Pépin tests of Fermat numbers beyond F24

[cxc]

Originally Posted by Gary

As a cross reference, I just posted a description of the Fermat cofactor study that Wilfrid and I completed here.


Hi Catherine. It sounds like you are thinking along the same lines as Wilfrid and I did. As far as I know, mprime has not yet added prints of the Suyama test Res64 and Selfridge-Hurwitz residues. That is why I wrote the "cofact" helper program. If you are interested, I can post the C source and Linux binary for it in the other thread.

Dear Gary,

I would be most interested in having a look at your cofact add-on, seeing as I saved proofs for the PRP runs on F17 to F26, generated by mprime 30.10; as a ‘sanity check’, I gather these ought to return the additional values I was after, by using cofact’s mode 3, which hopefully match the various residues in your spreadsheet. A Linux binary would be capital!

Of course in the long term, should another prime factor turn up for any of these smaller Fermats for which Pépin residues were obtained, something like cofact would be most useful for seeing whether the new factor helps complete the factorisation. (I know it’s unlikely, but one can dream.)

Edited to add (after reading Wilfrid’s page again, more carefully): Wow! Congrats on finding a factor for F1784!

[Gary]

Originally Posted by cxc

I would be most interested in having a look at your cofact add-on, seeing as I saved proofs for the PRP runs on F17 to F26, generated by mprime 30.10; as a ‘sanity check’, I gather these ought to return the additional values I was after, by using cofact’s mode 3, which hopefully match the various residues in your spreadsheet. A Linux binary would be capital!

Of course in the long term, should another prime factor turn up for any of these smaller Fermats for which Pépin residues were obtained, something like cofact would be most useful for seeing whether the new factor helps complete the factorisation. (I know it’s unlikely, but one can dream.)

I posted the cofact source and binary in the "Fermat cofactors" thread here. Just trying to keep all the Fermat cofactor / cofact stuff in one thread