[QUOTE=Batalov;353617]Thinking out of the box:
Might there be a benefit of, say, sieving all of them at once? (And maybe not on conventional hardware.)[/QUOTE]

Not without a new mathematical result.

While it is possible to sieve several at once (e.g. M1111, M1117 and M1123 would
share a common sextic polynomial) using current techniques, I don't see
how to generalize.

[QUOTE=R.D. Silverman;353619]Not without a new mathematical result.

While it is possible to sieve several at once (e.g. M1111, M1117 and M1123 would
share a common sextic polynomial) using current techniques, I don't see
how to generalize.[/QUOTE]

I wonder if someone managed to turn Joux's algorithm for finite
fields of small characteristic into a factoring method that works for b^n-1
with very small b and large n.........?

I think it's more likely they just have a ton of computers now, plus possibly a new version of lasieve. Either Franke or Kleinjung said about a year ago that they were working on a new siever, to be ready in a year or so.

NFS@Home can turn around one of those jobs in 2-3 months, so their reservations look ambitious but would be thin evidence of a theoretical improvement.

[QUOTE=jasonp;353664]I think it's more likely they just have a ton of computers now, plus possibly a new version of lasieve. Either Franke or Kleinjung said about a year ago that they were working on a new siever, to be ready in a year or so.

NFS@Home can turn around one of those jobs in 2-3 months, so their reservations look ambitious but would be thin evidence of a theoretical improvement.[/QUOTE]

This seems to be extremely optimistic. M1061 took quite a bit longer than
this and it is smaller than any of the reserved numbers... Adding 30 bits
will double that time.

3 months x 16 == 4 years of work.

I would be pleased to be proven wrong.

M1061 was done before the 64-bit windows siever doubled in speed, plus the sieving ran out of 32-bit special-q and the LA needed 50 days of wall clock time due to cluster management issues.

I'd love to see a theoretical improvement too; we'll have to see what their throughput is :)

[QUOTE=jasonp;353750]M1061 was done before the 64-bit windows siever doubled in speed, plus the sieving ran out of 32-bit special-q and the LA needed 50 days of wall clock time due to cluster management issues.

I'd love to see a theoretical improvement too; we'll have to see what their throughput is :)[/QUOTE]

It's been 24 years since the last theoretical improvement.

BTW, I am looking at trying to adapt Joux's algorithm for DL over
GF(p^n) to factoring its order (p^n-1). There does not seem
to be a connection. But then, I don't have the skills of Joux et.al.

One needs to pass from a function field to a number field; something
that is notoriously difficult. :smile:

[QUOTE=jasonp;353750]M1061 was done before the 64-bit windows siever doubled in speed, plus the sieving ran out of 32-bit special-q and the LA needed 50 days of wall clock time due to cluster management issues.

I'd love to see a theoretical improvement too; we'll have to see what their throughput is :)[/QUOTE]

Maybe they managed to get a lattice siever working on GPGPU or Phi hardware with reasonable efficiency/speedup.

[QUOTE=bsquared;353873]Maybe they managed to get a lattice siever working on GPGPU or Phi hardware with reasonable efficiency/speedup.[/QUOTE]

This appears to be an extremely plausible suggestion!

Would anyone like to put together a betting pool as to when they
will obtain their next factorization? Brownie points to the winner.

What? Not a $10 prize?

[QUOTE=bsquared;353873]Maybe they managed to get a lattice siever working on GPGPU or Phi hardware with reasonable efficiency/speedup.[/QUOTE]

Does anyone care to estimate how much GPU work would be necessary to sieve a number at the lower end of the reserved range?

[QUOTE=philmoore;357041]Does anyone care to estimate how much GPU work would be necessary to sieve a number at the lower end of the reserved range?[/QUOTE]

I suspect that the data needed to answer this question does not exist.
It is highly dependent on the GPU hardware (which may force constraints
on the lattice sieving). It is also implementation and compiler dependent.

Has anyone actually done a full port of GGNFS to a GPU??