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Old 2022-08-01, 02:22   #89
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Quote:
Originally Posted by storm5510 View Post
I have read on quite a few mathematical web sites over the years that, "If the square root of a number is prime then the number it was derived from is also prime. Not many natural primes will produce a whole number root. M1277 does.
<snip>
Sorry, this does not compute. The only positive integers with integer square roots are perfect squares, i.e. squares of integers. The square of an even integer is divisible by 4, and the square of an odd integer is congruent to 1 (mod 8).

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 โ‰ค 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
? n-precprime(n)
%3 = 86
? nextprime(n) - n
%4 = 108
?
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Old 2022-08-01, 13:34   #90
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Originally Posted by mathwiz View Post
...If you'd like to stop posting, then by all means, please do. But if you continue peddling nonsense, you will be called out on it.
I will just stick to the areas I know: Prime95, mfaktc, and gpuOwl. As for this place, it will be 90% read-only from now on. All subscriptions to mathematical areas, I will remove. I have been a member here since 2009 and I have had more than my share of spears, darts, and rocks hurled at me.

M1277 will be solved some day, or is this peddling nonsense too?
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Old 2022-08-01, 22:04   #91
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Originally Posted by storm5510 View Post
I will just stick to the areas I know: Prime95, mfaktc, and gpuOwl. As for this place, it will be 90% read-only from now on. All subscriptions to mathematical areas, I will remove. I have been a member here since 2009 and I have had more than my share of spears, darts, and rocks hurled at me.
Alternatively: Accept that there may be things in math you don't know; criticisms of your ideas / theories are not personal insults. Post, but with more humility.

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M1277 will be solved some day, or is this peddling nonsense too?
Yes. Some day, possibly in the next 5-10 years.
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Old 2022-08-02, 03:59   #92
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Quote:
Originally Posted by storm5510 View Post
I have been a member here since 2009 and I have had more than my share of spears, darts, and rocks hurled at me. M1277 will be solved some day, or is this peddling nonsense too?
Dude et al... Please calm down. And please don't leave this forum.

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.
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Old 2022-09-10, 17:29   #93
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An opinion:

After learning how to use CADO-NFS 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 late-model 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.
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Old 2022-09-10, 18:17   #94
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Quote:
Originally Posted by storm5510 View Post
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 late-model 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.
Many weeks, indeed. 660 core-years/12 cores * 52 weeks/year ~ 2860. weeks. I think it's going to take a sizable cluster of systems. No I'm not volunteering.

Last fiddled with by kriesel on 2022-09-10 at 18:20
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Old 2022-09-10, 18:55   #95
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Note that Ken's citation of 660 core-years 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 GPU-enhanced 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 GNFS-221 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 4-5 times as long to solve.

So, on the order of 20,000 weeks on a single 12-core machine to sieve, and one week on a really fancy 8-GPU machine for the matrix.
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Old 2022-09-10, 20:11   #96
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Quote:
Originally Posted by VBCurtis View Post
660 core-years was an estimate for the matrix step.
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 brute-general-largish-number-factoring area, so rely heavily on the posts of those that know it. Preceding post is a useful update.

Last fiddled with by kriesel on 2022-09-10 at 20:20
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Old 2022-09-10, 22:35   #97
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Quote:
Originally Posted by storm5510 View Post
[... 12 physical cores and 12 logical cores ...
There is no such thing as a logical core. All cores are physically implemented. Perhaps you mean 12 cores running 24 threads.
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Old 2022-09-11, 14:39   #98
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Quote:
Originally Posted by retina
There is no such thing as a logical core. All cores are physically implemented. Perhaps you mean 12 cores running 24 threads.
A better description.

Quote:
Originally Posted by VBCurtis
Note that Ken's citation of 660 core-years 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.

So, on the order of 20,000 weeks on a single 12-core machine to sieve, and one week on a really fancy 8-GPU machine for the matrix.
I was just taking a shot-in-the-dark. I pretty much figured my notion was greatly underestimated.
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Old 2022-09-11, 15:55   #99
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Quote:
Originally Posted by VBCurtis View Post
Note that Ken's citation of 660 core-years 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 GPU-enhanced 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 GNFS-221 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 4-5 times as long to solve.

So, on the order of 20,000 weeks on a single 12-core machine to sieve, and one week on a really fancy 8-GPU machine for the matrix.
That's not so big.

We used almost that much to factor RSA-129 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 512-bit 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 hand-holding.
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