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2020-04-21, 12:35   #78
kriesel

"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest

3·5·17·19 Posts

Quote:
 Originally Posted by kriesel 80-81 under way.
Done. Typical of the 8 processes is
Code:
M(60651732991) has 0 factors in range k = [9966119042880, 19932270758400], passes 14-15
Performed 47147307808 trial divides
Clocks = 05:46:53.712
mfactor-base-2w -m 60651732991 -bmin 80 -bmax 81 -passmin 14 -passmax 15 done at Tue 04/21/2020  7:23:50.14

 2020-04-23, 00:20 #79 paulunderwood     Sep 2002 Database er0rr 22·883 Posts Thanks kriesel. Now we have to wait for some revolutionary hardware to do the PRP/LL test of M(60651732991)
 2020-05-12, 05:35 #80 paulunderwood     Sep 2002 Database er0rr 22·883 Posts Another idea Code: {forprime(p=3,30000000000,if( Mod(Mod(1,p+17)*x+2,x^2-3)^lift(Mod(2,p+1)^p)==1&& Mod(Mod(1,p+257)*x+2,x^2-3)^lift(Mod(2,p+1)^p)==1&& Mod(Mod(1,p+65537)*x+2,x^2-3)^lift(Mod(2,p+1)^p)==1, print([p,factor(p+1)])))} [3, Mat([2, 2])][2147483647, Mat([2, 31])] [7, Mat([2, 3])] [31, Mat([2, 5])] [127, Mat([2, 7])] [4423, [2, 3; 7, 1; 79, 1]] [8191, Mat([2, 13])] [131071, Mat([2, 17])] [524287, Mat([2, 19])] [2147483647, Mat([2, 31])] Produces only one non-2^p-1 Mersenne exponent. The following produces two: Code: {forprime(p=3,30000000000,if( Mod(Mod(1,p+17)*x+2,x^2-3)^lift(Mod(2,p+1)^p)==1&& Mod(Mod(1,p+65)*x+2,x^2-3)^lift(Mod(2,p+1)^p)==1&& Mod(Mod(1,p+65537)*x+2,x^2-3)^lift(Mod(2,p+1)^p)==1, print([p,factor(p+1)])))} [3, Mat([2, 2])] [7, Mat([2, 3])] [31, Mat([2, 5])] [127, Mat([2, 7])] [607, [2, 5; 19, 1]] [4423, [2, 3; 7, 1; 79, 1]] [8191, Mat([2, 13])] [131071, Mat([2, 17])] [524287, Mat([2, 19])] [2147483647, Mat([2, 31])] Last fiddled with by paulunderwood on 2020-05-12 at 05:44
 2020-07-25, 13:11 #81 kriesel     "TF79LL86GIMPS96gpu17" Mar 2017 US midwest 10010111011012 Posts M60651732991 has been run with no factor found through 85 bits TF using Ernst Mayer's Mfactor program. Sixteen processes running a pass each on dual-E5-2690 gave the following range of run times (less than 3 days, ~0.97% range max-min). Impact on prime95 progress using all physical cores is about a 10% slowdown during that time. Apparently hyperthreading is pretty effective for Mfactor runs. I estimate from a large extrapolation of https://www.mersenneforum.org/showpo...7&postcount=12 that the TF optimal stopping point for this exponent on cpu is around 95 bits. An estimated bit level duration is 2(95-85) times 67.5 hours = 7.9 years for the last bit level, 15.8 years cumulative, well out of reach. The odds of finding a factor in those 10 bit levels are around 11%. A 64-bit mfaktc version on a modern gpu would be good for accelerating this, but none exists. (Estimated gpu TF limit 99 bits, ~15% odds of factor with an NVIDIA RTX 2080 Super.) Code: M(60651732991) has 0 factors in range k = [159458035376640, 318916087089600], passes 14-14 Performed 377347101769 trial divides Clocks = 67:47:56.301 mfactor-base-2w -m 60651732991 -bmin 84 -bmax 85 -passmin 14 -passmax 14 done at Sat 07/25/2020 4:05:44.19 M(60651732991) has 0 factors in range k = [159458035376640, 318916087089600], passes 9-9 Performed 377346866607 trial divides Clocks = 67:08:56.768 mfactor-base-2w -m 60651732991 -bmin 84 -bmax 85 -passmin 9 -passmax 9 done at Sat 07/25/2020 3:26:40.17 Last fiddled with by kriesel on 2020-07-25 at 14:02
2020-07-25, 16:03   #82
kriesel

"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest

10010111011012 Posts

Quote:
 Originally Posted by kriesel on dual-E5-2690
actually dual Xeon E5-2697v2, which are 12-core +HT each. So one could do TF n bits to n+1 on 8 cores, and n+1 to n+2 on 16 cores, simultaneously, and still leave considerable capacity for prime95.

 2020-08-18, 03:58 #83 paulunderwood     Sep 2002 Database er0rr 22×883 Posts Can someone with big RAM please test Code: p=60651732991;n=2^p-1;V=Vec(lift(lift(Mod(Mod(1,n)*x,x^2-2*x-2)^2^20)));print([p,(V[1]+V[2])%p==0])
 2020-08-19, 01:24 #84 lavalamp     Oct 2007 Manchester, UK 2·3·223 Posts How much RAM is big RAM?
2020-08-19, 02:14   #85
paulunderwood

Sep 2002
Database er0rr

22×883 Posts

Quote:
 Originally Posted by lavalamp How much RAM is big RAM?
60 Billion bits can be stored in ~8 GB. Then there are the arithmetic operations. I guess 128GB RAM is enough. Pari uses FFT. So 20 squaring iterations over x^2-2*x-2 should take a few minutes. But I am pretty sure the answer is known now. I am looking for similarities to p=607, but differences from other divisors of S_k where S_0 is 4 and S_i = S_{i-1}^2-2.

Last fiddled with by paulunderwood on 2020-08-19 at 02:18

2020-08-19, 02:18   #86
R. Gerbicz

"Robert Gerbicz"
Oct 2005
Hungary

1,429 Posts

Quote:
 Originally Posted by paulunderwood Can someone with big RAM please test Code: p=60651732991;n=2^p-1;V=Vec(lift(lift(Mod(Mod(1,n)*x,x^2-2*x-2)^2^20)));print([p,(V[1]+V[2])%p==0])
8 Mb memory is more than enough, what Pari Gp starts on my system:
Code:
parisize = 8000000, primelimit = 500000
? p=60651732991;e=20;V=Vec(lift(Mod(x,x^2-2*x-2)^2^e));
print([p,(V[1]+V[2])==0])
? [60651732991, 0]
? ##
***   last result computed in 0 ms.
?
not speaking about the running time. Notice that you can prove bounds for the coefficients, for this smallish iteration there will be no "overflow", so never ever calculate/store that silly n value.

 2020-08-19, 02:30 #87 paulunderwood     Sep 2002 Database er0rr DCC16 Posts Thanks Robert. I was actually seeking Code: ? print([p,(V[1]+V[2])%p==0]) [60651732991, 1] No surprises there.
 2020-08-19, 02:39 #88 lavalamp     Oct 2007 Manchester, UK 2×3×223 Posts Well I just tried it with 24GB allocated to it and it couldn't complete the first 2^p-1 instruction. Edit: attached screenshot. Attached Thumbnails   Last fiddled with by lavalamp on 2020-08-19 at 02:41

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