Forum: Math
2020-10-06, 18:20
|
|
Replies: 12
Views: 1,763
Thanks Dr Sardonicus.
I didn't think a...
Thanks Dr Sardonicus.
I didn't think a counter example could be found for such small n. My mistake was in assuming that the non-primitive part of 2^{n} + 1 must contain many factors from smaller...
|
|
Forum: Math
2020-10-03, 23:11
|
|
Replies: 12
Views: 1,763
Question about number of the form 2^n + 1
Let a_{n} be the nth Highly Composite Integer* and b_{n} = lcm(2^{a_{1}} + 1, 2^{a_{2}} + 1, ...,2^{a_{n}} + 1). If c_{n} = \frac{2^{a_{n}} + 1}{gcd(2^{a_{n}} + 1,b_{n-1})}, will c_{n} always be...
|
|
Forum: Number Theory Discussion Group
2020-10-01, 22:15
|
|
Replies: 22
Views: 6,640
|
|
Forum: Number Theory Discussion Group
2020-10-01, 20:15
|
|
Replies: 3
Views: 1,216
|
|
Forum: Number Theory Discussion Group
2020-09-30, 20:05
|
|
Replies: 3
Views: 1,216
|
|
Forum: Number Theory Discussion Group
2020-09-30, 02:11
|
|
Replies: 3
Views: 1,216
alternative 2nd stage of p-1 factoring algorithm
Suppose we're factoring an integer via the p-1 method and we've already completed the first stage ie. L = a^{B!} mod(n) where n is the composite we wish to factor.
In the 2nd stage, we assume...
|
|
Forum: Proth Prime Search
2020-06-11, 23:46
|
|
Replies: 5
Views: 4,295
|
|
Forum: Other Mathematical Topics
2019-12-19, 17:31
|
|
Replies: 5
Views: 2,299
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: 3,068
|
|
Forum: Number Theory Discussion Group
2019-12-15, 17:34
|
|
Replies: 4
Views: 3,068
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: 3,197
|
|
Forum: Number Theory Discussion Group
2019-11-24, 22:32
|
|
Replies: 10
Views: 3,197
|
|
Forum: Number Theory Discussion Group
2019-11-24, 22:24
|
|
Replies: 10
Views: 3,197
|
|
Forum: Number Theory Discussion Group
2019-11-24, 20:30
|
|
Replies: 10
Views: 3,197
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: 1,735
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: 1,735
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: 1,735
|
