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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...
Forum: Other Mathematical Topics 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...
Forum: Number Theory Discussion Group 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.
Forum: Number Theory Discussion Group 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...
Forum: Number Theory Discussion Group 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...
Forum: Number Theory Discussion Group 2019-11-24, 22:32
Replies: 10
Views: 1,028
Posted By jshort
Thank you for this.

Thank you for this.
Forum: Number Theory Discussion Group 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...
Forum: Number Theory Discussion Group 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 ThilaHarich…. Yeah...

Thanks for the reference ThilaHarich….

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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