20220801, 02:22  #89  
Feb 2017
Nowhere
7·857 Posts 
Quote:
Now 2^1277  1 is congruent to 1 (mod 8) so is not the square of an integer. Therefore its square root is not an integer. What else could "square root" mean that would always be an integer? The only common meaning that comes to mind is the "integer square root," the integer floor of the square root. Unfortunately, this doesn't have the stated property. If p is a prime number, the integer square root of N is equal to p for p^2 โค N < (p + 1)^2. And it is clear that not every such N is prime. Similar results pertain if you try the integer ceiling or the nearest integer to the square root. For the case at hand, Code:
? n=sqrtint(2^1277  1); ? ispseudoprime(n) %2 = 0 ? nprecprime(n) %3 = 86 ? nextprime(n)  n %4 = 108 ? 

20220801, 13:34  #90  
Random Account
Aug 2009
Not U. + S.A.
2×3×389 Posts 
Quote:
M1277 will be solved some day, or is this peddling nonsense too? 

20220801, 22:04  #91  
Mar 2019
303_{10} Posts 
Quote:
Yes. Some day, possibly in the next 510 years. 

20220802, 03:59  #92  
If I May
"Chris Halsall"
Sep 2002
Barbados
3^{2}×1,187 Posts 
Quote:
Having incoming questioning is just a sign of respect. Being able to defend against them (instantly) is just a regular Due Diligence exercise. Deal with it. 

20220910, 17:29  #93 
Random Account
Aug 2009
Not U. + S.A.
2×3×389 Posts 
An opinion:
After learning how to use CADONFS and doing some experimentation, it would seem this is the application to take a crack at M1277 in the coming years. Its current largest parameter file is for a C320. A larger one would be needed. I do not know that the current incarnation of CADO is capable of handling a composite of that size. My own observations have shown me that a lot of RAM would be required. 96 GB might work, but 128 GB would be better. A latemodel CPU would be a must, 12 physical cores and 12 logical cores, for example. CADO may not use all of it, but having more than required is preferable over not having enough. Even with this kind of setup, the process could take many weeks. 
20220910, 18:17  #94  
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
7·983 Posts 
Quote:
Last fiddled with by kriesel on 20220910 at 18:20 

20220910, 18:55  #95 
"Curtis"
Feb 2005
Riverside, CA
3·1,831 Posts 
Note that Ken's citation of 660 coreyears was an estimate for the matrix step. That step is usually 1/6 or so of the time spent sieving, so the whole job might be expected to take 7 times as long as the numbers Ken just mentioned.
Greg's development of GPUenhanced msieve matrix solving has dramatically reduced the time required for the matrix solving step. If we sieved this job enough to get a matrix that would fit onto 8x A100 GPUs, a single system could solve the matrix in something on the order of a week. These numbers are based on scaling up from the GNFS221 matrix job just completed (see Cunningham subforum), which was 114M matrix size, fit on 4x A100, and took 38 hours to solve on 8x A100. If we double the matrix size it would fit onto 8x A100 and take 45 times as long to solve. So, on the order of 20,000 weeks on a single 12core machine to sieve, and one week on a really fancy 8GPU machine for the matrix. 
20220910, 20:11  #96 
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
1AE1_{16} Posts 
Plus it's from a 4 year old post, so a few years of hardware development progress would change the numbers; software development too. I've never used CADO, yafu, msieve, etc, & am very unfamiliar with the whole brutegenerallargishnumberfactoring area, so rely heavily on the posts of those that know it. Preceding post is a useful update.
Last fiddled with by kriesel on 20220910 at 20:20 
20220910, 22:35  #97 
Undefined
"The unspeakable one"
Jun 2006
My evil lair
5×1,321 Posts 

20220911, 14:39  #98  
Random Account
Aug 2009
Not U. + S.A.
2×3×389 Posts 
Quote:
Quote:


20220911, 15:55  #99  
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across
2^{4}·719 Posts 
Quote:
We used almost that much to factor RSA129 almost thirty years ago. Sieving on moderately powerful machines by the standards of the day and linear algebra on a MasPar supercomputer. A comparable amount for 512bit GNFS a few years later. If anyone wants to take on the job I may be able to provide some generic advice on how to run a massive collaborative computation. The technology changes but the sociology remains much the same, AFAICT. However, I don't want to run one again. It was a lot of work doing all the handholding. 

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