[QUOTE=3.14159;227595]Also: Reply concerning Posts 1130 and 1131?[/QUOTE]

I know nothing. I have no particular interest in this sort of prime search; others on these boards know much more than I.

[QUOTE=3.14159;227595]What's your n-range?

Alternatively: What size are you aiming for? Is it top 5000 worthy?[/QUOTE]

I'm looking for the smallest prime of that form. Unfortunately it looks like that might be pretty big. :down:

I'm searching discontinuous ranges, but there are no candidates remaining with n < 700,000, and I have checked only a few with n > 1,000,000.

[QUOTE=CRGreathouse]I know nothing. I have no particular interest in this sort of prime search; others on these boards know much more than I.
[/QUOTE]

The best test is to start the thread and keep it going until someone gave me a link to a database.

[QUOTE=CRGreathouse]I'm searching discontinuous ranges, but there are no candidates remaining with n < 700,000, and I have checked only a few with n > 1,000,000.
[/QUOTE]

Did you check every exponent below 700k?

[QUOTE=3.14159;227598]Did you check every exponent below 700k?[/QUOTE]

Yes, either by sieving or direct testing.

Do you know if there is any project that tests numbers like this?

[QUOTE=CRGreathouse]Yes, either by sieving or direct testing.

Do you know if there is any project that tests numbers like this?[/QUOTE]

b^n - c primes? Besides Mersennes, I'm not sure.

Hey: I've started the thread for k-b-b's:

[URL="http://www.mersenneforum.org/showthread.php?t=13797"]Check it out.[/URL]

[QUOTE=3.14159;227592]Also: Is there any database for all the k-b-b primes? If so, can you link me to it? If not, I'll start my own via a new thread. I will begin where b > 60. I don't wish to waste time looking for small primes.

Okay: Using prime k-b-b: For b =2; The 4n + 1 primes (Pythagorean primes)
b = 3; 27n + 1 primes.
b = 5: 3125n + 1 primes.

Etc, etc.[/QUOTE]

For constant b:
[url]http://oeis.org/classic/A000040[/url]
[url]http://oeis.org/classic/A002144[/url]
[url]http://oeis.org/classic/A141948[/url]
. . .

For constant k:
[url]http://oeis.org/classic/A121270[/url]
2*1^1+1, 2*12^12+1, 2*18^18+1, 2*251^251+1, ... (see [url]http://oeis.org/classic/A110932[/url] )
3*2^2+1, 3*4^4+1, 3*6^6+1, 3*10^10+1, 3*286^286+1, 3*450^450+1, ...

Constant-b sequences are plain-vanilla Dirichlet's theorem sequences with well-studied behavior. Constant-k sequences are much more interesting to me, but they grow too quickly to collect many members. (Heuristically, they have log log x members up to x?) A diagonal slice (first term for b = 1, 2, ...) would also be nice.

Edit: The diagonal sequence is
[url]http://oeis.org/classic/A070855[/url]
and should be controlled by Linnik's theorem, though the sequence doesn't seem to mention it. :(

Hey: Where are you up to in computing the smallest k for which k * b[sup]b[/sup] + 1 ? On the ks between 1 and 10k: I'm up to b = 177

[QUOTE=3.14159;227620]Hey: Where are you up to in computing the smallest k for which k * b[sup]b[/sup] + 1 ?[/QUOTE]

608. But I'm not even devoting a full core to it at the moment.

The first 385 are all that will fit in a b-file, but I figure I can submit a new sequence (in October -- the OEIS is on hiatus through September) with the k-values only.

[QUOTE=CRGreathouse]608. But I'm not even devoting a full core to it at the moment.
[/QUOTE]

Ah. Excellent. I just need 20-40 minutes to complete my search for k-b-b's up to b = 250, thus completing my first file.

I think I need to start using the programs after about 300, as the primes become too large for PARI's APR-CL to prove.

[QUOTE=3.14159;227622]I think I need to start using the programs after about 300, as the primes become too large for PARI's APR-CL to prove.[/QUOTE]

Certainly if you want to find a lot of primes you would do best to use programs that can sieve. Since I'm only looking for the first example the benefits are smaller. A bit of sieving would be nice, if I could automate it properly, but right now CPU time is cheap and human time expensive.

I think you should put your files up on a web page -- or maybe a Google doc -- rather than on the forum. This way you could update them rather than make new posts....

[QUOTE=CRGreathouse]I think you should put your files up on a web page -- or maybe a Google doc -- rather than on the forum. This way you could update them rather than make new posts....
[/QUOTE]

A webpage? Only if I had the money to pay for upkeep. No, wait, freewebs sites. Thank you for the idea.

I guess I am unable to do much uploading, as the network is failing yet again.