PARI's commands

[CRGreathouse]

Originally Posted by 3.14159

Also: Reply concerning Posts 1130 and 1131?

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

Originally Posted by 3.14159

What's your n-range?

Alternatively: What size are you aiming for? Is it top 5000 worthy?

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

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.

[3.14159]

Originally Posted by CRGreathouse

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

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

Originally Posted by 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.

Did you check every exponent below 700k?

[CRGreathouse]

Originally Posted by 3.14159

Did you check every exponent below 700k?

Yes, either by sieving or direct testing.

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

[3.14159]

Originally Posted by CRGreathouse

Yes, either by sieving or direct testing.

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

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

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

Check it out.

[CRGreathouse]

Originally Posted by 3.14159

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.

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

For constant k:
http://oeis.org/classic/A121270
2*1^1+1, 2*12^12+1, 2*18^18+1, 2*251^251+1, ... (see http://oeis.org/classic/A110932 )
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
http://oeis.org/classic/A070855
and should be controlled by Linnik's theorem, though the sequence doesn't seem to mention it. :(

[3.14159]

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

[CRGreathouse]

Originally Posted by 3.14159

Hey: Where are you up to in computing the smallest k for which k * b^b + 1 ?

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.

[3.14159]

Originally Posted by CRGreathouse

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

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.

[CRGreathouse]

Originally Posted by 3.14159

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.

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....

[3.14159]

Originally Posted by 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....

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

[3.14159]

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