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Search: Posts Made By: Pascal Ochem
Forum: Factoring 2021-07-11, 13:17
Replies: 987
Views: 118,933
Posted By Pascal Ochem
Henry: Luckily, the ad-hoc argument is simple...

Henry:
Luckily, the ad-hoc argument is simple (and computer-free) thanks to a Fermat prime raised to large power (5^520) and a special prime that is already specified.
It is good enough for now, we...
Forum: Factoring 2021-07-09, 10:49
Replies: 987
Views: 118,933
Posted By Pascal Ochem
no OPN is smaller than 10^2200

The run for [$]10^{2200}[/$] is now over. The program gave up on the following branches:

[$]127^{192}[/$] / [$]19^2[/$] [$]3^6[/$] [$]1093^2[/$] [$]398581^{102}[/$] / [$]7^2[/$] / [$]13^1[/$]...
Forum: Factoring 2021-05-24, 21:35
Replies: 987
Views: 118,933
Posted By Pascal Ochem
The run with bound [$]10^{2100}[/$] just finished...

The run with bound [$]10^{2100}[/$] just finished and we see the impact of the C301.
The old file has 1589 composites.
http://www.lirmm.fr/~ochem/opn/old_mwrb2100.txt
The new file has 1192...
Forum: Factoring 2021-05-10, 20:26
Replies: 987
Views: 118,933
Posted By Pascal Ochem
For the factor P220 of the C301, I have factored...

For the factor P220 of the C301, I have factored 1+P220 by finding a P48.
And now the roadblock has completely disappeared for the bound [$]10^{2200}[/$].
I started the full run for proving the...
Forum: Factoring 2021-05-05, 20:19
Replies: 987
Views: 118,933
Posted By Pascal Ochem
Ryan, frmky, thank you. Now I explore the...

Ryan, frmky, thank you.
Now I explore the subtrees unlocked by the new factors for lower bounds on many parameters of an OPN.
Forum: Factoring 2021-03-25, 12:10
Replies: 987
Views: 118,933
Posted By Pascal Ochem
Thanks! That is a lot of factors, with an...

Thanks! That is a lot of factors, with an explicit lower bound on the ECM effort for these numbers.
Forum: Factoring 2020-12-18, 21:58
Replies: 987
Views: 118,933
Posted By Pascal Ochem
The run for [$]10^{2200}[/$] hit this roadblock: ...

The run for [$]10^{2200}[/$] hit this roadblock:
[$]11^{18}[/$] [$]6115909044841454629^{16}[/$] / [$]3^4[/$] / [$]5^1[/$] / [$]103^{172}[/$] / [$]227^4[/$] [$]2666986681^{36}[/$].
It is difficult...
Forum: Factoring 2020-12-03, 13:18
Replies: 987
Views: 118,933
Posted By Pascal Ochem
The old and new mwrb2100 are here: ...

The old and new mwrb2100 are here:
http://www.lirmm.fr/~ochem/opn/old_mwrb2100.txt
http://www.lirmm.fr/~ochem/opn/mwrb2100.txt

The run for 10^2200 started 17 days ago and is about halfway...
Forum: Factoring 2020-11-24, 13:34
Replies: 987
Views: 118,933
Posted By Pascal Ochem
mwrb2100 will be updated soon, but I can already...

mwrb2100 will be updated soon, but I can already tell that the weight of sigma(6115909044841454629^16) drops from 65263134 to 60351951.

Both! However, ECM on mwrb2100 will not be very fruitful:...
Forum: Factoring 2020-11-08, 14:05
Replies: 987
Views: 118,933
Posted By Pascal Ochem
There is already a file t2200 of...

There is already a file t2200 of first-encountered composites replacing t2100.
There will be a last update of mwrb2100 in a week or two, only to see the impact of your nearly 300 factors.
There...
Forum: Factoring 2020-11-02, 13:21
Replies: 987
Views: 118,933
Posted By Pascal Ochem
Thank you Ryan ! You factored more than one in...

Thank you Ryan !
You factored more than one in ten most wanted composites.
Now I can try to get to 10^2200.
Forum: Factoring 2020-08-09, 21:03
Replies: 987
Views: 118,933
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: 987
Views: 118,933
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: 987
Views: 118,933
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: 51,077
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: 49,450
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: 45,229
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: 3,069
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: 3,069
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: 3,069
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: 3,069
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: 3,069
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: 159,084
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: 2,786
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: 2,786
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...
Showing results 1 to 25 of 103

 
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