New Mersenne number with 12 known prime factors

alpertron · 2021-12-26, 13:37

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.

nordi · 2021-12-27, 09:34

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.

alpertron · 2021-12-27, 12:50

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.

ATH · 2021-12-27, 14:49

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.

alpertron · 2021-12-27, 15:07

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.

axn · 2021-12-28, 13:10

And Mike's factor makes it 12.

alpertron · 2021-12-28, 14:16

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).

nordi · 2021-12-28, 17:32

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"

2021-12-26, 13:37	#1
alpertron Aug 2002 Buenos Aires, Argentina 1,447 Posts	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

2021-12-27, 12:50	#3
alpertron Aug 2002 Buenos Aires, Argentina 1,447 Posts	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.

2021-12-28, 14:16	#7
alpertron Aug 2002 Buenos Aires, Argentina 10110100111₂ Posts	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

2021-12-28, 17:32	#8
nordi Dec 2016 1111000₂ Posts	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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2021-12-27, 09:34	#2
nordi Dec 2016 170₈ Posts	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.

2021-12-27, 14:49	#4
ATH Einyen Dec 2003 Denmark CF1₁₆ Posts	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.

2021-12-27, 15:07	#5
alpertron Aug 2002 Buenos Aires, Argentina 1,447 Posts	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.

2021-12-28, 13:10	#6
axn Jun 2003 2×2,683 Posts	And Mike's factor makes it 12.