011  23:53:18 UTC: GF_sprime_11: 3*2^7033641+1 1102500/7033640
3 Mar 2011  14:30:29 UTC: GFN testing completed
Initial Results COMPLETE
3*2^7033641+1 is a Factor of GF(7033640? ,3)!!!! (239601.293177 seconds)
3*2^7033641+1 is a Factor of xGF(7033640,5,2)!!!! (239601.299181 seconds)
3*2^7033641+1 is a Factor of xGF(7033640,6,5)!!!! (0.005470 seconds)
3*2^7033641+1 is a Factor of xGF(7033640? ,7,4)!!!! (0.002565 seconds)
3*2^7033641+1 is a Factor of GF(7033640? ,8)!!!! (0.004734 seconds)
3*2^7033641+1 is a Factor of xGF(7033640? ,8,3)!!!! (0.005920 seconds)
3*2^7033641+1 is a Factor of xGF(7033640? ,9,8)!!!! (0.013459 seconds)
3*2^7033641+1 is a Factor of xGF(7033640,10,7)!!!! (0.003695 seconds)
3*2^7033641+1 is a Factor of xGF(7033640,11,4)!!!! (0.005135 seconds)
3*2^7033641+1 is a Factor of xGF(7033640,11,7)!!!! (0.003988 seconds)
3*2^7033641+1 is a Factor of xGF(7033640? ,11,10)!!!! (0.001959 seconds)
3*2^7033641+1 is a Factor of xGF(7033640? ,12,7)!!!! (0.006395 seconds)
3*2^7033641+1 is a Factor of xGF(7033640,12,11)!!!! (0.001326 seconds)
Unfortunately, not a Fermat number divisor.
Additional Results COMPLETE
As you can see above, we know 6 divisibilities and now need to run additional testing on the following:
GF tests
pfgw l3_1.log gxo3,1 a2 q"3*2^7033641+1" John COMPLETE
3*2^7033641+1 is a Factor of GF(7033639,3)!!!! (61048.849232 seconds)
pfgw l8_1.log gxo8,1 a2 q"3*2^7033641+1" Hammeh COMPLETE
3*2^7033641+1 is a Factor of GF(7033639,8)!!!! (188482.798000 seconds)
xGF tests
pfgw l7_4.log gxo7,4 a2 q"3*2^7033641+1" John COMPLETE
3*2^7033641+1 is a Factor of xGF(7033639,7,4)!!!! (108899.976090 seconds)
pfgw l8_3.log gxo8,3 a2 q"3*2^7033641+1" pschoefer COMPLETE
3*2^7033641+1 is a Factor of xGF(7033637,8,3)!!!! (156655.594000 seconds)
pfgw l9_8.log gxo9,8 a2 q"3*2^7033641+1" pschoefer COMPLETE
3*2^7033641+1 is a Factor of xGF(7033639,9,8)!!!! (159767.811000 seconds)
pfgw l11_10.log gxo11,10 a2 q"3*2^7033641+1" TheDawgz COMPLETE
3*2^7033641+1 is a Factor of xGF(7033638,11,10)!!!! (769.035360 seconds)
pfgw l12_7.log gxo12,7 a2 q"3*2^7033641+1" TheDawgz COMPLETE
3*2^7033641+1 is a Factor of xGF(7033638,12,7)!!!! (768.795360 seconds)
Final Results COMPLETE
3*2^7033641+1 is a Factor of GF(7033639,3)!!!! (61048.849232 seconds)
3*2^7033641+1 is a Factor of GF(7033639,8)!!!! (188482.798000 seconds)
3*2^7033641+1 is a Factor of xGF(7033640,5,2)!!!! (239601.299181 seconds)
3*2^7033641+1 is a Factor of xGF(7033640,6,5)!!!! (0.005470 seconds)
3*2^7033641+1 is a Factor of xGF(7033639,7,4)!!!! (108899.976090 seconds)
3*2^7033641+1 is a Factor of xGF(7033637,8,3)!!!! (156655.594000 seconds)
3*2^7033641+1 is a Factor of xGF(7033639,9,8)!!!! (159767.811000 seconds)
3*2^7033641+1 is a Factor of xGF(7033640,10,7)!!!! (0.003695 seconds)
3*2^7033641+1 is a Factor of xGF(7033640,11,4)!!!! (0.005135 seconds)
3*2^7033641+1 is a Factor of xGF(7033640,11,7)!!!! (0.003988 seconds)
3*2^7033641+1 is a Factor of xGF(7033638,11,10)!!!! (769.035360 seconds)
3*2^7033641+1 is a Factor of xGF(7033638,12,7)!!!! (768.795360 seconds)
3*2^7033641+1 is a Factor of xGF(7033640,12,11)!!!! (0.001326 seconds)
____________
 


Hello!
I don't understand what GF_sprime_X means. Could somebody please explain it to me?
Also, has it already been determined that this new prime does not divide a classical Fermat number?  

JohnHonorary cruncher
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Joined: 21 Feb 06 Posts: 2876 ID: 2449 Credit: 2,681,934 RAC: 0

I don't understand what GF_sprime_X means. Could somebody please explain it to me?
That's pfgw logging while it tests the 5 prime bases: 2, 3, 5, 7, 11.
Also, has it already been determined that this new prime does not divide a classical Fermat number?
Initial testing is complete and the prime is not a Fermat number divisor.
____________
 

JohnHonorary cruncher
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Joined: 21 Feb 06 Posts: 2876 ID: 2449 Credit: 2,681,934 RAC: 0

Initial Testing Complete
The quick test is complete. Results are in the first post of this thread. I have started one GF and one xGF test. The others are available for anyone interested in testing. Just post in this thread which test(s) you'd wish to do.
The latest pfgw is available in the PRPNet packages or you can download it here. I'm using pfgw64.
To run the test, simply copy the line, paste and run. For example, in my case for (3,1) I run the following:
./pfgw64 l3_1.log gxo3,1 a2 q"3*2^7033641+1"
It is unknown right now how long these tests will take. However, the initial quick test completed two days ahead of expectations. :)
____________
 


I would love you help you out with this.
I have downloaded and unziped pfgw. Would you be able to tell me which file to run inside the folder?
Thanks
Peter
____________
My Top 5000 Primes:
110059!+1 is prime! (FPS)
14493618614235*2^6666661 is prime! (SGS)  


Oh ok I think I have got it running
I ran Win32PFGW and entered pfgw l8_1.log gxo8,1 a2 q3*2^7033641+1, which is number 2 on the list, and its running.
Can you just confirm that is correct?
Thanks
Peter
____________
My Top 5000 Primes:
110059!+1 is prime! (FPS)
14493618614235*2^6666661 is prime! (SGS)  

JohnHonorary cruncher
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Joined: 21 Feb 06 Posts: 2876 ID: 2449 Credit: 2,681,934 RAC: 0

I ran Win32PFGW and entered pfgw l8_1.log gxo8,1 a2 q3*2^7033641+1, which is number 2 on the list, and its running.
Can you just confirm that is correct?
Yes, that is correct.
____________
 


Ok great =)
I'll post back the results when it finishes.
Peter
____________
My Top 5000 Primes:
110059!+1 is prime! (FPS)
14493618614235*2^6666661 is prime! (SGS)  


...always a bridesmaid ...never a bride. I'll take
pfgw64 l11_10.log gxo11,10 a2 q"3*2^7033641+1"
and
pfgw64 l12_7.log gxo12,7 a2 q"3*2^7033641+1"
____________
There's someone in our head but it's not us.  

pschoeferVolunteer developer Volunteer tester
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Joined: 20 Sep 05 Posts: 635 ID: 845 Credit: 1,489,461,949 RAC: 1,587,222

I'll do the rest:
pfgw l8_3.log gxo8,3 a2 q"3*2^7033641+1"
pfgw l9_8.log gxo9,8 a2 q"3*2^7033641+1"
____________
 


...always a bridesmaid ...never a bride. I'll take
pfgw64 l11_10.log gxo11,10 a2 q"3*2^7033641+1"
and
pfgw64 l12_7.log gxo12,7 a2 q"3*2^7033641+1"
Unable to run pfgw64  causes my system to hang after about 2 hours of runtime.
So I am running with pfgw32 instead.
Log files remain empty while running???
Current status after 3hrs running:
$ ./pfgw32 l12_7.log gxo12,7 a2 q"3*2^7033641+1"
PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5]
Output logging to file 12_7.log
xGF_'12'_7: 3*2^7033641+1 1082500/7033610
and
$ ./pfgw32 l11_10.log gxo11,10 a2 q"3*2^7033641+1"
PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5]
Output logging to file 11_10.log
xGF_'11'_10: 3*2^7033641+1 1102500/7033610
____________
There's someone in our head but it's not us.  


Yeah its the same for me running pfgw32, log file is empty.
Currently still running, 15 hours so far.
GF_8: 3*2^7033641+1 1947500/7033610
____________
My Top 5000 Primes:
110059!+1 is prime! (FPS)
14493618614235*2^6666661 is prime! (SGS)  

JohnHonorary cruncher
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Joined: 21 Feb 06 Posts: 2876 ID: 2449 Credit: 2,681,934 RAC: 0

...always a bridesmaid ...never a bride. I'll take
pfgw64 l11_10.log gxo11,10 a2 q"3*2^7033641+1"
and
pfgw64 l12_7.log gxo12,7 a2 q"3*2^7033641+1"
Unable to run pfgw64  causes my system to hang after about 2 hours of runtime.
So I am running with pfgw32 instead.
Log files remain empty while running???
Yes, sadly pfgw does not log while running these types of tests. All output will come at the end of the test.
NOTE: the xGF tests will take 3 to 4 times longer than the GF tests.
____________
 

pschoeferVolunteer developer Volunteer tester
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Joined: 20 Sep 05 Posts: 635 ID: 845 Credit: 1,489,461,949 RAC: 1,587,222

Progress after ~18 hours:
xGF_'8'_3: 3*2^7033641+1 5962500/7033610
xGF_'9'_8: 3*2^7033641+1 5807500/7033610
IIRC, it'll do a second step (xGF_8_'3' and xGF_9_'8') once this first step is finished, so I expect the tests to be completed about 24 hours from now. :)
____________
 


My progress after ~22 hours....
GF_8: 3*2^7033641+1 3207500/7033610
Seems like its going to be at least another 24h
____________
My Top 5000 Primes:
110059!+1 is prime! (FPS)
14493618614235*2^6666661 is prime! (SGS)  


Just shy of 21 cpu hours and both the xGF 11,10 and the xGF 12,7 tests have moved into the 2nd pass; will post the contents (should there be any) of the log files tomorrow when 2nd pass has completed.
____________
There's someone in our head but it's not us.  

JohnHonorary cruncher
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Joined: 21 Feb 06 Posts: 2876 ID: 2449 Credit: 2,681,934 RAC: 0

IIRC, it'll do a second step (xGF_8_'3' and xGF_9_'8') once this first step is finished...
Confirmed, only two passes.
____________
 

pschoeferVolunteer developer Volunteer tester
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Joined: 20 Sep 05 Posts: 635 ID: 845 Credit: 1,489,461,949 RAC: 1,587,222

While (9,8) needs another hour or two, test for (8,3) is just finished:
>pfgw64.exe l8_3.log gxo8,3 a2 q"3*2^7033641+1"
PFGW Version 3.4.5.64BIT.20110215.Win_Dev [GWNUM 26.5]
Output logging to file 8_3.log
3*2^7033641+1 is a Factor of xGF(7033637,8,3)!!!! (156655.594000 seconds)
____________
 

pschoeferVolunteer developer Volunteer tester
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Joined: 20 Sep 05 Posts: 635 ID: 845 Credit: 1,489,461,949 RAC: 1,587,222

Second test done:
>pfgw64.exe l9_8.log gxo9,8 a2 q"3*2^7033641+1"
PFGW Version 3.4.5.64BIT.20110215.Win_Dev [GWNUM 26.5]
Output logging to file 9_8.log
3*2^7033641+1 is a Factor of xGF(7033639,9,8)!!!! (159767.811000 seconds)
____________
 


Both tests completed.
./pfgw32 l11_10.log gxo11,10 a2 q"3*2^7033641+1"
PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5]
Output logging to file 11_10.log
3*2^7033641+1 is a Factor of xGF(7033638,11,10)!!!! (769.035360 seconds)
And
./pfgw32 l12_7.log gxo12,7 a2 q"3*2^7033641+1"
PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5]
Output logging to file 12_7.log
3*2^7033641+1 is a Factor of xGF(7033638,12,7)!!!! (768.795360 seconds)
____________
There's someone in our head but it's not us.  


My test is completed:
3*2^7033641+1 is a Factor of GF(7033639,8)!!!! (188482.798000 seconds)
Any other tests that need run??
____________
My Top 5000 Primes:
110059!+1 is prime! (FPS)
14493618614235*2^6666661 is prime! (SGS)  

JohnHonorary cruncher
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Joined: 21 Feb 06 Posts: 2876 ID: 2449 Credit: 2,681,934 RAC: 0

Any other tests that need run??
No, that completes the testing.
Thank you to all that helped out. Final results are listed at the bottom of the first post. Wilfrid Keller will list them on the following page: Factors of generalized Fermat numbers found after Björn & Riesel
Your names will appear next to your discovery as well as in the credits. :) On to the next prime...searching for that next Fermat number divisor.
____________
 


cool
 

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321 Prime Search :
3*2^7033641+1 is prime! 