Double Checking Factors

[eepiccolo]

OK, this is most likely a dumb question (unless you believe the old adage of there being no such thing ;) ). Of course, we double check LL test to make sure they are OK, but is there some sort of checking to make sure factors that are found are valid?

[Kevin]

Yes, I believe all factors found are immediately tested by the server. Checking to see if an individual number is a factor is trivial work.

[ewmayer]

Originally Posted by Kevin

Yes, I believe all factors found are immediately tested by the server. Checking to see if an individual number is a factor is trivial work.

I'm not 100% sure about this. One of the folks beta-testing my factor.c code recently submitted a batch of factors they found, but later it turned out that there was an output-print bug in the particular version of the code they were using which caused the printed "factors" to be 6 larger (6 = 2^64 mod 10) than the true factor. The server didn't give them any kind of error message, however. Since they submitetd their results using the manual test pages, perhaps this only applies to those. Even if the server actually does check reported factors and reassign for factoring any that are incorrect, there's still the more insidious problem of the program missing factors, which appears to happen with a non-negligible frequency. Obviously subsequent p-1 will catch many of these (that's how I first happened onto the problem), but only those for which q-1 happens to be smooth enough for the p-1 method with the default bounds to find it. I don't know if any of the QA effort is devoted to checking for missed factors, but it would be nice to have a quantitative estimate of how frequently this occurs.

[trif]

Do you happen to know the exponents they reported and did they submit the exponents without factors as well?

[Prime95]

The server does have this check, but it may not be hooked into the manual reporting web pages. Not to worry, as my master database update programs also check the factor. Ernst's off-by-6 factors never made it into the master database. The only known flaw in my program is that it does not check to see if the reported factor is composite.

[ewmayer]

Originally Posted by trif

Do you happen to know the exponents they reported and did they submit the exponents without factors as well?

I do, and the exponents with the true factors have since been resubmitted.
But it would have been nice to get some kind of error message from the server, so the problem would have been spotted immediately, not left to chance.

[Darak]

Ahhhh, I'm glad you asked the question as I've been wondering this for years but too lazy to ask...