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 Showing results 1 to 11 of 11 Search took 0.01 seconds. Search: Posts Made By: jshort
 Forum: Proth Prime Search 2020-06-11, 23:46 Replies: 5 Views: 1,127 Posted By jshort Proths of the form 2^{k+1}(2^{k} - 1) + 1, 2k+1 is prime (I guess am sort of answering my own question here......but here goes) Are Proth Primes of the form 2^{k+1} \cdot (2^{k} - 1) + 1 worthwhile to search for? Fyi - I'm specifically referring to...
 2019-12-19, 17:31 Replies: 5 Views: 725 Posted By jshort How much smaller can "primitive" factors be? When looking for "easy" to find integers N that are forced to be congruent to 1 + k \cdot p where the congruence factor p is "as large as possible" compared to N, are the primitive factors of...
 2019-12-15, 22:48 Replies: 4 Views: 1,004 Posted By jshort Thank you sir. Interesting that the p-1 test... Thank you sir. Interesting that the p-1 test isn't used straight away, but rather a trivial Sieve of Eratosthenes. Anyways, I'd imagine that the bounds B and B' must be awfully small.
 2019-12-15, 17:34 Replies: 4 Views: 1,004 Posted By jshort How are composite Mersenne's sieved (weeded) out? Is there a sieving process that is done before the Lucas-Lehmer primality test is run to test if a Mersenne is prime? Normally (that is for random integers), one simply uses a primordial number...
 2019-11-25, 00:41 Replies: 10 Views: 1,028 Posted By jshort Looking at these results F(n,p) for n = 1 - 6 it... Looking at these results F(n,p) for n = 1 - 6 it looks rather discouraging to say the least! I knew that as n increase the number of primes drops drastically, however for n > 3, the frequency of...
 2019-11-24, 22:32 Replies: 10 Views: 1,028 Posted By jshort Thank you for this. Thank you for this.
 2019-11-24, 22:24 Replies: 10 Views: 1,028 Posted By jshort Thank you for the references. I wasn't aware of... Thank you for the references. I wasn't aware of Mike Oakes's work, but will definitely read up on him :) I haven't considered [$]b^{2^n} +1[/$], with b > 2 because their bit-size is even bigger...
 2019-11-24, 20:30 Replies: 10 Views: 1,028 Posted By jshort Other ways of finding WR primes I've been thinking about this for some time as to why Mersenne integers are the #1 candidate for finding WR prime numbers, and have basically come to these two reasons: 1) There is a fast...
 Forum: Factoring 2019-03-20, 22:52 Replies: 9 Views: 942 Posted By jshort Re - storing residues You generally only... Re - storing residues You generally only need to store one residue. It's a "reference" point that we assume is already inside the periodic cycle for which we compare future residues with. If our...
 Forum: Factoring 2019-03-17, 23:45 Replies: 9 Views: 942 Posted By jshort Thanks for the reference ThilaHarichâ€¦. Yeah... Thanks for the reference ThilaHarichâ€¦. Yeah the factorization of F_{8} was the most successful application of the Pollard Rho method to date for sure. Interestingly Brent mentions that there...
 Forum: Factoring 2019-03-14, 20:23 Replies: 9 Views: 942 Posted By jshort Factoring composite Mersenne numbers using Pollard Rho First post here - sorry if this is either an obvious or mundane question. The Pollard Rho factoring method is suppose to have a running time proportional to n^{\frac{1}{4}}, however if you're...
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