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Old 2016-03-08, 06:54   #1
PawnProver44
 
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Post 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.
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Old 2016-03-08, 11:42   #2
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I can't find one here.

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

Last fiddled with by paulunderwood on 2016-03-08 at 11:46
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Old 2016-03-08, 11:56   #3
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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?
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Old 2016-03-08, 11:56   #4
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srsieve
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Old 2016-03-08, 12:02   #5
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Quote:
Originally Posted by PawnProver44 View Post
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
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Old 2016-03-08, 12:04   #6
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Quote:
Originally Posted by LaurV View Post
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.
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Old 2016-03-08, 12:05   #7
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Quote:
Originally Posted by LaurV View Post
srsieve
Thanks. here is the link.
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Old 2016-03-08, 12:10   #8
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Quote:
Originally Posted by PawnProver44 View Post
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
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Old 2016-03-08, 12:11   #9
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Quote:
Originally Posted by paulunderwood View Post
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?
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Old 2016-03-08, 12:14   #10
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Quote:
Originally Posted by PawnProver44 View Post
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.

Last fiddled with by paulunderwood on 2016-03-08 at 12:16
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Old 2016-03-08, 12:19   #11
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Quote:
Originally Posted by paulunderwood View Post
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?
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