mersenneforum.org  

Go Back   mersenneforum.org > Search Forums

Showing results 1 to 25 of 56
Search took 0.01 seconds.
Search: Posts Made By: mickfrancis
Forum: Number Theory Discussion Group 2020-07-20, 15:55
Replies: 4
Views: 917
Posted By mickfrancis
Thanks for this. I shall cogitate upon it!

Thanks for this. I shall cogitate upon it!
Forum: Number Theory Discussion Group 2020-07-20, 08:04
Replies: 4
Views: 917
Posted By mickfrancis
Thanks for the reply, Robert. I don't think this...

Thanks for the reply, Robert. I don't think this is quite what I'm saying, though I may just be misunderstanding - forgive me if so.

What I have noticed is that \phi\left(p^{n} \pm q^{n}\right) is...
Forum: Number Theory Discussion Group 2020-07-18, 19:17
Replies: 4
Views: 917
Posted By mickfrancis
Factors of Euler Totient Function of sum/difference of prime powers

It appears that for prime p and q, p>= q, \phi\left(p^{n} \pm q^{n}\right) is divisible by (often a high power of) n. The power of n seems to increase with the number of distinct prime factors of n....
Forum: Math 2017-03-01, 07:17
Replies: 16
Views: 1,351
Posted By mickfrancis
I'd never come across this before - thanks! ...

I'd never come across this before - thanks!

Mick.
Forum: Math 2017-02-28, 13:44
Replies: 16
Views: 1,351
Posted By mickfrancis
Thanks for your input on this, Mick.

Thanks for your input on this,

Mick.
Forum: Math 2017-02-27, 21:42
Replies: 16
Views: 1,351
Posted By mickfrancis
Changing the question...

Having given some thought to this, I realise that what I really want is a way to find integer values for m such that


(ceil(mr))^2- (mr)^2 < (mr)^s




where s <= 1. I'm guessing this is a...
Forum: Math 2017-02-27, 15:51
Replies: 16
Views: 1,351
Posted By mickfrancis
Really helpful - thank you - plenty for me to get...

Really helpful - thank you - plenty for me to get my teeth into there!

Regards,

Mick.
Forum: Math 2017-02-27, 15:20
Replies: 16
Views: 1,351
Posted By mickfrancis
Thanks for the response. I'm afraid you'll have...

Thanks for the response. I'm afraid you'll have to forgive my ignorance, but I can't see at the moment how continued fractions help me here - any hints appreciated.

Mick.
Forum: Math 2017-02-27, 14:39
Replies: 16
Views: 1,351
Posted By mickfrancis
Finding multiples of a real number that are close to a whole number

Given a real number r, and a small positive value e arbitrarily close to 0, does anyone know of a fast way to find integer multipliers m such that either:
{mr} < e
or
1 - {mr} < e

(where {mr}...
Forum: Factoring 2016-11-09, 12:19
Replies: 2
Views: 733
Posted By mickfrancis
Interesting - thanks Jason.

Interesting - thanks Jason.
Forum: Factoring 2016-11-09, 10:41
Replies: 2
Views: 733
Posted By mickfrancis
Zhang's Special Quadratic Sieve

Has anyone had any experience with implementing Zhang's Quadratic Sieve?

I can't seem to find the implementation referred to (as being included with the paper) in Eric Landquist's paper "An...
Forum: Math 2016-08-15, 13:08
Replies: 4
Views: 827
Posted By mickfrancis
It can be rewritten as...

It can be rewritten as \displaystyle\prod_{i=1}^{p} {(1 + \frac{n-p}{i+p})} , I think, but I'm not sure this helps...
Forum: Math 2016-08-15, 12:23
Replies: 4
Views: 827
Posted By mickfrancis
Good thought. I think the p and 2p are transposed...

Good thought. I think the p and 2p are transposed in that ratio? I get: ((n+p)! * p!)/((2p)! * n!), which can be written as \frac{\displaystyle\prod_{i=1}^{p} {(n+i)}} {\displaystyle\prod_{i=1}^{p}...
Forum: Math 2016-08-15, 09:31
Replies: 4
Views: 827
Posted By mickfrancis
Fast calculation of binomial coefficients

If I know {n} \choose {p} (mod m), is there a way of calculating {n+p} \choose {2p} (mod m) with time complexity better than $\mathcal{O}(p)$?
m <= n
p <= n/2
Forum: Factoring 2016-05-06, 08:13
Replies: 2
Views: 1,693
Posted By mickfrancis
Makes sense - thanks Jason.

Makes sense - thanks Jason.
Forum: Factoring 2016-05-04, 14:39
Replies: 2
Views: 1,693
Posted By mickfrancis
Sieving with powers of small primes in the Small Prime variation of the Quadratic Sieve

As I understand it, in the Small Prime Variation of the Quadratic Sieve, primes less than a threshold (Pmin, say) are not used for sieving, as the cost of sieving is disproportionately high given the...
Forum: Factoring 2016-05-03, 08:50
Replies: 3
Views: 825
Posted By mickfrancis
Thanks Jason.

Thanks Jason.
Forum: Factoring 2016-05-02, 17:54
Replies: 3
Views: 825
Posted By mickfrancis
Special-q method for Quadratic Sieve

Does anyone have a reference to / copy of a good description of the special q method as used with the Quadratic Sieve? All I can find is a brief reference in a paper entitled "On the Amount of...
Forum: Factoring 2016-03-31, 06:21
Replies: 5
Views: 936
Posted By mickfrancis
Ah, well, this is my point you see :) I have a...

Ah, well, this is my point you see :) I have a non-sieving implementation, in Haskell, that does generate enough relations to factor a C80 in 14 hours. As far as I can tell, this is currently the...
Forum: Factoring 2016-03-30, 20:57
Replies: 5
Views: 936
Posted By mickfrancis
Can CFRAC really factor a C80 (in less than 14...

Can CFRAC really factor a C80 (in less than 14 hours)?
Forum: Factoring 2016-03-30, 15:24
Replies: 5
Views: 936
Posted By mickfrancis
Thanks Jason. Interestingly, because of the way...

Thanks Jason. Interestingly, because of the way the candidate x values are chosen, subsequent factoring is on values less than sqrt(n), sometimes by a factor of more than 10. Also, the values being...
Forum: Factoring 2016-03-30, 13:47
Replies: 5
Views: 936
Posted By mickfrancis
Non-sieving version of Quadratic Sieve

I've been experimenting with a non-sieving version of the Quadratic Sieve algorithm. To date the performance is nowhere near as good as the basic Quadratic Sieve, let alone SIQS; gathering relations...
Forum: Math 2016-03-29, 18:49
Replies: 9
Views: 1,069
Posted By mickfrancis
I knew I should have invested in those volumes!

I knew I should have invested in those volumes!
Forum: Math 2016-03-29, 14:52
Replies: 9
Views: 1,069
Posted By mickfrancis
I'm not sure why it would be a problem - it's...

I'm not sure why it would be a problem - it's really just modular subtraction on the left and subtraction in a Residue Number System on the right isn't it? (I'm probably missing something here...
Forum: Computer Science & Computational Number Theory 2016-03-29, 14:26
Replies: 9
Views: 1,099
Posted By mickfrancis
Hi Jason, Do you use Bernstein's Scaled...

Hi Jason,

Do you use Bernstein's Scaled Remainder Trees? If not, have you experimented with them at all?

Mick.
Showing results 1 to 25 of 56

 
All times are UTC. The time now is 02:46.

Sun Nov 29 02:46:59 UTC 2020 up 79 days, 23:57, 3 users, load averages: 1.21, 1.19, 1.21

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2020, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.