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Forum: Science & Technology 2021-06-10, 18:12
Replies: 223
Views: 13,647
Posted By alpertron
Unfortunately in Argentina we cannot receive...

Unfortunately in Argentina we cannot receive vaccines from the USA. Pfizer is banned by law and Moderna and Johnson and Johnson are not approved by the government. So we can receive only Astra Zeneca...
Forum: Science & Technology 2021-06-10, 17:48
Replies: 223
Views: 13,647
Posted By alpertron
I've just received the first shot of Sputnik V....

I've just received the first shot of Sputnik V. The second dose will be in September.
Forum: News 2021-06-10, 12:26
Replies: 11
Views: 3,155
Posted By alpertron
I've just checked that I can select Mersenne...

I've just checked that I can select Mersenne Research on smile.amazon.com using my account, but the last time I used Amazon was in 2011, because it is very expensive for me.

I have to pay 65% of...
Forum: PrimeNet 2021-05-27, 23:55
Replies: 9
Views: 362
Posted By alpertron
Problem when sending manual results on M10855723

I've just sent to Primenet three results of running P-1 on exponents M10,xxx,xxx using Colab work using the manual submission form.

Two of them were accepted successfully, but the third number...
Forum: Data 2021-05-08, 23:30
Replies: 107
Views: 4,848
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: 107
Views: 4,848
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: 107
Views: 4,848
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: 107
Views: 4,848
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: 107
Views: 4,848
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: 107
Views: 4,848
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: 107
Views: 4,848
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: 290
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: 544
Views: 65,128
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: 1,447
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: 1,447
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: 2,061
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: 482
Views: 75,049
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: 17,929
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: 741
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: 17,929
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: 17,929
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: 17,929
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: 17,929
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: 17,929
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: 17,929
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.
Showing results 1 to 25 of 1000

 
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