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Search: Posts Made By: Sam Kennedy
Forum: Factoring 2020-06-14, 11:05
Replies: 22
Views: 1,174
Posted By Sam Kennedy
So I implemented Till's method of trial division,...

So I implemented Till's method of trial division, however it takes the same amount of time to complete (give or take a few 1/100ths of a second).

I did however remove all the string -> mpz_t...
Forum: Factoring 2020-06-13, 22:46
Replies: 22
Views: 1,174
Posted By Sam Kennedy
This is very interesting, thank you for...

This is very interesting, thank you for explaining it. I’ll implement this approach tomorrow and see how it performs. Do you divide by powers of primes? I currently use a while loop, so while the...
Forum: Factoring 2020-06-12, 18:43
Replies: 22
Views: 1,174
Posted By Sam Kennedy
I tried implementing a map of sieve indices to a...

I tried implementing a map of sieve indices to a set of indices in the factor base which are divisible at that location. It worked but was slower than scanning the sieve array and checking the sieve...
Forum: Factoring 2020-06-11, 22:52
Replies: 22
Views: 1,174
Posted By Sam Kennedy
I've played around with the parameters, I've also...

I've played around with the parameters, I've also taken jasonp's suggestion of sieving from [0, 2*M] instead of [-M,M], the time for sieving and trial division is down to 26 seconds now :)

...
Forum: Factoring 2020-06-11, 19:38
Replies: 22
Views: 1,174
Posted By Sam Kennedy
Thank you for this suggestion, I've just run the...

Thank you for this suggestion, I've just run the timings now, I've also calculated how many polynomials are used and how many times the trial division routine is called, which seems a lot compared to...
Forum: Factoring 2020-06-11, 15:38
Replies: 22
Views: 1,174
Posted By Sam Kennedy
Question Optimising Sieving & Trial Division for SIQS

I finally managed to get a working implementation of SIQS :smile:

However it still has a long way to go in terms of efficiency and speed.

My code can be found here:...
Forum: Factoring 2020-06-09, 21:38
Replies: 13
Views: 684
Posted By Sam Kennedy
That was part of it, I managed to fix that but it...

That was part of it, I managed to fix that but it turns out the issue was a mix of my factor base indices being off-by-one and my partial-combining routine interacting incorrectly with my trial...
Forum: Factoring 2020-06-09, 11:56
Replies: 13
Views: 684
Posted By Sam Kennedy
This is weird, I could have sworn I got 79 a...

This is weird, I could have sworn I got 79 a bunch of times using the calculator that comes with windows, but now I'm getting 26, maybe I imagined it, maybe I was temporarily teleported to an...
Forum: Factoring 2020-06-09, 10:11
Replies: 13
Views: 684
Posted By Sam Kennedy
Thank you very much for your response, I'm...

Thank you very much for your response, I'm looking at things a lot closer and I have a specific example to show:

N = 523022617466601111760007224100074291200000001
A = 539044587247440481
B =...
Forum: Factoring 2020-06-08, 21:50
Replies: 13
Views: 684
Posted By Sam Kennedy
MPQS Trial Division Optimisation

I've been adding debugging statements to my MPQS implementation and I can't figure out why this is happening:

I'm currently trial dividing by every prime in the factor base, and as far as I...
Forum: Factoring 2020-06-07, 15:58
Replies: 2
Views: 306
Posted By Sam Kennedy
I figured it out, turns out I needed to maintain...

I figured it out, turns out I needed to maintain both sides of the relation X^2 = Y^2 (mod N), I was attempting to combine x1 and x2 to get X, then use X to calculate Y which was not correct.

Just...
Forum: Factoring 2020-06-07, 08:44
Replies: 2
Views: 306
Posted By Sam Kennedy
How to combine relations for MPQS?

I am attempting to combine two relations for MPQS but I'm having trouble with the mathematics behind it:

I have:

x1 = ((-4102948192782457639498)^2 - N) / 425579045527454809
x2 =...
Forum: Factoring 2016-12-02, 19:01
Replies: 0
Views: 439
Posted By Sam Kennedy
Are these polynomials being generated correctly?

I'm just double checking that the polynomials in my upcoming implementation of the MPQS are being generated correctly:

n = 1287871475892167
First prime is near sqrt(sqrt(2*N)/M), where M is the...
Forum: Factoring 2016-11-28, 15:13
Replies: 1
Views: 574
Posted By Sam Kennedy
Bypass Sieving Stage?

I had an idea but I thought I would ask here as to not waste time. After the first pass of the sieving algorithm, there will be a set of indices which have accumulated a value higher than some...
Forum: jasong 2013-02-08, 11:10
Replies: 30
Views: 1,300
Posted By Sam Kennedy
But then there's the question of which version of...

But then there's the question of which version of the bible? King James? American Standard? Common English? New International Version?

There's loads of variations, each would result in different...
Forum: Miscellaneous Math 2013-02-07, 11:53
Replies: 4
Views: 767
Posted By Sam Kennedy
Depending on the complexity of the maths...

Depending on the complexity of the maths involved, I might be able to write my own sieve.

The way I'm searching is fixing k and incrementing n.

The limit for k is the same as the limit for an...
Forum: Miscellaneous Math 2013-02-07, 11:35
Replies: 4
Views: 767
Posted By Sam Kennedy
I'm not sure how sieving applies to this, I know...

I'm not sure how sieving applies to this, I know it's used in the other prime searching projects but I've never understood how it's actually used.

The only thing I can think of is generating a...
Forum: Miscellaneous Math 2013-02-07, 10:36
Replies: 4
Views: 767
Posted By Sam Kennedy
Fun Sequence

I've started searching this sequence for prime numbers:
((n+1)\mathrm{!}\ - \ n\mathrm{!})k + 1

I like this sequence because N-1 is easy to factor so proving primality is straight forward.

Are...
Forum: Programming 2013-01-25, 16:50
Replies: 4
Views: 917
Posted By Sam Kennedy
Would the extended Euclidean algorithm suffice?...

Would the extended Euclidean algorithm suffice? Or would I have to use something more advanced?
Forum: Programming 2013-01-25, 11:41
Replies: 4
Views: 917
Posted By Sam Kennedy
Modular Inversion Bottleneck

I finally got my MPQS code working, it's much faster than my QS implementation, but it's still pretty slow once the numbers get up to around 70 digits.

I have experimented with smaller blocks...
Forum: Programming 2013-01-21, 14:23
Replies: 18
Views: 836
Posted By Sam Kennedy
It's working now, it turns out there was a small...

It's working now, it turns out there was a small error in how I was calculating the solutions, the speed increase is quite noticeable, thank you for explaining this optimisation :smile:
Forum: Programming 2013-01-20, 08:30
Replies: 18
Views: 836
Posted By Sam Kennedy
It's just when I use the range 0 to M, instead of...

It's just when I use the range 0 to M, instead of -M to M, everything works as it should, when I switch back to [-M, M], the solutions calculated for which index to begin sieving at are completely...
Forum: Programming 2013-01-20, 01:23
Replies: 18
Views: 836
Posted By Sam Kennedy
I've been assuming that when you have a sieve...

I've been assuming that when you have a sieve array from [-M, M], it is indexed as follows:

Say M = 15, so the array runs from -15 to 15, and contains 31 elements. Element 0 would be -15, element...
Forum: Programming 2013-01-19, 01:53
Replies: 18
Views: 836
Posted By Sam Kennedy
Of course I could test it, I just thought it...

Of course I could test it, I just thought it would be worth asking since it may not necessarily speed up the sieving by much, and I still have the linear algebra phase to code, and I need to fix this...
Forum: Programming 2013-01-18, 23:27
Replies: 18
Views: 836
Posted By Sam Kennedy
I've still got quite a bit to code before I start...

I've still got quite a bit to code before I start with that
Showing results 1 to 25 of 82

 
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