14306Re: [PrimeNumbers] Re: Modification of PFGW
- Dec 31, 2003Ok then. Now, Who's willing to act? We need a 1M digit Carol/Kynea
(I tried to join the PFGW group, but that site is blocked from work. I will try to log on outside of work and try to join...)
Paul Underwood <paulunderwood@...> wrote:
--- In firstname.lastname@example.org, Cletus Emmanuel <cemmanu@y...>
> Guys,especially when it is math). You guys have a wealth of information
> Again, this is why I love this group. I live to learn(and
which I don't have and it is great to learn from all of you. I
hearing from Mike that testing for Carol/Kynea can be improved by 50%.
As Phil ( the silent ) pointed out this won't be 50%, it will be
approxiamately 0% :-(
> And hearing from Paul that we can even save more time. I can'timplement these changes in PFGW. Can anyone of you do it?
The best place to lobby for these changes is the primeform Yahoo
and probably the best people to make the changes are the OpenPFGW
developement team. Perhaps we could have a switch instead of relying
on the application to recogonise these forms.
> I think that it will be worth it considering that there are 40Kynea, 32 Carol for k<= 100,000 and 52 Generalized Carol Primes
(273*2^k-1)^2 - 2 for K<= 100,000 (but not all k-values checked).
These are more dense than Mersenne and the number of digits are twice
Yes, but the Mersennes are counted over the primes.
> Isn't this incentive enough to modify PFGW and coordinate a search?I think a lot of people would benefit from the changes:
You: Carol/Kynea (+ generalisations)
Mike: Gaussian Mersennes
Jiong: AP3 searches
Me: generating loads of trinomials of the form 2^n-2^k-1 ;-)
I programmed something like this in C long before I got on the Net
and ... During exponentiation a number is squared ( and sometimes
multiplied by the base of the Fermat depending on whether is a one or
a nought in the binary representation of N. ) This results in a
number that is twice as long in computer memory. Modular reduction is
performed to reduce this size back down. Using O(N) shifts, adds and
mults, it should be possible for any trinomial of the form A*2^n-
B*2^k-C, where A,B and C are small, much more quickly modularly
reduced than PFGW does it now.
Paul ( hardly capable of RTFS )
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