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Cruelty 2006-02-14 14:32

NewPGen reliability
I am experimenting with different values of "k" and by accident I have come across following situation.
For k=617 I have sieved 2<n<20000 till 10^8 and among other things in NewPGen.del file I found that:
p=10108927 divides n=14

However afterwards, I have tested 2<n<76 with LLR v.3.6.2 and found that:
617*2^14-1 = 10108927 is prime! (trial divisions)

This is at least odd I would say - I have verified my findings on two different PCs.
Has anyone else seen similar behaviour?

Mystwalker 2006-02-14 14:54

That's the problem when the factor to try is equal to the candidate to sieve out.

Of course, this can either only happen for prime numbers (as they don't get sieved out before) or when the trial factoring doesn't start at the beginning...

Kosmaj 2006-02-14 23:02

1 Attachment(s)
As Mystwalker explained, NewPGen expects users to sieve for large primes, not so small ones. To check primality of small exponents it's better to use Proth.exe for a single [I]k[/I], or PrimeForm (now called "pfgw") for several k's. I'm enclosing the file to use with PrimeForm. On a fast machine you can check exponents 1-500 of several k's in seconds.

Cruelty 2006-02-15 05:15


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