2^772+1 has started

[fivemack]

Since about 11pm on 25th January, my machine's been sieving on 2^772+1.

So I guess we'll see the factors of 10^229+1 around the end of February.

I notice that people seem to be doing the linear algebra on dual-G5 systems; is the code multi-threaded, or are G5 systems just convenient platforms in which to put enough memory to fit an SNFS matrix?

Once I've convinced Mastercard to smite appropriately the supplier of the Kentsfield system I bought whose PSU exploded after three hours' operation, and who took the machine back and refunded me the price of the PSU (I'm guessing end February for this) I'll have a Kentsfield (quad Core2 2.66GHz); I'd be happy to run LA or filtering on it if it's a useful platform for that, though I appreciate that filtering seems more to require knowledge of the black arts than pure gigaops.

[xilman]

Originally Posted by fivemack

Since about 11pm on 25th January, my machine's been sieving on 2^772+1.

So I guess we'll see the factors of 10^229+1 around the end of February.

It's possible, but it would be a rush.

Originally Posted by fivemack

I notice that people seem to be doing the linear algebra on dual-G5 systems; is the code multi-threaded, or are G5 systems just convenient platforms in which to put enough memory to fit an SNFS matrix?

"People" in this context is Richard Wackerbarth. I'm using a single-cpu AMD64 3500+ to run linear algebra for NFSNET. The machine is currently about 30% through the matrix for 5,313+ and it should finish in about a week.

The choice of systems is dictated by what we own. It turns out that my box is markedly faster than Richard's for reasons we don't really understand. My guess is that the SSE2 instructions are particularly effective.

Originally Posted by fivemack

Once I've convinced Mastercard to smite appropriately the supplier of the Kentsfield system I bought whose PSU exploded after three hours' operation, and who took the machine back and refunded me the price of the PSU (I'm guessing end February for this) I'll have a Kentsfield (quad Core2 2.66GHz); I'd be happy to run LA or filtering on it if it's a useful platform for that, though I appreciate that filtering seems more to require knowledge of the black arts than pure gigaops.

Thanks for the offer. We may well take you up on it.

We'd need to know what OS you'll be running (Linux would be by far the easiest for us, hint, hint ) and how much memory it has. Unfortunately, linear algebra in particular uses a lot of memory and at least 2G RAM is needed for the matrices we're now doing. My system has 2.5G and Richard's 4G, I believe.



Paul

[fivemack]

I originally ordered the machine with 2G, once I've got my money back I'll order a 4G system. It doesn't seem possible to put more than 4G into an Intel single-socket system (only four slots, and 2GB DDR2 DIMMs appear not to exist), but 4G ought to suffice.

It will run Linux, probably Ubuntu since Canonical seem to have hired half the Cambridge geeks of my acquaintance as Ubuntu developers.

I assume that the linear algebra is done on 128 bit-vectors in parallel using SSE2, so the large Core2 caches aren't going to fit the whole V ... I assume the linalg does all the obvious tiling optimisations so it tries to stay within cache, I don't know how nicely that'll work in the two-shared-caches environment. Will be interesting to find out.

[is the linear algebra routine available as source-code, or is it more tightly licensed like the linesiever executable?]

[fivemack]

Ah, I'd inadvertently selected a 'show only affordable memory' option; Crucial can sell me 2GB DDR2 DIMMs, but they cost four times as much as 1GB DIMMs, and my budget is finite.

[R.D. Silverman]

Originally Posted by fivemack

Since about 11pm on 25th January, my machine's been sieving on 2^772+1.

What's the current status?

What's next?

[Wacky]

Bob,

We are currently nearing 50% of the sieving on 2,772+. It is projected to run until mid June since the U Gent computers are presently busy on another computation and expect to remain so until some time this Summer.

As a result, I have not worried about "what's next" to any great extent.
I know that Paul and Bruce have discussed some possibilities taking Bruce's ECM work into account.

Richard

[fivemack]

Originally Posted by Wacky

Bob,

We are currently nearing 50% of the sieving on 2,772+. It is projected to run until mid June since the U Gent computers are presently busy on another computation and expect to remain so until some time this Summer.

Richard

Would it be useful for me to run some lattice sieving on 2,772+ (what's the polynomial and the rat/alg bounds?), or would that contend unhelpfully with the line-sievers?

[R.D. Silverman]

Originally Posted by fivemack

Would it be useful for me to run some lattice sieving on 2,772+ (what's the polynomial and the rat/alg bounds?), or would that contend unhelpfully with the line-sievers?

There would be some duplication, but the exact amount would be
almost impossible to predict in advance. I believe that it would be
useful.

[bdodson]

Originally Posted by Wacky

We are currently nearing 50% of the sieving on 2,772+. It is projected to run until mid June since the U Gent computers are presently busy on another computation ...

As a result, I have not worried about "what's next" to any great extent.
I know that Paul and Bruce have discussed some possibilities ...

Not sure that an email or two qualifies as a continuing discussion, but
among the available More Wanted numbers I reported

Maybe some of the base-6 or base-7's? [Paul's] surely
familiar with 6,283- (having done the +), fairly easy at 220;
and 6,284+ also easy at 221. We could clean those up.

There are/were four base-7's; 222.26, then -- ah, there's
7, 269- at 227.33 perhaps in the right range? --- and 7,271-
right nearby at 229 --- then 7,268+ at 226.49. All four seem
to still be on the ecmnet input file; any of these look OK?

Any interest in these; or alternate suggestions that ought to be
considered? The current number has difficulty 233, which seems to
have been a bit long without the Gent cpus. The wanted/most_wanted
base-2s seem to be harder yet (and will move up on the list to be
more attractive on the next list); we finished the base-5s; and the
remaining base-10s also look harder. [cf. 10,239+/- at (233 -vs 239);
likewise 10,236+ (236), with 10,232 at 232.] -Bruce

[R.D. Silverman]

Originally Posted by bdodson

Not sure that an email or two qualifies as a continuing discussion, but
among the available More Wanted numbers I reported



Any interest in these; or alternate suggestions that ought to be
considered? The current number has difficulty 233, which seems to
have been a bit long without the Gent cpus. The wanted/most_wanted
base-2s seem to be harder yet (and will move up on the list to be
more attractive on the next list); we finished the base-5s; and the
remaining base-10s also look harder. [cf. 10,239+/- at (233 -vs 239);
likewise 10,236+ (236), with 10,232 at 232.] -Bruce

The remaining numbers under 768 bits are:

5,317-, 323-
6,283-
284+, 292+
7,263-, 269-, 271-
268+

[bdodson]

Originally Posted by R.D. Silverman

The remaining numbers under 768 bits are:

5,317-, 323-
6,283- 284+, 292+
7,263-, 269-, 271- 268+

Six of these nine numbers are the ones I referred to in my post; these
being the base-6 and base-7 ones on the current More Wanted list.
We've already done four base-5's; other things being equal (such
as ease of polyn and sieving range estimation; snfs difficulty),
Cunningham etiquette suggests wanted numbers before unwanted
(even just not-quite-yet wanted ones), yes? That's two of your
nine that I didn't mention (the base 5s), the third one being 6, 292+.
If this were an issue of a vote, I'd vote to pick from the six ones on
the Selfridge-Wagstaff list first, then the other three.

In any case, neither six nor nine is the correct order of magnitude;
the intended question is which two numbers ought to be done next
(three, maybe if the Gent cpus return). In terms of ecm pretesting,
four of the "wanted six" have already had 2*t50, which is the level
I've been working to (since Bob's 6,281- c162 with three factors in
ecm range). Looks like it wouldn't hurt to take the two large base-7's
early (as they're already in the Opteron queue).

Any other suggestions from c190-c233, difficulty 220-229.9, that seem
plausible candidates to be one of the next three? The base-5s are already
done (to 2*t50). I can also do the large base-6 early (just on case
someone decides on that one? Or to see to larger likelihood that it's
going to need sieving, also). There, that covers Bob's new suggestions.
Any others? And which 2-3 should be next (any other candidates?).
-Bruce