me, myself and I
 

Hi,

I started a LL Test and simultaneously already the DoubleCheck on different hardware (CPU vs GPU) on another system.

Now my question is, will the PrimeNet server accept my 2nd result of the same exponent when I'm submitting it?

Yes, it will.
If [U]both[/U] tests were on a GPU, it wouldn´t.

To be sure, report the manual one (GPU) first. It will, anyhow, finish faster. The other way around you risk to get "this computer already reported this result" when you do the manual report after P95 reported the CPU result.

Thanks for the info, I'll give it a try.
I wouldn't bet on the GPU though. ;)
At the moment the estimations are that the GPU finishes 2nd.

[QUOTE=ramgeis;343028]Thanks for the info, I'll give it a try.
I wouldn't bet on the GPU though. ;)
At the moment the estimations are that the GPU finishes 2nd.[/QUOTE]

So- really fast CPU, or relatively slow GPU? Some combination? Inquiring minds, and all that.....:smile:

And another one for the inquiring minds:

Has GIMPS finally ditched the principle that double checks ought to be carried out by a different user than the original test was? Or, more accurately, that an LL test result is considered definitive when two independent users have produced the same residue?

Different LL runs with P95 are certainly accepted and relatively "safe" even if they are ran by the same user, as they contain different shifts and checksums. It will take an user with some knowledge of the P95's internals to falsify such reports, and those users won't waste the time and won't risk their reputation just to get few more GHzDays. When a "manual" (GPU) run comes into equation, the things are tricky, as such report can be done by anybody. One childish user could run LL test and report (eventually incorrect) results as both first-time-LL and DC-LL, therefore causing GIMPS to miss primes for a while (until triple tests). Two GPU results are not accepted anyhow, no matter if they come from the same user or not. There should be at least a P95 run with a different shift (all GPU runs have the shift zero).

[QUOTE=kladner;343038]So- really fast CPU, or relatively slow GPU? Some combination? Inquiring minds, and all that.....:smile:[/QUOTE]

Actually both quite fast in their area. :) In the blue corner a dual e5-2670 xeon system (which means 32 cores with hyperthreading) and in the red corner a quadro k5000... for the given exponent the time per iteration is approx. 7ms vs approx. 8ms

[QUOTE=ramgeis;343170]Actually both quite fast in their area. :) In the blue corner a dual e5-2670 xeon system (which means 32 cores with hyperthreading) and in the red corner a quadro k5000... for the given exponent the time per iteration is approx. 7ms vs approx. 8ms[/QUOTE]

Yikes! :shock: Nice box, if I may say so!

[STRIKE]Producing[/STRIKE]Faking the second manual result "on the GPU" after having the complete residue known from the CPU can be easily done even by a 9-year old. Changing the order and submitting the "GPU" result first - by a clever 9-year old ...or by any 10-year old.

It has been demonstrated that two matching results (with different shifts, and produced with unfettered Prime95 binary) are easily produced for any input. Maybe not by a 10-year old though...

[QUOTE=Batalov;343222][STRIKE]Producing[/STRIKE]Faking the second manual result "on the GPU" after having the complete residue known from the CPU can be easily done even by a 9-year old. Changing the order and submitting the "GPU" result first - by a clever 9-year old ...or by any 10-year old.

It has been demonstrated that two matching results (with different shifts, and produced with unfettered Prime95 binary) are easily produced for any input. Maybe not by a 10-year old though...[/QUOTE]

In other words, the whole LL-checking process only reduces the chance to prove that M( p ) is prime and can't prove that M( p ) isn't prime, right?

If false reports are possible, wouldn't that mean that the announcement of M( p ) as the n-th Mersenne prime must include at least one factor for each non-prime M( p' ) with p' < p ?

[QUOTE=ramgeis;343271]If false reports are possible, wouldn't that mean that the announcement of M( p ) as the n-th Mersenne prime must include at least one factor for each non-prime M( p' ) with p' < p ?[/QUOTE]
Factorizing is very, very difficult.

[QUOTE=Batalov;343222][STRIKE]Producing[/STRIKE]Faking the second manual result "on the GPU" after having the complete residue known from the CPU can be easily done even by a 9-year old. Changing the order and submitting the "GPU" result first - by a clever 9-year old ...or by any 10-year old.

It has been demonstrated that two matching results (with different shifts, and produced with unfettered Prime95 binary) are easily produced for any input. Maybe not by a 10-year old though...[/QUOTE]
I was a clever 9-year-old 54 years ago.
Are you suggesting that finding a square root in modular arithmetic is about as simple as division? (extended Euclid or the like).

David

[QUOTE=ramgeis;343271]In other words, the whole LL-checking process only reduces the chance to prove that M( p ) is prime and can't prove that M( p ) isn't prime, right?

If false reports are possible, wouldn't that mean that the announcement of M( p ) as the n-th Mersenne prime must include at least one factor for each non-prime M( p' ) with p' < p ?[/QUOTE]

As long as we accept results from untrusted parties, you're right, we can't be absolutely sure that we haven't missed a prime. Mentions of which Mersenne prime you're dealing with already must (to be accurate) carry disclaimers that some numbers smaller than the prime have yet to be checked and double checked (e.g. [URL="http://en.wikipedia.org/wiki/Mersenne_prime#List_of_known_Mersenne_primes"]Wikipedia on M43-M48[/URL]). There is still the exceedingly small chance that a Mersenne prime was missed due to everyone's standards not being good enough, but it's generally not mentioned.

If you want to improve the standards, you can begin by triple checking the most suspicious residues (e.g. ones submitted by the same user on the same date), then moving on to less suspicious ones. I recall a mini-project being formed to do just this and dying out due to lack of interest.

If you want factors, then you really don't know things starting as low as M1277. Is M1279 [I]really[/I] the 15th Mersenne prime? If I said that I LL tested M1277, would you believe me, or do you only trust yourself? For that matter, why trust the software that runs LL tests, or tells you that 3454817 is a factor of M1009? Should you trust hand calculations more? I certainly wouldn't. [URL="http://www.mersenneforum.org/showthread.php?t=17747"]So what does it really mean to know something?[/URL] To what standards do [I]you[/I] want composite Mersenne numbers checked? GIMPS has its own standards, albeit somewhat easily gamed. The standards for primes are much higher: different software, different hardware, different trusted people. I think most would agree this is overkill for composites.

[QUOTE=ramgeis;343271]In other words, the whole LL-checking process only reduces the chance to prove that M( p ) is prime and can't prove that M( p ) isn't prime, right?[/QUOTE]
No. Correctly done LL test paired with a correctly done double-check is conclusive. But the server is insufficiently protected from fake results and fake double-checks.

[QUOTE=davieddy;343275]I was a clever 9-year-old 54 years ago.
Are you suggesting that finding a square root in modular arithmetic is about as simple as division? (extended Euclid or the like).
[/QUOTE]
No square roots were involved and only Prime95 27.9 was used for submissions: all legal and clear from the GIMPS server point of view. The exact procedure was sent to George. (Not described here to avoid copycats.) Some patches to the code might help this situation.

[QUOTE=Mini-Geek;343280]As long as we accept results from untrusted parties, you're right, we can't be absolutely sure that we haven't missed a prime. [/QUOTE]
This is exactly right.

[QUOTE=Mini-Geek;343280]If you want to improve the standards, you can begin by triple checking the most suspicious residues (e.g. ones submitted by the same user on the same date), then moving on to less suspicious ones. I recall a mini-project being formed to do just this and dying out due to lack of interest.[/QUOTE]
The lower ranges have been well tested.
[URL="http://mersenneforum.org/showthread.php?t=10789"]GIMPS competition[/URL] ([URL="http://web.archive.org/web/20120321234425/http://neoview.kicks-ass.net/mersenne/"]on the wayback machine[/URL]) Dan Holle

[url]http://mersenneforum.org/showthread.php?t=7479[/url]

[url]http://mersenneforum.org/showthread.php?t=17108[/url]

Factors, factors and factors
 

[QUOTE=Mini-Geek;343280]As long as we accept results from untrusted parties, you're right, we can't be absolutely sure that we haven't missed a prime.[/QUOTE]
So true, we just need to reduce the possible candidates by finding factors of the composite exponents. And re-test the holes :smile:. We will never be sure as the rest of the post suggests.
[QUOTE=Mini-Geek;343280]
If you want factors, then you really don't know things starting as low as M1277. Is M1279 [I]really[/I] the 15th Mersenne prime? If I said that I LL tested M1277, would you believe me, or do you only trust yourself? For that matter, why trust the software that runs LL tests, or tells you that 3454817 is a factor of M1009? Should you trust hand calculations more? I certainly wouldn't. [URL="http://www.mersenneforum.org/showthread.php?t=17747"]So what does it really mean to know something?[/URL] To what standards do [I]you[/I] want composite Mersenne numbers checked? GIMPS has its own standards, albeit somewhat easily gamed. The standards for primes are much higher: different software, different hardware, different trusted people. I think most would agree this is overkill for composites.[/QUOTE]
Who can argue with the presence of a factor(s)? With LL test is not the test per se, which is wrong, but the possibility to submit a wrong/manipulated result. If there are factors for all M<1279 and M1279 is prime by all standards you mentioned, than it is hard to say that is not the 15th. Here is one number only (M1277), but for the Mersenne primes to follow, the gaps are vast. Thereafter, I believe more factors are needed. One can check the divisibility of a composite by the factor with many different algorithms in a fraction of a second (no need of paper and pen I believe). So once we have factors, the tests on those numbers are easier (even with a pen, for the most pedantic ones :smile:). The factors are the golden standard to prove a composite, right?

[QUOTE=bloodIce;343367]So true, we just need to reduce the possible candidates by finding factors of the composite exponents. And re-test the holes :smile:. We will never be sure as the rest of the post suggests.

Who can argue with the presence of a factor(s)? With LL test is not the test per se, which is wrong, but the possibility to submit a wrong/manipulated result. If there are factors for all M<1279 and M1279 is prime by all standards you mentioned, than it is hard to say that is not the 15th. Here is one number only (M1277), but for the Mersenne primes to follow, the gaps are vast. Thereafter, I believe more factors are needed. One can check the divisibility of a composite by the factor with many different algorithms in a fraction of a second (no need of paper and pen I believe). So once we have factors, the tests on those numbers are easier (even with a pen, for the most pedantic ones :smile:). The factors are the golden standard to prove a composite, right?[/QUOTE]

Finding factors is a great way to be sure a number is composite, but here's the problem: it's often EXTREMELY hard to find a factor. As an example, we can look at the lower bounds of what each (factoring vs LL) has yet to prove: The smallest Mersenne number with no factors known is M 1 277 (and I'll point out that a great deal of effort goes into fully factoring small Mersenne numbers - I'm sure that a lot of ECM has been run on this number). The smallest Mersenne number without matching LLs (to GIMPS's standards) is M 26 114 633.

I think the best bang-for-your-buck for raising the certainty of composite Mersenne numbers is, perhaps after a small amount of extra TF and/or P-1, simply to run another LL. (the factoring might be useful because GPUs are so good at TF and and poor P-1s might've been run the first time around)