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Search took 0.14 seconds. Search: Posts Made By: alpertron
Forum: PrimeNet 2021-04-16, 19:00
Replies: 498
Views: 59,447
Posted By alpertron
It appears that user TJAOI reached the 67.000 bit...

It appears that user TJAOI reached the 67.000 bit mark three days ago, as stated in https://www.mersenne.ca/tjaoi.php

We can see that in the last batch, he uploaded a few factors out of order with...
Forum: Data 2021-04-15, 13:36
Replies: 17
Views: 564
Posted By alpertron
In Prime95 running one curve with specified B1...

In Prime95 running one curve with specified B1 and B2 is 10 times slower than running P-1 with the same bounds.

So I think that for some cases with exponents less than about 10 million, P+1 could...
Forum: Data 2021-04-14, 18:52
Replies: 17
Views: 564
Posted By alpertron
When B1 > e (e = exponent), the algorithm p-1...

When B1 > e (e = exponent), the algorithm p-1 loses the advantage of the free "2p" you said above. I found that for several exponents less than 10M, there are people running p-1 with B1 > e.
Forum: Factoring 2021-04-03, 15:59
Replies: 5
Views: 1,800
Posted By alpertron
Solving Diophantine equations of second degree on...

Solving Diophantine equations of second degree on two variables requires integer factorization.

For example: find the integer solutions (x, y) of a circle represented by x2 + y2 = N where N is a...
Forum: Data 2021-03-29, 12:14
Replies: 429
Views: 61,198
Posted By alpertron
The speed of srbase depends also on how many...

The speed of srbase depends also on how many users donate GPU time to the trial factoring project.

According to https://srbase.my-firewall.org/sr5/server_status.php , there are 121 active users,...
Forum: Programming 2021-03-02, 01:53
Replies: 38
Views: 14,950
Posted By alpertron
There were several buffer overflows that I've...

There were several buffer overflows that I've just fixed during this week. Now it works.
Forum: Miscellaneous Math 2021-01-24, 16:14
Replies: 2
Views: 591
Posted By alpertron
I've just tested the first sentence written by...

I've just tested the first sentence written by the OP with values of x up to 10 million using the following line in PARI-GP:

for (x=2,10000000,n=x^3-x-1;if (Mod(x,n)^n==Mod(x,n) &&...
Forum: Programming 2020-12-25, 19:05
Replies: 38
Views: 14,950
Posted By alpertron
You are right. But the Eisenstein criterion...

You are right. But the Eisenstein criterion cannot be used for all polynomials.

There is still more room for optimization.
Forum: Programming 2020-12-25, 18:21
Replies: 38
Views: 14,950
Posted By alpertron
I've just added FFT for modular polynomial...

I've just added FFT for modular polynomial multiplications when the modulus is small. This enables faster factoring when trying to factor integer polynomials, especially when the number of modular...
Forum: Programming 2020-12-13, 21:06
Replies: 38
Views: 14,950
Posted By alpertron
I've just added TeX output to my polynomial...

I've just added TeX output to my polynomial factorization calculator located at https://www.alpertron.com.ar/POLFACT.HTM

For example, the roots of x17 + 1 are:

\begin{array}{l}...
Forum: Programming 2020-11-30, 17:15
Replies: 38
Views: 14,950
Posted By alpertron
I should add TEX output to my calculators when...

I should add TEX output to my calculators when requested by user. That would be an interesting addition to the programs.
Forum: Programming 2020-11-30, 15:47
Replies: 38
Views: 14,950
Posted By alpertron
There is a copy error. Using your input I get: ...

There is a copy error. Using your input I get:


x1 to x3 = 0
r = (19 + 3 * 33^(1/2))^(1/3)
s = (19 - 3 * 33^(1/2))^(1/3)
x4 = 1 + r + s
x5 = 1 - (r + s) / 2 + (i/2) * (r - s) * 3^(1/2)
x6 =...
Forum: Programming 2020-11-28, 23:13
Replies: 38
Views: 14,950
Posted By alpertron
I fixed the LLL routine and optimized the Hensel...

I fixed the LLL routine and optimized the Hensel Lifting. Now the factorization of polynomials of degree less than 1000 with small coefficients can be done in seconds.
Forum: Data 2020-11-26, 02:28
Replies: 7
Views: 1,638
Posted By alpertron
Thanks. So this was a false alarm.

Thanks. So this was a false alarm.
Forum: Data 2020-11-26, 01:06
Replies: 7
Views: 1,638
Posted By alpertron
Too few factors found in 600M to 620M

I've just looked at https://www.mersenne.ca/status/tf/0/1/2/60000 and I found that there should be some hardware error:

21192 factors in the range 600M-610M today in the 72-bit range: only 3...
Forum: Number Theory Discussion Group 2020-10-17, 02:44
Replies: 3
Views: 1,314
Posted By alpertron
Computing the Jacobi symbol is a lot faster than...

Computing the Jacobi symbol is a lot faster than modular exponentiation.

This is the source code I wrote in C language based on Crandall's and Pomerance's Prime Number book:


// Calculate...
Forum: Programming 2020-10-04, 21:20
Replies: 38
Views: 14,950
Posted By alpertron
When the irreducible polynomial has degree >= 5,...

When the irreducible polynomial has degree >= 5, now my code performs the factorization of this polynomials with prime modulus up to 100.

If the conditions of Keith Conrad's paper that you can...
Forum: FermatSearch 2020-10-03, 18:15
Replies: 65
Views: 8,150
Posted By alpertron
Before even thinking on performing the primality...

Before even thinking on performing the primality check of F33, a lot more trial factoring is needed and then someone has to run P-1.
Forum: Programming 2020-10-02, 19:42
Replies: 38
Views: 14,950
Posted By alpertron
All these examples are working now. Thanks for...

All these examples are working now. Thanks for finding the errors.

Please refresh the page to get the current version.
Forum: Programming 2020-10-02, 01:18
Replies: 38
Views: 14,950
Posted By alpertron
I fixed this error. Please refresh the page and...

I fixed this error. Please refresh the page and retry.


Since the application works with integer polynomials, the slash operator performs the division disregarding the remainder.

This means...
Forum: Programming 2020-10-01, 18:32
Replies: 38
Views: 14,950
Posted By alpertron
I've just fixed this error. Please refresh the...

I've just fixed this error. Please refresh the page so the Web page is dated 1 October 2020 and try again.
Forum: Programming 2020-09-30, 03:40
Replies: 38
Views: 14,950
Posted By alpertron
Now the response of the Web application is...

Now the response of the Web application is shorter for polynomials of the form x5+n (n = integer).
Forum: Programming 2020-09-30, 02:53
Replies: 38
Views: 14,950
Posted By alpertron
The values found by the solver are correct as you...

The values found by the solver are correct as you can see by unsetting pretty print, and then factoring it again.

This is the output of the calculator.


R1 = 0
R2 = (15625)^(1/5)
R3 = 0
R4...
Forum: Programming 2020-09-27, 22:47
Replies: 38
Views: 14,950
Posted By alpertron
Hello folks, I have added more features to...

Hello folks,

I have added more features to this calculator at https://www.alpertron.com.ar/POLFACT.HTM

Now it quickly factors integer polynomials with degree up to 1000 using Van Hoeij...
Forum: Factoring 2020-09-25, 03:28
Replies: 40
Views: 17,991
Posted By alpertron
I've just updated the page...

I've just updated the page https://www.alpertron.com.ar/BRILLIANT3.HTM with your results. Thanks a lot.
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