PARI's commands

[mdettweiler]

Originally Posted by 3.14159

Well, you stated that this happened to you as well, which makes me doubt that it happens to be only me.

And, it only up when dealing with k * 308³⁰⁸ + 1. There have been no other errors before or afterwards. I'm going to test the original Primeform to make sure that this is just a minor problem.

The errors I encountered before were repeatable, i.e. program errors not hardware errors. Your error is not repeatable, which usually indicates a hardware error. (Sorry for the ambiguity there.)

The same number working just fine with the original Primeform is consistent with what I'd expect with a hardware error. Hardware errors are often not exactly repeatable even with the same test on the same software. Try running k*308^308+1 again with the latest PFGW--my guess is that the error won't show up again. Your issue looks to me like a mild CPU instability; hence my suggestion of a 12-hour Prime95 stress test which should be able to better uncover sporadic errors than lots of tiny tests, many of which can "slip between the errors" and turn out just fine. Also note that many errors are undetectable, i.e. they don't produce visible roundoff errors but nonetheless do not produce the correct residue on tests; your one roundoff error may be a symptom of undetectable errors happening more often. Prime95 will detect these as well.

Oh, and BTW--it's Max, not Matt, though it's a common mistake. (mdett... tends to get alliterated to matt...)

[3.14159]

Originally Posted by Max

Try running k*308^308+1 again with the latest PFGW--my guess is that the error won't show up again.

Are the latest binaries pfgw 3.3.4 ?

[mdettweiler]

Originally Posted by 3.14159

Are the latest binaries pfgw 3.3.4 ?

Yes. (The latest client is always available from http://sourceforge.net/projects/openpfgw/files/.)

[3.14159]

Originally Posted by Max

Yes. (The latest client is always available from http://sourceforge.net/projects/openpfgw/files/.)

That's the version I have.

Also: I'll subject it to p95's wrath later tonight. 12 hours? p95 recommends 16. I just have to decide which 12-hour period to use.

What happens when p95 does catch errors? Blue screen of death? Or does it stop immediately?

[mdettweiler]

Originally Posted by 3.14159

That's the version I have.

Also: I'll subject it to p95's wrath later tonight. 12 hours? p95 recommends 16. I just have to decide which 12-hour period to use.

What happens when p95 does catch errors? Blue screen of death? Or does it stop immediately?

16 hours is even better.

As to what happens when an error is found, that depends on the type and severity of the error. If the system is seriously unstable, you can get a BSOD. But in this case, if there is a problem with your system I suspect it's a minor one, in which case Prime95 would stop the stress test upon detecting the error and output the details of the error to the screen and log file.

[3.14159]

Originally Posted by Max

As to what happens when an error is found, that depends on the type and severity of the error. If the system is seriously unstable, you can get a BSOD. But in this case, if there is a problem with your system I suspect it's a minor one, in which case Prime95 would stop the stress test upon detecting the error and output the details of the error to the screen and log file.

To see the logs, I'll move p95 to my main primefinding equipment folder.

[3.14159]

Well, I'm going to be working on the collection of k-b-b's for a while, eliminating the need to search for small b values. (< 500 is what's been done, for now.)

[3.14159]

Commencing work on 501-750.

I got to the range where I predicted the error would happen.

And.. no error has occurred.

Dammit. Let's hope I didn't speak too soon!

[3.14159]

Okay: Back to previous topic:

@CRG: Concerning the OEIS sequence: You suggested I start with b = 2, and continue from there?

[CRGreathouse]

Originally Posted by 3.14159

Concerning the OEIS sequence: You suggested I start with b = 2, and continue from there?

We need to find a good sequence without arbitrary points. So no minimum of 60 on b and no maximum of 10,000 on k.

I can think of a few ways to do this, but I'll let you decide. One example: consider a two-dimensional array where each row corresponds to a b-value and the values in a row are the least k-values that produce a prime. Then read this array by antidiagonals (or some other reasonable way). The first column is A070855, while the first row is A000040.

Another way: for each prime p, give the largest b value such that there exists a k with k*b^b+1 = p. Then give the values for 2, 3, 5, ....

Maybe both of these are good.


These examples avoid not only the arbitrariness of bounds, but also make ordinary sequences or 'tabl's rather than 'tabf's.

[3.14159]

Originally Posted by CRGreathouse

We need to find a good sequence without arbitrary points. So no minimum of 60 on b and no maximum of 10,000 on k.

Oh.

We can construct it similarly to how the Proth numbers are constructed. Should there be a k < b^b restriction? Or do we allow all the 4n + 1 primes in?