Iterating through 15-APs of primes?

[CRGreathouse]

I'd like to extend A291525. Is there good software to generate arithmetic progressions of primes? Math::Prime::Util doesn't seem to do it, but surely some of the sieves we have floating around the forum can handle this easily enough.

[mackerel]

Nearest I can think of is the AP project at PrimeGrid. More about the software used can be found the the below links. I believe it searches for primes of no specific type. If that is required, then I'd imagine either the code would need to be changed for the desired prime type, or you could kinda brute-force it and separately filter the output to look for sequences of the desired type.

http://www.primegrid.com/forum_thread.php?id=6359
https://github.com/ibethune/ap26

[henryzz]

Polysieve might be able to handle APs https://mersenneforum.org/showthread.php?t=16705&page=9
The gap between primes in the progression would have to be known in advance and can then be put in as c(the values for c currently need to fit in a signed long but that restriction is probably liftable.

Checking for Chen-ness of all the terms is a whole different kettle of fish though.

[CRGreathouse]

Originally Posted by henryzz

Checking for Chen-ness of all the terms is a whole different kettle of fish though.

I'm happy to handle that part myself. (If it's a beautiful simpole C tool like polysieve I might even be able to modify it to do some simple checks on the Chen part during the sieving, but doing all of the Chen checks in postprocessing wouldn't be bad.)

Originally Posted by henryzz

Polysieve might be able to handle APs https://mersenneforum.org/showthread.php?t=16705&page=9
The gap between primes in the progression would have to be known in advance and can then be put in as c(the values for c currently need to fit in a signed long but that restriction is probably liftable.

How would this work? I don't quite understand what polysieve does.

[mathwiz]

I am a bit confused by the definition of this sequence: "a(n) is the largest number in an n-term AP of Chen primes".

But one of the papers cited proves "Theorem 1.6. The Chen prime numbers contain infinitely many arith-
metic progressions of length k for all k".

So should the definition of the OEIS sequence specify "the largest number in the FIRST n-term AP" or something similar?

[CRGreathouse]

Originally Posted by mathwiz

So should the definition of the OEIS sequence specify "the largest number in the FIRST n-term AP" or something similar?

I was hoping to revise the definition when I added the first term I found. It should mirror the definition of A005115, being the largest prime in the n-AP of Chen primes such that the largest is minimized.

In order to find such a creature, you pretty much just have to try all the candidates up to that point. Of course you can do a lot with sieving, but you can't skip candidates entirely AFAICT.