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Forum: Computer Science & Computational Number Theory 2019-12-09, 22:10
Replies: 28
Views: 10,916
Posted By nesio
Fermat group factorization methods when factors have small prime difference

Here is the test case of Fermat group factorization methods when factors x, y of n = x * y have small prime difference.

The initial data are as follows.
Size number of n is 15 decimal digits.
n...
Forum: Computer Science & Computational Number Theory 2019-12-01, 11:35
Replies: 28
Views: 10,916
Posted By nesio
Are we at the math discussion? ...

Are we at the math discussion?
-------------------------------------
The original topic about "sieve" has changed to "is Fermat's method useful?". Some think it’s useful, others disagree. Thank you...
Forum: Computer Science & Computational Number Theory 2019-11-29, 00:32
Replies: 28
Views: 10,916
Posted By nesio
For instance one can find some examples of cases...

For instance one can find some examples of cases regarding Fermat, factorization, analysis, improvement and so on here:
...
Forum: Computer Science & Computational Number Theory 2019-11-27, 11:07
Replies: 28
Views: 10,916
Posted By nesio
Posted by R.D. Silverman: To factor N it is...

Posted by R.D. Silverman: To factor N it is O(N^(1/2)).
Posted by nesio: Running time of Fermat's method is O(N).
Posted by R.D. Silverman: Wrong. If N = pq it is (p+q)/2 - sqrt(N)....
Forum: Computer Science & Computational Number Theory 2019-11-26, 11:28
Replies: 28
Views: 10,916
Posted By nesio
Running time of Fermat's method is O(N). ...

Running time of Fermat's method is O(N).



Fermat's method is good to fast test whether factors x and y are near at sqrt(N).



Here is another my and co-author paper where improved Fermat's...
Forum: Computer Science & Computational Number Theory 2019-11-25, 10:00
Replies: 28
Views: 10,916
Posted By nesio
If it will be convenient for someone, then this...

If it will be convenient for someone, then this article can be viewed here:...
Forum: Computer Science & Computational Number Theory 2019-10-24, 16:07
Replies: 28
Views: 10,916
Posted By nesio
Hidden numerical sieve with adjustable sieving ability within Fermat's factorization method

Hi! If someone is interested in the subject and knows the Russian language then you can see a new publication here:...
Forum: Factoring 2019-04-12, 21:29
Replies: 55
Views: 5,642
Posted By nesio
Small clarification (we wrote about above): ...

Small clarification (we wrote about above):

5. if the value "k" becomes k > (m*n)^(1/3) then continue the calculations by the RM (Recursive Multiplication) algorithm using rules №№3,4 there also.
Forum: Factoring 2019-04-12, 17:53
Replies: 55
Views: 5,642
Posted By nesio
To get shown improvement of metric q(r) you...

To get shown improvement of metric q(r) you should

1. take SM (Simple Multiplication) algorithm (see pseudo-code in our paper which was pointed out in post #1);
2. add there constant multiplier...
Forum: Factoring 2019-04-11, 18:50
Replies: 55
Views: 5,642
Posted By nesio
In private forum correspondence we have been...

In private forum correspondence we have been asked about examples of speedups for multiplication method of factoring numbers.
Here we attach the results of simple ways of speedups. We took the Table...
Forum: Factoring 2019-04-09, 10:59
Replies: 55
Views: 5,642
Posted By nesio
Til! So for each n that you want to factor,...

Til!

So for each n that you want to factor, you have to evaluate score(m,n) for several m first in order to find a good m. Evaluating score(m,n) includes computing the sum of divisors of m.
...
Forum: Factoring 2019-04-08, 18:55
Replies: 55
Views: 5,642
Posted By nesio
we understood that. you make preliminary...

we understood that.
you make preliminary calculations and place them in captured memory to speed up calculations.we understood that.
you make preliminary calculations and place them in captured...
Forum: Factoring 2019-04-08, 17:15
Replies: 55
Views: 5,642
Posted By nesio
It seems natural for us. There is n as input. So...

It seems natural for us. There is n as input. So we need to define suitable m. After that we can start SM or RM algorithm.
Forum: Factoring 2019-04-08, 13:53
Replies: 55
Views: 5,642
Posted By nesio
Thilo! 36 = (2^2)*(3^2), so "number" = 2*2+1=5,...

Thilo!
36 = (2^2)*(3^2), so "number" = 2*2+1=5, as you wrote.
all divisors of 36 (excluding 1 and 36) are: 2, 3, 4, 6, 9, 12, 18, so "number" = 7, as we wrote.
Forum: Factoring 2019-04-07, 21:29
Replies: 55
Views: 5,642
Posted By nesio
For example such rough model (procedure) gives...

For example such rough model (procedure) gives these values m from n
n m
555 6
5555 12
55555 36
555555 60
5555555 ...
Forum: Factoring 2019-04-07, 19:04
Replies: 55
Views: 5,642
Posted By nesio
Is it working on your data and what are the...

Is it working on your data and what are the results?
Forum: Factoring 2019-04-07, 18:31
Replies: 55
Views: 5,642
Posted By nesio
A rough model of m: Find the maximum of...

A rough model of m:
Find the maximum of (S/(m^1/3)) when m < n^1/3,
where S - the number of all divisors of m (excluding 1 and m).
Here are S and m^1/3 have equal weights in maximize function.
Forum: Factoring 2019-04-07, 17:03
Replies: 55
Views: 5,642
Posted By nesio
Sum means here the amount, quantity.

Sum means here the amount, quantity.
Forum: Factoring 2019-04-07, 12:46
Replies: 55
Views: 5,642
Posted By nesio
I have suggested you to test new rough model on...

I have suggested you to test new rough model on your data that I wrote about.
Forum: Factoring 2019-04-06, 23:42
Replies: 55
Views: 5,642
Posted By nesio
Hi, Thilo! You can check this rough (very...

Hi, Thilo!
You can check this rough (very rough) model of m on your source data of n:
maximum(S/(m^1/3)) and m < n^1/3,
where S - the sum of all divisors of m.
Here are S and m^1/3...
Forum: Factoring 2019-04-04, 19:18
Replies: 55
Views: 5,642
Posted By nesio
We think that we understand "multiplication...

We think that we understand "multiplication method" a little )) But maybe you know better how to choose a multiplier m for your program.
Forum: Factoring 2019-04-04, 14:52
Replies: 55
Views: 5,642
Posted By nesio
That was because we took Hart as is (we wrote...

That was because we took Hart as is (we wrote above).



We meant flexible way (not constant).


See
[1] R. Lehman, ‘Factoring Large Integers’. Mathematics of Computation, Volume 28, Number...
Forum: Factoring 2019-04-04, 14:21
Replies: 55
Views: 5,642
Posted By nesio
DukeBG! You are quite right. We meant curiosly,...

DukeBG! You are quite right. We meant curiosly, interestingly. Thanks.
Forum: Factoring 2019-04-04, 13:11
Replies: 55
Views: 5,642
Posted By nesio
Till! If you dream to accelerate SM...

Till!
If you dream to accelerate SM (a-la-Hart) algorithm please take our advices which are based on our work on MMFFNN method.
1. use constant multiplier 4 in all sqrt equations (4*k*n*m - you...
Forum: Factoring 2019-04-03, 21:15
Replies: 55
Views: 5,642
Posted By nesio
Till! We are not ready to comment on your test...

Till!
We are not ready to comment on your test results now because it needs to analyze your program realization. But it'll demand the time.
However, we have a question. Why your listing contains...
Showing results 1 to 25 of 32

 
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