How can I enter a larger exponent?

[VBCurtis]

Originally Posted by evanh

with all of the numbers I have tested with my method up to... 1,000,000,000,000 I have been able to find a prime with this method... no I have not tested ALL of the numbers up to this and I know that just because it holds true for what I have shown that does not mean it holds true for ALL cases...

Waaaiiiit..... you've tested your "method" up to thirteen digits? 13? One-three? You've skipped from 13 to.... how big?

You didn't consider trying 20, or 100, or 300 digits first, to see how many tries (and how many seconds) your method takes to find a prime as the length increases?

If the current state-of-the-art software used to prove arbitrary forms prime could be extended to the length you're considering and still fit in memory (it can't, and it wouldn't), you're looking at something on the order of the age of the Earth to complete the proof.

[science_man_88]

Originally Posted by VBCurtis

If the current state-of-the-art software used to prove arbitrary forms prime could be extended to the length you're considering and still fit in memory (it can't, and it wouldn't), you're looking at something on the order of the age of the Earth to complete the proof.

Yes , even at 1 nanosecond I get roughly 278 million years for just the multiplies to do an LL test on the lowest exponents using the grade school multiply.

[LaurV]

Originally Posted by evanh

I see. Thank you very much. So is it correct that a result of "C-Mismatch" means that the result is composite but did not match someone else result?

A mismatch just means that two people ran the test and got different results. We don't know if the number is composite or not, until we get a "match". Up to now, all mismatches turned out to be composite, but that means statistically nothing (as almost all tests turn out to be composite anyhow, and only 49 of them up to now turned out to be prime, ever...)

Until we get a match, we don't know.

[LaurV]

Originally Posted by retina

That time is for 4M FFT only. For the required 1Gdigit check the FFT iteration time would be a lot more. Since P95 can't do tests that large the times will have to come from another application. Is there any program currently existing that can handle numbers of 1Gdigit? A single iteration could take a few minutes. Multiply that by 1G iterations and you need to have the lifetime of a few Methuselahs to see it finish.

Have you read my post? The one you quote...

Edit: a Titan (classic) tests M666666667 in 217 days. I know because I am working on it (see my reservation, already almost two years old - that is because I had big "gaps" in the work, due to fun adventures, hardware smoking, etc, haha). I never touched the new Big Pascal, and Big Volta, which Oliver plays with, but from his benchmarks, that looks about triple fast, so the "giga-digit test in a year" is not so far away.

You will live to see in each house the hardware able to do it, much sooner than you expect.

[evanh]

Originally Posted by LaurV

Have you read my post? The one you quote...

Edit: a Titan (classic) tests M666666667 in 217 days. I know because I am working on it (see my reservation, already almost two years old - that is because I had big "gaps" in the work, due to fun adventures, hardware smoking, etc, haha). I never touched the new Big Pascal, and Big Volta, which Oliver plays with, but from his benchmarks, that looks about triple fast, so the "giga-digit test in a year" is not so far away.

You will live to see in each house the hardware able to do it, much sooner than you expect.

Yes I worked through the numbers you gave me and found the same you did. Now it is much easier to see why so many are laughing at me! lol I kind of laughed at myself once I did the math....

is this the Titan you are referring to? https://www.olcf.ornl.gov/titan/

even if not this one but a different supercomputer type I have a question regarding languages.. Is Maple a language that is accepted by these types of computers? Maple does have a code generator that can convert the Maple code to others but I am just curious if these supercomputers accept Maple.

[retina]

Originally Posted by LaurV

Have you read my post? The one you quote...

Edit: a Titan (classic) tests M666666667 in 217 days. I know because I am working on it (see my reservation, already almost two years old - that is because I had big "gaps" in the work, due to fun adventures, hardware smoking, etc, haha). I never touched the new Big Pascal, and Big Volta, which Oliver plays with, but from his benchmarks, that looks about triple fast, so the "giga-digit test in a year" is not so far away.

You will live to see in each house the hardware able to do it, much sooner than you expect.

Okay, the progress is better than I was aware of. I didn't consider the GPU side of things because the OP only showed two quite ordinary CPU boxes. But I wonder if the OP has enough patience to complete a "one billion dollars" digit test?

[evanh]

Originally Posted by VBCurtis

Waaaiiiit..... you've tested your "method" up to thirteen digits? 13? One-three? You've skipped from 13 to.... how big?

You didn't consider trying 20, or 100, or 300 digits first, to see how many tries (and how many seconds) your method takes to find a prime as the length increases?

If the current state-of-the-art software used to prove arbitrary forms prime could be extended to the length you're considering and still fit in memory (it can't, and it wouldn't), you're looking at something on the order of the age of the Earth to complete the proof.

Yes I am now trying longer digits and what not based off of the recommendations of others and yourself on this forum.

I am simply learning by trial and error, seeing what works and what doesn't work, but also understanding what works and does not work as well as why it does and does not work.

[CRGreathouse]

Originally Posted by LaurV

@OP:
Your best computer can do one iteration in ~16ms, according with the benchmark you posted.

Originally Posted by retina

That time is for 4M FFT only. For the required 1Gdigit check the FFT iteration time would be a lot more. Since P95 can't do tests that large the times will have to come from another application. Is there any program currently existing that can handle numbers of 1Gdigit?

I believe Mlucas can. Does anyone have timings for large FFTs?

[ewmayer]

Originally Posted by CRGreathouse

I believe Mlucas can. Does anyone have timings for large FFTs?

Toward the bottom of the Mlucas readme page I give some numbers for the smallest billion-digit Mersenne number - on a octocore Ryzen it needs ~550 msec/iter at the required 192Mdoubles FFT length.

On the close-to-the-limit-of-current-practicability front I am currently doing side-by-side primality tests of F30, a gibabit-plus-one number with a known small factor. Even though said number is known composite via the factor it's still useful to do such testing to push the current hardware and software, and the resulting residue will be used for fast cofactor-PRP testing. One run @60M FFT is getting ~52 msec/iter on a 32-core Xeon using an AVX2 build of the code; the other @64M is getting ~60 msec/iter (best timing, it ranges up to 68 msec for mysterious reasons) on the 64-core "GIMPS KNL" using an AVX512 build. I cross-check residues for highest-iteration-reached-by-both-runs roughly daily.

[retina]

Originally Posted by ewmayer

Toward the bottom of the Mlucas readme page I give some numbers for the smallest billion-digit Mersenne number - on a octocore Ryzen it needs ~550 msec/iter at the required 192Mdoubles FFT length.

So about 58 years.

[ewmayer]

Originally Posted by retina

So about 58 years.

That's a more-or-less "budget system" - perhaps ~20 years on the kind of systems I'm using for F30.