mersenneforum.org  

Go Back   mersenneforum.org > Great Internet Mersenne Prime Search > Data

Reply
 
Thread Tools
Old 2019-06-04, 16:27   #221
CRGreathouse
 
CRGreathouse's Avatar
 
Aug 2006

22·5·293 Posts
Default

Quote:
Originally Posted by Madpoo View Post
I think it's pretty clear that these additional FFT sizes were going to be added no matter what.
A major motivation for my initial CEMPLLA thread was to nudge this forward.
CRGreathouse is offline   Reply With Quote
Old 2019-06-04, 17:08   #222
kriesel
 
kriesel's Avatar
 
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest

28·3·5 Posts
Default

Quote:
Originally Posted by GP2 View Post
I hesitate to post in a thread that should have died a long time ago. (At the very least, it ought to be retitled.)

But the exponent M1,073,741,827 figures in the "new Mersenne conjecture". First it should probably be TF'd a bit more, though.
https://www.mersenneforum.org/showthread.php?p=369976

http://www.hoegge.dk/mersenne/NMC.html has entries for M82589933, M268435459, M1073741827, M2147483647; some rather long gaps there. Maybe add ~134M and ~537M.

M1073741827 would take nearly 2 years to PRP test on an NVIDIA GTX 1080 Ti in gpuowl v6.5. That's a lot of gpu throughput to invest in one more data point for what RDS calls basically a joke.
kriesel is offline   Reply With Quote
Old 2019-06-04, 18:19   #223
Batalov
 
Batalov's Avatar
 
"Serge"
Mar 2008
Phi(3,3^1118781+1)/3

903010 Posts
Default

Quote:
Originally Posted by kriesel View Post
...what RDS calls basically a joke.
He is not alone.
Batalov is offline   Reply With Quote
Old 2019-06-04, 18:28   #224
xilman
Bamboozled!
 
xilman's Avatar
 
May 2003
Down not across

100111000011112 Posts
Default

Quote:
Originally Posted by Batalov View Post
He is not alone.
Neither are you.
xilman is offline   Reply With Quote
Old 2019-06-04, 19:05   #225
GP2
 
GP2's Avatar
 
Sep 2003

2·1,289 Posts
Default

Quote:
Originally Posted by kriesel View Post
http://www.hoegge.dk/mersenne/NMC.html has entries for M82589933, M268435459, M1073741827, M2147483647; some rather long gaps there. Maybe add ~134M and ~537M.

M1073741827 would take nearly 2 years to PRP test on an NVIDIA GTX 1080 Ti in gpuowl v6.5. That's a lot of gpu throughput to invest in one more data point for what RDS calls basically a joke.
Sure, it's not really a meaningful conjecture, that's why I put it in scare quotes.

Until new Mersenne primes are discovered, the only exponents that could possibly refute the conjecture in our lifetimes are 1,073,741,827 = 4**15+3 and 2,147,483,647 = 2**31−1 (aka MM31). The latter already has known factors (as a Mersenne number, not as a Wagstaff number). After that the next possible exponent is 2**61−1 (aka MM61), which is utterly infeasible. I'm not sure what your "~134M and ~537M" refer to.

It's hardly a priority, but on the other hand someone actually completed an LL test of M999,999,937 for no particular reason. And this number has only 7.37% more digits. If anyone has an appetite for more senselessly large exponents, might as well do that one.
GP2 is offline   Reply With Quote
Old 2019-06-04, 20:17   #226
kriesel
 
kriesel's Avatar
 
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest

1111000000002 Posts
Default

Quote:
Originally Posted by GP2 View Post
I'm not sure what your "~134M and ~537M" refer to.
p near 227 and 229. But that would require prime p's in the right places. And they're not there.
k=27, 2^k:134,217,728
+1= 3^4 × 19 × 87211
-1= 7 × 73 × 262657
4^k not applicable

k=29, 2^k: 536,870,912
+1= 3 × 59 × 3 033169
-1= 233 × 1103 × 2089

So we keep hunting for Mersenne primes.

Last fiddled with by kriesel on 2019-06-04 at 20:21
kriesel is offline   Reply With Quote
Old 2019-06-04, 21:08   #227
GP2
 
GP2's Avatar
 
Sep 2003

2×1,289 Posts
Default

Quote:
Originally Posted by GP2 View Post
Until new Mersenne primes are discovered, the only exponents that could possibly refute the conjecture in our lifetimes are 1,073,741,827 = 4**15+3 and 2,147,483,647 = 2**31−1 (aka MM31).
To be more specific: the "new Mersenne conjecture" can be only be untrue under one of the following conditions:
  1. Either M1,073,741,827 or W1,073,741,827 is prime (but not both!)
  2. W2,147,483,647 is prime
  3. One of an (infinite?) set of untestably large exponents (OEIS A122834) produces either a Mersenne prime or Wagstaff prime (but not both). The smallest elements of this set that have not been ruled out or mentioned above are approximately 2.3 quintillion, 19 septillion (i.e., extremely sparse and rapidly increasing). Note that the probability that a 2p−1 is prime for a specific p is proportional to log p / p.
  4. A new Mersenne prime is discovered (other than M1,073,741,827), and the Wagstaff number with the same exponent is also prime

Thus it is almost certainly trivially true.

Last fiddled with by GP2 on 2019-06-28 at 15:20 Reason: a factor was discovered for M1,073,741,827
GP2 is offline   Reply With Quote
Old 2019-06-10, 20:14   #228
kriesel
 
kriesel's Avatar
 
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest

74008 Posts
Default

Quote:
Originally Posted by GP2 View Post
To be more specific: the "new Mersenne conjecture" can be only be untrue under one of the following conditions:
  1. Either M1,073,741,827 or W1,073,741,827 is prime (but not both!)
  2. W2,147,483,647 is prime
How far have W1073741827 and W2147483647 been trial factored? (Or where could such be found?) Presumably TF goals for these are similar to roughly equally large Mersennes.
mersenne.ca shows M1073741827 TF is done to 82 bits (vs. GPU72 goal 86), and M2147483647 done up to 86 bits (vs. GPU72 goal 89), with 4 factors already found.
I'm not aware of any software available suitable for reasonable speed P-1 factoring attempts on these 3. Nor primality testing software for reasonable speed PRP testing of these, except gpuowl for M1073741827.
kriesel is offline   Reply With Quote
Old 2019-06-10, 20:50   #229
GP2
 
GP2's Avatar
 
Sep 2003

A1216 Posts
Default

Quote:
Originally Posted by kriesel View Post
[/LIST] How far have W1073741827 and W2147483647 been trial factored? (Or where could such be found?) Presumably TF goals for these are similar to roughly equally large Mersennes.
mersenne.ca shows M1073741827 TF is done to 82 bits (vs. GPU72 goal 86)
M1073741827 and W1073741827 and W2147483647 were all done to 82 bits (by me).

mfaktc can factor Wagstaff numbers if you edit the params.h file to uncomment the #define WAGSTAFF line and recompile everything. If you do that, it's best to rename the executable to something like "wfaktc.exe" so you don't accidentally use it on Mersennes.
GP2 is offline   Reply With Quote
Old 2019-06-10, 21:46   #230
kriesel
 
kriesel's Avatar
 
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest

28×3×5 Posts
Default

Quote:
Originally Posted by GP2 View Post
M1073741827 and W1073741827 and W2147483647 were all done to 82 bits (by me).
Thanks for the TF level info.
Quote:
mfaktc can factor Wagstaff numbers if you edit the params.h file to uncomment the #define WAGSTAFF line and recompile everything. If you do that, it's best to rename the executable to something like "wfaktc.exe" so you don't accidentally use it on Mersennes.
Or get and use the appropriate extra-versions precompiled executables from https://download.mersenne.ca/mfaktc/mfaktc-0.21. (Windows-mostly here.)
Have you tackled any Wagstaff TF above W2147483647? (Mfaktx and variants are I think limited to 2^32 exponent.)
kriesel is offline   Reply With Quote
Old 2019-06-10, 23:06   #231
GP2
 
GP2's Avatar
 
Sep 2003

50228 Posts
Default

Quote:
Originally Posted by kriesel View Post
Have you tackled any Wagstaff TF above W2147483647? (Mfaktx and variants are I think limited to 2^32 exponent.)
No, I am only doing much smaller Wagstaff exponents, such as P−1 in the 15M range. These two very large exponents were done exceptionally for their significance to the "new Mersenne conjecture".

If I recall, doing TF to 82 bits for these exponents on a Tesla V100 took maybe one or two days. If I had full-time use of one of the new fast GPUs, I'd take them to 86 bits myself.
GP2 is offline   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
Java applet alternative a1call Programming 19 2019-11-08 22:31
Alternative to LL paulunderwood Miscellaneous Math 36 2019-08-26 08:09
Fulsorials a1call Miscellaneous Math 41 2019-07-21 14:19
Is CEMPLLA 1.5 "the only software in the world capable of discovering" something? Not really. CRGreathouse Number Theory Discussion Group 51 2018-12-16 21:55
free alternative to EasyFit? ixfd64 Software 1 2008-04-26 21:28

All times are UTC. The time now is 07:03.

Fri Jun 5 07:03:59 UTC 2020 up 72 days, 4:37, 0 users, load averages: 0.95, 1.08, 1.06

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2020, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.