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Search: Posts Made By: alpertron
Forum: Data 2021-05-08, 23:30
Replies: 100
Views: 3,329
Posted By alpertron
The number was based in the tests I performed in...

The number was based in the tests I performed in 2015. If in the meantime, you optimized step 2, it is clear that you can use a larger value of B2 / B1.
Forum: Data 2021-05-08, 15:44
Replies: 100
Views: 3,329
Posted By alpertron
There is no difference because all these...

There is no difference because all these algorithms use smooth numbers. The difference is that we are requiring that p-1, p+1 or p+a are smooth (the absolute value of a in ECM is less than 2*sqrt(p)...
Forum: Data 2021-05-08, 14:08
Replies: 100
Views: 3,329
Posted By alpertron
The algorithms p-1 and p+1 try to find a factor p...

The algorithms p-1 and p+1 try to find a factor p of the Mersenne number when p-1 or p+1 respectively are smooth. This means that all factors of p-1 or p+1 are less than B1 except for one that must...
Forum: Data 2021-05-08, 13:06
Replies: 100
Views: 3,329
Posted By alpertron
It is far better to use B2 = 30 B1. In an...

It is far better to use B2 = 30 B1. In an optimized setting you should get about 5 factors in step 2 for each factor found in step 1.
Forum: Data 2021-05-05, 22:32
Replies: 100
Views: 3,329
Posted By alpertron
The range 400K to 1M was done by myself in 2014.

The range 400K to 1M was done by myself in 2014.
Forum: Data 2021-05-05, 21:16
Replies: 100
Views: 3,329
Posted By alpertron
I believe the complete range 300K-400K with known...

I believe the complete range 300K-400K with known factors is complete with P1=5M, B2=40M. I do not know what bounds you are using.
Forum: Data 2021-05-03, 19:37
Replies: 100
Views: 3,329
Posted By alpertron
In 2015 I ran the P-1 algorithm for all exponents...

In 2015 I ran the P-1 algorithm for all exponents between 0.0M to 2.8M with a known factor with B1 = 500K, B2 = 15M. Unfortunately at that time the server rejected manual results if no factors were...
Forum: PrimeNet 2021-04-24, 16:14
Replies: 2
Views: 244
Posted By alpertron
Missing P+1 type in account summary

I found that the type is blank in the row that corresponds to P+1 in the account summary, in page https://www.mersenne.org/account/?details=1 .

I also found that in...
Forum: PrimeNet 2021-04-16, 19:00
Replies: 498
Views: 61,189
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: 23
Views: 1,138
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: 23
Views: 1,138
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: 1,933
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: 457
Views: 67,824
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: 16,372
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: 663
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: 16,372
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: 16,372
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: 16,372
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: 16,372
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: 16,372
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: 16,372
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: 21
Views: 2,128
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: 21
Views: 2,128
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: 1,505
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: 16,372
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...
Showing results 1 to 25 of 1000

 
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