Fastest sieving program?

[PawnProver44]

I am looking for the fasted sieving program I can use to find (probable) primes of the form k*b^n+-c. Also, which value: k, b, n, or c would be the easiest to (substitute) find primes for? For a sample test, try the form 31*52^n+21, or just fix the variables for this form and choose a high n value.

[paulunderwood]

I can't find one here.

There are plenty of sieves for c=1. This would also make this form provable.

[PawnProver44]

I looked on a version of Proth's Theorem and says the base b must be prime for k*b^n+1. Is this true?

[LaurV]

srsieve

[paulunderwood]

Originally Posted by PawnProver44

I looked on a version of Proth's Theorem and says the base b must be prime for k*b^n+1. Is this true?

No

[PawnProver44]

Originally Posted by LaurV

srsieve

What zip file and script do I need to test the sequence k*b^n+c for fixed k, b, and c (run the file along with Pfgw). Please let me know.

[paulunderwood]

Originally Posted by LaurV

srsieve

Thanks. here is the link.

[paulunderwood]

Originally Posted by PawnProver44

What zip file and script do I need to test the sequence k*b^n+c for fixed k, b, and c (run the file along with Pfgw). Please let me know.

srsieve-0.6.17-bin.zip and run the ".exe". But first

[PawnProver44]

Originally Posted by paulunderwood

Thanks. here is the link.

Do you think any primes of the form k*b^n+-c could make the Top 5000 for primes.utm.edu?

[paulunderwood]

Originally Posted by PawnProver44

Do you think any primes of the form k*b^n+-c could make the Top 5000 for primes.utm.edu?

No. The current record for Primo is 30k digits. To make the top5000 you need ~400k digits. Only c=+-1 will get you into the top5000, because the proof is rapid.

[PawnProver44]

Originally Posted by paulunderwood

No. The current record for Primo is 30k digits. To make the top5000 you need ~400k digits. Only c=+-1 will get you into the top5000, because the proof is rapid.

Any other forms available? The only test that I think would Work is Lucas's Test (N-1), I do not know where I am going to calculate large exponents. Are there any mathematics libraries that would allow me to do large exponent and modular computation?