Factoring humongous Cunningham numbers

[xilman]

Originally Posted by R.D. Silverman

It is quite possible. I have not checked them.

Which factor?

When I get my act together (the Easter weekend, I hope) I'll run the same data-preening code that is used on the other tables I maintain.


Paul

[Phil MjX]

400 (16,80) 19995617469086942401.C134

19995617469086942401=P10 * P10
P10 = 4388625601
P10 = 4556236801

with Tomabechi P-1 (including apr-cl)

oops, 3 min too late !!
P.S.

[R.D. Silverman]

Originally Posted by Greenbank

400 (16,80) 19995617469086942401.C134

19995617469086942401 = 4388625601 x 4556236801

It is probable that this was found by P-1 and that the factor
was not checked for primality...... mea culpa.

[Andi47]

Originally Posted by Andreas Schinde

Done 648 curves on 3^379+2^379 using GMP-ECM at B1=1e6 and B2=default, no factor found. Together with Silverman's ~300 curves this should have finished the 35 digit range.

Now running a some curves with B1=3e6 at this number.

Done 300 curves with B1=3e6, no factor found.

[Greenbank]

Originally Posted by R.D. Silverman

It is probable that this was found by P-1 and that the factor
was not checked for primality...... mea culpa.

Looks that way, those factors are both very smooth:-

4388625600 = 2^6 x 3 x 5^2 x 89 x 10273
4556236800 = 2^11 x 3 x 5^2 x 29663

[Jushi]

Some ECM work (format: [#curves]@[B1 bound], other parameters are the ecm default)

3,2,343- (C136) 650@1e6, 40@3e6
3,2,371- (C141) 2440@3e6
3,2,391- (C161) 345@1e6

[Yamato]

For those who are interested: Look at
http://www.cip.mathematik.uni-stuttg...nt/ex3k2k.html

[R.D. Silverman]

Originally Posted by Yamato

For those who are interested: Look at
http://www.cip.mathematik.uni-stuttg...nt/ex3k2k.html

You have some composites in your results that I have already finished.
I have finished everything for 3^n +/- 2^n up to n = 336 (3^335 - 2^335)
was just finished here a day or two ago by someone else.

I could easily finish everything to n = 400, but I am busy with other
things...

[akruppa]

This thread fits better into Factoring than GMP-ECM. Moved.

Alex

[Pascal Ochem]

The factors of the C111 from 3^372+2^372 are:

840497702349180597209469882198293789055301120886641 (pp51)
766974650561302741840583863816378225180158232426458907919137 (pp60)

with ggnfs (pp=probable prime)

[R.D. Silverman]

Originally Posted by Pascal Ochem

The factors of the C111 from 3^372+2^372 are:

840497702349180597209469882198293789055301120886641 (pp51)
766974650561302741840583863816378225180158232426458907919137 (pp60)

with ggnfs (pp=probable prime)

Nice. I am a bit surprised however. I didn't think enough ECM
effort had been expended to proceed with NFS on these numbers.