Has SB missed a prime?

[Moo_the_cow]

While browsing the project stats, I found out that 126,000 tests were completed, and they do not include the tests done by secret/supersecret. I also read somewhere that the error rate for a PRP test is about 1%. Therefore, about 1,260
tests are incorrect and may be primes. So, does anyone here think that we've missed one?

[jjjjL]

the 126,000 tests do include secret/supersecret tests. it also includes test primes that are periodically assigned. of those, none has ever been falsely reported composite.

-Louie

[eatmadustch]

Originally posted by jjjjL
the 126,000 tests do include secret/supersecret tests. it also includes test primes that are periodically assigned. of those, none has ever been falsely reported composite.

Hm, so I guess that means if you actually find a prime, the chances are rather high that it's just a test prime? How do you know you found a prime? Is it when you get a completed proth test, result: 1 or 2?

[jjjjL]

you know that you've found a prime when you get an email from me. :D

also, the test primes are for k's other than the main 12. if i had known primes for the 12 in the project, they wouldn't be part of it anymore.

the prime result code is result 2.

result 1 is what it reports for intermediate blocks. there is also another result code that is no longer used to represent that a proper base could not be selected. now the base is 3 reguardless of whether it is proper or not for a proth proof. that is the reason why a prp test is only a probable test and also the reason this code no longer exists.

-Louie

[Moo_the_cow]

The 126,000 do NOT include the secret/supersecret tests:
From the Project Stats page:

Proth tests completed- 150637 tests
secret- 18235 tests
supersecret- 5668 tests

If my calculator is right :) there should be 126,734 tests not done by
secret/supersecret.
Anyways, about how many of those "tests primes" have been assigned so far,
and how big are they?

[Lagardo]

Originally posted by Moo_the_cow
I also read somewhere that the error rate for a PRP test is about 1%.

Rate for false positives or for false negatives?
Care to quote a source on that?

[smh]

Originally posted by Lagardo
Care to quote a source on that?

There was some talking about error rates in this (http://www.free-dc.org/forum/showthread.php?threadid=2884&perpage=25&highlight=error*%20GIMPS&pagenumber=2) thread.

And this (http://www.mersenneforum.org/viewtopic.php?t=49) thread shows that the GIMPS error rate is about 3,5%

[philmoore]

I haven't voted because it seems to me that it would be more valuable for the project to get some data on error rates first. If 1% of the tests are in error, the chance that we have missed a prime are small, but at 3%, the chance becomes significantly larger. The number of errors per test should be approximately proportional to the length of the test, so we can expect, similarly to GIMPS, that the error rate will increase with time. Do the "secret" tests shed any light on error rates?

[jjjjL]

considering we use GIMPS object files, it stands to reason our error rates would be nearly identical to theirs. the secret tests give no idea what error rates are since they are all matches. a perfect 5936 for 5936.

-Louie

[Jwb52z]

Louie, I'm glad you mentioned GIMPS because, although not through with the double check, they have most likely found the 40th Mersennne Prime. They have yet to say what number it is exactly.

[Mystwalker]

Old news - I already posted it here (http://www.free-dc.org/forum/showthread.php?s=&threadid=3120) :neener: ;)

[philmoore]

That is good news for the project, that all of the "secret" tests have been in agreement. It at least puts some sort of upper bound on the error rate. I'm going to vote "no", I think that the project was extraordinarily lucky last November and December, and that Mr. Poisson has just been taking his revenge since then. But sooner or later, our luck will change, that is a virtual certainty!

[Lagardo]

If there's simply a symmetric error probability, then we should be able to tell it approximately like this: We've done 120000 test. The vast, vast, vast majority of them return "3", i.e. composite. If the error probability were 1%, then there should have been about 1200 false positives. As I assume that any reported positive is double checked, we'd simply have to ask Mr. jjjjL politely how many reported positives there have been that were eliminated in some kind of double-check...

[eatmadustch]

a lot of these tests (especially secret and supersecret) are much smaller than the numbers we are testing now! I think the 1% is only for rather high numbers (around 1-5 million). I'm not sure, though!

[philmoore]

The most likely kind of error would be for a test to report "composite" but to submit an incorrect residue. Such an error would never be detected until another test reports a different residue. The chance of a false positive (actual composite reported "prime") is extremely remote, but the chance of an actual prime testing to show composite is a more realistic concern.

[Moo_the_cow]

quote:
______________________________________
The chance of a false positive (actual composite reported "prime") is extremely remote
______________________________________

It appears that that has just happened to GIMPS.
So, does anyone think that SB has missed one
or more primes now?


:Pokes:

[sobo]

When SB reports that a number is not prime does it report only that it is not prime or does it send a 64-bit residue like GIMPS. The residues allow GIMPS to be completely sure that a number is composite after a double check becasue the residues will match.

[jjjjL]

there have been residues since v0.97. the server no longer accepts connections from older clients so all our tests are checkable.

-Louie