mersenneforum.org  

Go Back   mersenneforum.org > Search Forums

Showing results 1 to 25 of 92
Search took 0.03 seconds.
Search: Posts Made By: Pascal Ochem
Forum: Factoring 2020-08-09, 21:03
Replies: 775
Views: 54,708
Posted By Pascal Ochem
My policy is to increase the lower bound by a...

My policy is to increase the lower bound by a factor 10^100 when the run takes less than one week.
A couple of years ago, it took 3 weeks to prove 10^2100.
The goal of the run of july 2020 was to...
Forum: Factoring 2020-08-02, 20:05
Replies: 775
Views: 54,708
Posted By Pascal Ochem
The new list of roadblock composites is here ...

The new list of roadblock composites is here
http://www.lirmm.fr/~ochem/opn/mwrb2100.txt
and the old one is here
http://www.lirmm.fr/~ochem/opn/old_mwrb2100.txt
Most of the changes are due to the...
Forum: Factoring 2020-07-04, 18:08
Replies: 775
Views: 54,708
Posted By Pascal Ochem
Yes, it is good to see this one down. Thank you...

Yes, it is good to see this one down. Thank you very much, Ryan!
No auto-update, I removed the line from the MWRB file.
The weight of the remaining composites will be updated in a month or so....
Forum: Cunningham Tables 2020-05-15, 23:48
Replies: 112
Sticky: 3- table
Views: 20,849
Posted By Pascal Ochem
3,661- is done. ...

3,661- is done.
http://factordb.com/index.php?query=3%5E661-1
Forum: Cunningham Tables 2020-03-15, 21:47
Replies: 82
Sticky: 5- table
Views: 18,874
Posted By Pascal Ochem
5,449- is done. ...

5,449- is done.

http://factordb.com/index.php?query=5%5E449-1
Forum: Factoring 2019-05-30, 07:19
Replies: 463
Views: 33,288
Posted By Pascal Ochem
The t-files are updated almost daily. Factored...

The t-files are updated almost daily. Factored numbers from mwrb are also quickly removed. However, I do not recompute the weights of the remaining composites.
Also, updating the web page is...
Forum: Factoring 2017-10-16, 22:54
Replies: 17
Views: 1,527
Posted By Pascal Ochem
Forget about the word "forbidden". Just consider...

Forget about the word "forbidden". Just consider the proof as a case analysis. We look for an odd perfect N < 10^2000.

First, we consider the case "127 divides N".
So, we explore the tree for...
Forum: Factoring 2017-10-16, 16:56
Replies: 17
Views: 1,527
Posted By Pascal Ochem
no, p1 < (2/3)k +2 does not help. It does not say...

no, p1 < (2/3)k +2 does not help. It does not say anything in the case of an OPN that is divisible by 3 and some other small primes.

Look at the paper by Pace Nielsen showing that k>=10...
Forum: Factoring 2017-10-14, 23:42
Replies: 17
Views: 1,527
Posted By Pascal Ochem
You are referring to circumvention of roadblocks....

You are referring to circumvention of roadblocks.
This is a different kind of problem.

end game:
Suppose that N is coprime to 3*5*7*11*13*31.
Give a lower bound on N.

circumvention of...
Forum: Factoring 2017-10-14, 22:12
Replies: 17
Views: 1,527
Posted By Pascal Ochem
Sure, an OPN with no factor less than a billion...

Sure, an OPN with no factor less than a billion has at least 693,147,181 prime factors.
This is the easy part, that I call "end game" on my page.
The hard part is the proof that an OPN smaller than...
Forum: Factoring 2017-10-14, 20:05
Replies: 17
Views: 1,527
Posted By Pascal Ochem
Suppose N has no small factor. Say small is less...

Suppose N has no small factor. Say small is less than 1000.
Then every prime factor contributes to at most 1.001 to the abundancy.
Since 1.001^693 < 2, N has at least 694 prime factors.
So N >...
Forum: NFS@Home 2016-09-30, 08:50
Replies: 2,466
Views: 104,356
Posted By Pascal Ochem
FYI, 70841 comes from sigma(19^6) = 701 * 70841. ...

FYI, 70841 comes from sigma(19^6) = 701 * 70841.
With no known factors for sigma(70841^52), we have to branch on 701, which creates a large subtree.
Forum: Factoring 2016-07-28, 23:14
Replies: 14
Views: 1,560
Posted By Pascal Ochem
We may have a better candidate for NFS with two...

We may have a better candidate for NFS with two non-linear polys.
sigma(3^190) = 383*311713*9593931911*P73 (http://factordb.com/index.php?query=%283%5E191-1%29%2F2)
sigma(P73^4) =...
Forum: Factoring 2016-06-22, 18:01
Replies: 14
Views: 1,560
Posted By Pascal Ochem
CADO can use two non-linear polynomials. The...

CADO can use two non-linear polynomials. The third form is proposed by Cyril Bouvier.
We need a cubic polynomial (with small coeffs) that is 0 mod C168 for the common root x=127^33.
It is given by...
Forum: Factoring 2016-06-22, 16:48
Replies: 14
Views: 1,560
Posted By Pascal Ochem
127^131-1

For the remaining composite C168 of 127^131-1 (http://factordb.com/index.php?query=127^131-1), would you use GNFS or one of these polynomials ?

x^6 - 127
x - 127^22

127*x^5 - 1
x - 127^26
...
Forum: Factoring 2015-02-14, 22:06
Replies: 463
Views: 33,288
Posted By Pascal Ochem
Thank you all for the factors. We write N =...

Thank you all for the factors.

We write N = p^e*m^2 for an OPN.
The latest run took about 12 days to obtain N > 10^2000.
The next goal is m > 10^1000.
This will imply the current bound N >...
Forum: Factoring 2015-02-14, 22:06
Replies: 775
Views: 54,708
Posted By Pascal Ochem
Thank you all for the factors. We write N =...

Thank you all for the factors.

We write N = p^e*m^2 for an OPN.
The latest run took about 12 days to obtain N > 10^2000.
The next goal is m > 10^1000.
This will imply the current bound N >...
Forum: Factoring 2014-11-17, 10:34
Replies: 775
Views: 54,708
Posted By Pascal Ochem
Thank you for handling these hard and wanted...

Thank you for handling these hard and wanted composites.
Yes, it is worth factoring the cofactor.
Would GNFS be faster than SNFS now ?
If not, how much running time do we gain thanks to this P43 ?
Forum: Factoring 2014-09-16, 16:02
Replies: 775
Views: 54,708
Posted By Pascal Ochem
You can start at T40. And thank you for the...

You can start at T40. And thank you for the factors you already obtained.
Forum: Factoring 2014-09-11, 11:19
Replies: 775
Views: 54,708
Posted By Pascal Ochem
http://www.lirmm.fr/~ochem/opn/i_51_2000_101.txt ...

http://www.lirmm.fr/~ochem/opn/i_51_2000_101.txt
This file is the intersection of the composites encountered in the proof of the bounds
\Omega(N) >= 2\omega(N)+51, N > 10^2000, and \omega(N) >=...
Forum: Puzzles 2014-08-11, 22:44
Replies: 7
Views: 626
Posted By Pascal Ochem
We can take residues mod 5 in [-2,2] instead of...

We can take residues mod 5 in [-2,2] instead of [0,4] and then factorize.
1^n + 2^n + 3^n + 4^n = 1 + 2^n + (-2)^n + (-1)^n = 1 + 2^n + (-1)^n * (2^n + 1) = (1 + 2^n) * (1 + (-1)^n).
Using...
Forum: Miscellaneous Math 2014-07-21, 09:44
Replies: 5
Views: 1,067
Posted By Pascal Ochem
Your mistake is page 3 when you say 3 |...

Your mistake is page 3 when you say

3 | (P^{alpha+1}/(2*(P-1)))

Take P=13 and alpha=1.
Then P^{alpha+1}/(2*(P-1)) = (13^2-1)/(2*(13-1)) = (13+1)/2 = 7.
And 7 is not divisible by 3.

This is...
Forum: Factoring 2014-01-15, 23:31
Replies: 775
Views: 54,708
Posted By Pascal Ochem
I do not keep track of the ECM work done. We can...

I do not keep track of the ECM work done. We can safely assume that the 37755 composites in t1600 have not been ECMed to the 40 digit level. You can work on a bunch of them, e.g. between lines 6200...
Forum: Factoring 2013-01-15, 00:59
Replies: 463
Views: 33,288
Posted By Pascal Ochem
For the largest component, we deal with numbers...

For the largest component, we deal with numbers with at most 63 digits: everything has been factored. For the total number of prime factors, we do not have many roadblocks, and their impact on the...
Forum: Factoring 2012-10-04, 16:04
Replies: 463
Views: 33,288
Posted By Pascal Ochem
As expected, there are no more roadblocks of...

As expected, there are no more roadblocks of depth 6 in the proof tree for the lower bound of 10^1600. Thank you all for this ! As I see that such factorizations might improve people skills at SNFS,...
Showing results 1 to 25 of 92

 
All times are UTC. The time now is 18:18.

Tue Oct 20 18:18:19 UTC 2020 up 40 days, 15:29, 1 user, load averages: 2.11, 2.00, 2.08

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2020, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.