Now what (III)

[bsquared]

Originally Posted by fivemack

2^827-1 is the same sort of size and is a Mersenne number (also a C171, but I'd do it by SNFS to avoid the extra logistics involved with a polynomial search), though that's starting to impinge on NFSNET's realm.

Does anyone else have a favourite C170ish general composite or S250ish SNFS number?

I guess I would rather do 2^857-1. The same(ish) difficulty as 2^827-1 (258 vs. 249), but it is a C255 so there is no GNFS ambiguity. Also because I have a childish delight in finding the factors of really big numbers.

Whatever the project, I will contribute some effort toward sieving and/or poly search, but not at the level as for 5-421. Got a number of other projects on my plate right now.

- ben.

[bdodson]

Originally Posted by bsquared

I guess I would rather do 2^857-1.
- ben.

We'd rather you didn't!! It's reserved for Childers/Dodson, sieving
is done; matrix will take about 3 weeks. -Bruce

[bsquared]

Very sorry! I didn't check the reservation page.

[bdodson]

Originally Posted by bsquared

...it is a C255 so there is no GNFS ambiguity. Also because I have a childish delight in finding the factors of really big numbers.

If you don't mind the 2+ list (instead of 2-), there's 2, 923+ c254
at difficulty c. 257. Larger index, so not near the first_five_holes.
Already tested past t55. A plausible candidate for the champion
pentultimate factor (second place ..., needs a p121).

Greg sent in the M857 reservation along with M823 and P823,
both recently completed by NFSNET. For a challenge somewhat
closer than M1061, I like M941 at C280. The first large 2- snfs
that seems to be a bit past current C/D range. (M937 being no
longer large, c221/2 = p111 below p120, after a recent p57.
M919 C261 large, almost within range; next large one way out
at M991 C264.)
-bd

[R.D. Silverman]

Originally Posted by bdodson

If you don't mind the 2+ list (instead of 2-), there's 2, 923+ c254
at difficulty c. 257. Larger index, so not near the first_five_holes.
Already tested past t55. A plausible candidate for the champion
pentultimate factor (second place ..., needs a p121).

Greg sent in the M857 reservation along with M823 and P823,
both recently completed by NFSNET. For a challenge somewhat
closer than M1061, I like M841 at C280. The first large 2- snfs
that seems to be a bit past current C/D range. (M937 being no
longer large, c221/2 = p111 below p120, after a recent p57.
M919 C261 large, almost within range; next large one way out
at M991 C264.)
-bd

??? M841 is C254, not C280.....Perhaps you mean M941???
M841 was completed.

There is also M907, M919, M923

If you like base 12, there is 254+ and 257-.

[bsquared]

Originally Posted by bdodson

For a challenge somewhat
closer than M1061, I like M841 at C280. The first large 2- snfs
that seems to be a bit past current C/D range.

I think you mean M941. That would be a (2nd place) Champion in two different spots, as well as possibly a third (largest penultimate factor). It's also "efficient", in that there are no large known factors, so the difficulty is very near the composite size. For all those reasons it would be cool to do, but also very difficult, especially in the linalg.

[Andi47]

...EM43...

Originally Posted by Andi47

Has this one been p+1'ed?

yes it has - I did it myself back in may. 3 runs with B1 = 2^32-1 and B2 = 1e15, no factor found. If somebody (Alex?) wants to extend B2 to 1e18, the savefiles can be found in this post.

Sean also reports, that he has extended the p-1 effort for EM43 to B1 = 1e12, B2 = 1e17.

[bdodson]

Originally Posted by R.D. Silverman

??? M841 is C254, not C280.....Perhaps you mean M941???
M841 was completed.

There is also M907, M919, M923

If you like base 12, there is 254+ and 257-.

The typo correction is recorded here at :24, the reply at :25, but
thanks anyway. M919 is listed in my post as nearby the current
Childers/Dodson range; I've already spent quite some time on ecm
(on pcs not suitable for sieving). M923 is small by the condition
referred to, 240/2 = p120 would be an extremely narrow window
for bumping the current 2nd champion (pending Sam's next update,
with the 6,392+ factorization, p127*p136). M907 seems to be
already factored.

Greg reported that 12,257- is hard (in discussions following 12,241-).
The largest, likely hardest among the first five holes.

Ben: Yes (aside from the typo; since corrected), M941 (that'd
be the unique c280 on the 2- list) is a nice challenge; Sam has
M941 = 7529*M280. That number. Sorry for the distraction.
-Bruce

[bsquared]

Originally Posted by bdodson

M941 ..... Sorry for the distraction.
-Bruce

To continue the distraction to this thread (since I'm not trying to advocate it as a possibility for Tom to consider)... I test sieved this number just for kicks a few months ago.

Using 32 bit lp bounds on both sides (requiring a half billion or so total relations) produces about 0.85 rels/q on average over a 100Mq range using gnfs-lasieve4I15e. This roughly extrapolates to sieving about 600Mq, taking about 100 days per CPU of each of 64 continuously applied cpus (I used 2GHz opteron 270's for that estimate). The 100Mq test range doesn't do justice to the likely much larger yield decrease in very high Q ranges, so this is probably optimistic. Going to 33 bits per side (maximum possible using gnfs-lasieve* without a recompile) might help with this, and requires about the same 600Mq to get ~ 900Mrels.

I've no idea what size matrix these would produce, other than *big*, even though I've factored in a healthy amount of oversieving. I'd hope for < 25M square. This is the real limiter, IMO. Assuming it comes in at that size, I have a machine that could tackle it, but it would take months, even with 8 threads, and assuming the sysadmins would let me have it for that long.

Anyway. I change my vote to σ(3221^72).

[frmky]

I also will be contributing only a few resources to this effort, but I agree that both 3221^73-1 and EM43 are desirable candidates of a reasonable size.

Greg

[rogue]

Originally Posted by frmky

I also will be contributing only a few resources to this effort, but I agree that both 3221^73-1 and EM43 are desirable candidates of a reasonable size.

Greg

Pardon me for asking what some might deem a stupid question, but what is EM43? Googling doesn't help.