The factorization of primorials +/- 1

[Joppe_Bos]

Originally Posted by fivemack

P155+, 5000 curves @ 3e6, no factor. Stopping for the time being.

Ok thanks for the help. I will continue the remaining primorials + 1 with B1=3e6.

I found the following factor:
P154# + 1 (c329) = p40 * c290
With p40 = 3303596594386506896234719892581600613351

and run the following curves:
Done 6170 curves on P101# - 1 with B1=11e6
Done 5180 curves on P104# - 1 with B1=11e6
Done 3900 curves on P106# - 1 with B1=11e6

Done 5200 curves on P135# - 1 with B1=3e6
Done 2500 curves on P136# - 1 with B1=3e6
Done 2500 curves on P144# - 1 with B1=3e6
Done 2500 curves on P145# - 1 with B1=3e6
Done 2500 curves on P147# - 1 with B1=3e6
Done 2500 curves on P148# - 1 with B1=3e6

[Joppe_Bos]

After 7411 curves with B1=43e6 I found a nice p57 using B1=43000000, B2=240490660426, polynomial Dickson(12), sigma=1911078686.
This is my personal record for ECM!

(P86# - 1) / 16054891 = (443# - 1) / 16054891 = (c175) = p57 * p119
With p57 = 655434840668053073728154994129346913485884418128724135229

Furthermore I ran:
Done 3000 curves on P131# - 1 with B1=3e6
Done 4000 curves on P151# - 1 with B1=3e6

Done 3000 curves on P151# + 1 with B1=3e6
Done 3000 curves on P152# + 1 with B1=3e6
Done 3000 curves on P154# + 1 with B1=3e6

Tables have been updated.

BTW fivemack are you still running P109+ with GNFS?

[sean]

Originally Posted by Joppe_Bos

After 7411 curves with B1=43e6 I found a nice p57 using B1=43000000, B2=240490660426, polynomial Dickson(12), sigma=1911078686.
This is my personal record for ECM!

(P86# - 1) / 16054891 = (443# - 1) / 16054891 = (c175) = p57 * p119
With p57 = 655434840668053073728154994129346913485884418128724135229

Very nice. Congratulations.

[wblipp]

Originally Posted by Joppe_Bos

With p57 = 655434840668053073728154994129346913485884418128724135229

Congratulations! Be sure to notify Paul Zimmermann. This is the 10th largest factor found so far in 2007, and the 20th largest factor ever found!

http://www.loria.fr/~zimmerma/records/ecmnet.html#top10

http://www.loria.fr/%7Ezimmerma/records/top100.html

William

[fivemack]

I'm still running P109+; at least, I hope I am: I'm in a hostel in Serbia at the moment, but I left the computers running in England, and they generally don't crash over a two-week period.

[Joppe_Bos]

After 2500 curves with B1=43e6 I found a new p49:
(P106# + 1) / 10304867 = c230 = p49 * c182
With p49 = 1238100941122198276782644721797024153390458544753

Furthermore I ran the following curves:
Done 3000 curves on P152# - 1 with B1=3e6
Done 3000 curves on P153# + 1 with B1=3e6

this means all numbers have been checked with ECM up to the 40-digit level.

[roger]

This thread caught my eye a while ago, and in my spare time I worked on some factorizations of similar numbers. Instead of p(n)#+-1 I worked on p(n)#+p(n). Of course these can't be prime - always divisible by p(n) - but a coordinated effort on something looked interesting.

When I plotted the values of the penultimate factor onto a graph, it was an interesting picture. Hope this is noteworthy to the mersenne demigods!

Note that because it's been a spare time project, I have not done much.

Roger

[wblipp]

Congratulations! Paul Zimmermann's lists have been updated to show this is the 10th largest factor found so far in 2007, and the 20th largest factor ever found.

http://www.loria.fr/~zimmerma/records/ecmnet.html#top10

http://www.loria.fr/%7Ezimmerma/records/top100.html

[Jens K Andersen]

Originally Posted by roger

Instead of p(n)#+-1 I worked on p(n)#+p(n). Of course these can't be prime - always divisible by p(n)

In what is the quotient?
(p(n)#+p(n))/p(n) = p(n)#/p(n)+1 = p(n-1)#+1

[henryzz]

surely u could use msieve for some of these

[roger]

surely u could use msieve for some of these

I have, and actually, the smallest composite is only 95 digits - around 5 hours on my computer. I have barely checked these composites with ECM though, and I plan to do this first.

Currently though, I am working on a C114 with msieve (a personal Homeprime) which will probably take around 200 hours, if not more.

As for the quotient, I don't know in algebraic terms. I'll have a look through the factor file.

Roger