F12

[pakaran]

Hi,

Is F12 likely to be a feasible target for NFSnet in the forseeable future? It would definately give great publicity to the project.

[dsouza123]

What is F12 ?

[apocalypse]

The comments in the thread below (What traits make a number a good choice for NFSNET?) indicate that the 12th Fermat number 2^(2^12) + 1, whose composite cofactor is currently 1187 digits, is quite out of the range of NFSNET.

[xilman]

Originally posted by apocalypse
The comments in the thread below (What traits make a number a good choice for NFSNET?) indicate that the 12th Fermat number 2^(2^12) + 1, whose composite cofactor is currently 1187 digits, is quite out of the range of NFSNET.

Correct.

The bleeding edge for SNFS is at 810 bits: M809 has been done, with great effort by Jens Franke and cow-orkers, and NFSET is currently sieving M811.

F_12 has 4096 bits!

We could barely do F_10 (1024 bits) using todays technology, and that would take a massive global collaboration. Just as well that number has already been completely factored by the Elliptic Curve Method.


Paul

[ewmayer]

F_12 has 4096 bits!

We could barely do F_10 (1024 bits) using todays technology, and that would take a massive global collaboration. Just as well that number has already been completely factored by the Elliptic Curve Method.

Plus, there is still a decent chance F12 has a factor of 50-70 digits, in which case it could with reasonable probability be found using ECM or p-1 and a sufficiently large distributed effort (70 digits is probably out of practical reach at presnt, but with enough machines and faster CPUs will probably begin to approach feasibility within the next 10 years). NFS has the better asymptotics in terms of effort vs. factor size, but ECM/p-1/p+1/rho have better asymptotics in terms of effort vs. size of the number being factored.