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Old 2021-12-26, 13:37   #1
alpertron
 
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Default New Mersenne number with 12 known prime factors

Up to now there were only 4 Mersenne numbers with 11 known prime factors. They are M7 508 981, M9 100 919, M3 356 318 939 and M3 930 621 659.

Today I added another Mersenne number to this list: using the algorithm P-1 with B1 = B2 = 1M, I found the eleventh prime factor known of M726 064 763: 10702385060027676180416983.

Last fiddled with by alpertron on 2021-12-26 at 14:31 Reason: Added links to mersenne.ca
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Old 2021-12-27, 09:34   #2
nordi
 
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Awesome! Until a few days ago, there were only 3 such numbers, and all their factors had been found in 2014 or earlier. And now we have two more within two weeks! Are you still going to do P-1 stage 2? If we get very lucky, there might be a 12th factor.
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Old 2021-12-27, 12:50   #3
alpertron
 
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Unfortunately there is bug in 30.8 build 6 when running step 2.

I used the following line in worktodo.txt:

Code:
Pminus1=1,2,726064763,-1,1000000,10000000,"1452129527,1023751315831,1030134877226297,7106729160891631,7236079050549607,12965740712769703,37915764094923857,7565365825277361223,34153055801363324180057,490609746862823011746041,10702385060027676180416983"
Prime95 selected D=90 and then started to show the progress. After about 13 hours running step 2, the last line was 99.98%, then the window closed immediately, the process died and the file results.json.txt did not update.

I reserved 20 GB for Prime95.
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Old 2021-12-27, 14:49   #4
ATH
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Did it really use B2=10M or did it choose it's own value? If it did not use 10M then try Pminus1BestB2=0 in prime.txt.
Otherwise it probably needs more than 20GB RAM.
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Old 2021-12-27, 15:07   #5
alpertron
 
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I really used B2 = 10M in this test.

It is strange that the step 2 has completed except for the final GCD. But the GCD works OK because it found the prime factor in step 1.

I had the same problem some days ago when I selected B1 = 100K, B2 = 0 (so Prime95 selected automatically B2 = 9*B1 = 900K.
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Old 2021-12-28, 13:10   #6
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And Mike's factor makes it 12.
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Old 2021-12-28, 14:16   #7
alpertron
 
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Yes, that's a "world record". There is a non-negligible probability of finding the 13th known prime number by increasing B2 to 200M (but this would require a lot of RAM).

Last fiddled with by alpertron on 2021-12-28 at 14:29
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Old 2021-12-28, 17:32   #8
nordi
 
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That was super lucky! The first time since 2014 that a new record gets set. Congrats to Alpertron and Xyzzy!


And we can actually try our luck a bit more: The P-1 can still be extended and TF could be done for some more bit levels. I, for one, will give P+1 factoring a chance, using nth_run=1. If someone with plenty of RAM (I'm allowing 90GB for stage 2) wants to try nth_run=2, use


Code:
Pplus1=N/A,1,2,726064763,-1,1000000,10000000,2,82,"1452129527,1023751315831,1030134877226297,7106729160891631,7236079050549607,12965740712769703,37915764094923857,7565365825277361223,34153055801363324180057,490609746862823011746041,7170112396664438582504527,10702385060027676180416983"
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