Fastest sieving program?
 

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.:smile::smile::smile:

I can't find one [URL="http://primes.utm.edu/bios/index.php"]here[/URL]. :sad:

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

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?:smile:

srsieve

[QUOTE=PawnProver44;428382]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?:smile:[/QUOTE]

No :no:

[QUOTE=LaurV;428383]srsieve[/QUOTE]

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.:smile:

[QUOTE=LaurV;428383]srsieve[/QUOTE] Thanks. here is [URL="http://primes.utm.edu/bios/page.php?id=905"]the link[/URL]. :smile:

[QUOTE=PawnProver44;428385]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.:smile:[/QUOTE]

[URL="https://sites.google.com/site/geoffreywalterreynolds/programs/srsieve"]srsieve-0.6.17-bin.zip[/URL] and run the ".exe". But first :rtfm:

[QUOTE=paulunderwood;428386]Thanks. here is [URL="http://primes.utm.edu/bios/page.php?id=905"]the link[/URL]. :smile:[/QUOTE]

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

[QUOTE=PawnProver44;428388]Do you think any primes of the form k*b^n+-c could make the Top 5000 for primes.utm.edu?:smile:[/QUOTE]

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.

[QUOTE=paulunderwood;428389]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.[/QUOTE]

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?
:smile: