How much memory do you have?

[fivemack]

You will see attached a list of the numbers mersenneforum has factorised in the last not-quite-two-years.

The sensible thing to do would be to keep attacking the Mersenne numbers from the bottom; 2^863-1 and 2^887-1 are obvious SNFS candidates, 2^899-1 could be either (G185/S271), the time for polynomial selection I think makes it SNFS though G185 would almost certainly get on the Champions list.

I'm wondering whether we might want to leave sense behind and attack 2^941-1. It will take probably six concerted months of sieving by the forces that can be gathered here - a bit less if Dodson joins the fray. But it needs -16e, and that means memory. Hence the poll.

[bsquared]

I voted 1.5 GB/core, as everything I have access to has at least that. Most have more.

How about for the LA? You'd probably need a 16GB machine for that, no? There are 8 cpu workstations around here that scoff at 16GB; I'd need special permission to confiscate one for the time needed to do it but I'd be willing to ask if necessary.

[Andi47]

My machines are running windows XP (32 bit). The largest one (but not running 24/7) has 3 GB available. If 16e is needed, I will be definitely out of the game as I have no machine which has enough memory. (I could run something like Q=10M to 10.1M on the office PC during the christmas holidays if it will still needed then (with the second thread doing prime95 trial factoring or something like this)... )

Originally Posted by fivemack

I'm wondering whether we might want to leave sense behind and attack 2^941-1. It will take probably six concerted months of sieving by the forces that can be gathered here - a bit less if Dodson joins the fray. But it needs -16e, and that means memory. Hence the poll.

How much ECM and P+/-1 did this one have? (it might be worth to do P-1 with B1=1e11 and B2=1e16 or 1e17?)

[FactorEyes]

Good wording on that poll: using units of per core/thread.

This leads to another question: How do core i7 quad-core processors handle 8 threads o' seiving at once?

[Andi47]

Originally Posted by FactorEyes

This leads to another question: How do core i7 quad-core processors handle 8 threads o' seiving at once?

If the machine doesn't have PLENTY of memory, I guess it will be necessary to do less then 8 threads of sieving with 16e and use the other threads for less memory-extensive things.

[Mini-Geek]

My CPU is 64-bit, (and dual-core) it's the OS that's 32-bit. (need a :splittinghairs: smilie) I have a total of 2 GB of memory in this computer, but I also use this computer, so the max memory I'd give it is 1 GB (whether one or two threads). So if it could use 512 MB or less, I could run two threads, otherwise my limit is 1 GB.
Not that my ability to participate should hold too much weight in this...

[FactorEyes]

Originally Posted by Andi47

If the machine doesn't have PLENTY of memory, I guess it will be necessary to do less then 8 threads of sieving with 16e and use the other threads for less memory-extensive things.

I'm more worried about how Intel's memory bus handles the I-O to RAM for 8 such memory-intensive processes. I believe fivemack has an i7 920 in his server farm.

[Andi47]

Which poly would be used for M941? This one? (parameters are an extrapolation of those I have seen in the mersenneforum for large SNFSes;
skew: I guess 2^1/6?)

n: 2468815427808777830385945175570959888649322954010151512577652841207233127175594988619285951813249353482864131674513502872982111245757912252275917421142241044267118542381889815949472721865947896251559297022100274282885756253947868389157090816092206938192397903861973556952725044519
c6: 1
c0: -2
Y0: 182687704666362864775460604089535377456991567872
Y1: 1
skew: 1.12
rlim: 200000000
alim: 200000000
lpbr: 32
lpba: 32
mfbr: 64
mfba: 64
rlambda: 2.6
alambda: 2.6

Edit: Sieving with this poly from Q=70M to Q=70,000,200 with 16e takes 792 MB RAM and ~1.65 GB virtual memory (disk space).

total yield: 44, q=70000213 (7.73545 sec/rel)

(hyperthreaded P4 @ 3.4 GHz, windows XP, second thread busy with yafu)

[fivemack]

On previous large, but not 16e, NFS sieving jobs, I've found that running eight jobs, each assigned with taskset to one thread of the i7/920, gives about 40% more throughput than running four jobs each assigned to one core of the i7/920 with the other threads unloaded.

(IE it can be a 4 x 2.8GHz machine or effectively an 8 x 2GHz machine)

I think I've done the measurements to show that 2^941-1 is still a 32/32 problem, meaning the matrix shouldn't be worse than 30M on a side and will be happy on the i7 that I have already. The sieving's the hard part. I need to figure out whether 200M is the right limit, and for a job this big I ought to get round to doing the analysis of duplication rates to see if it's better to do one side or both.

On a 2.66GHz Core2Duo that I have lying around here, running

./batalov-lasieve/gnfs-lasieve4I16e -a M941.poly -f 70000000 -c 200

top says

22952 twomack   25   0  978m 456m  504 R  100 22.9   1:32.15 gnfs-lasieve4I1

and the output is a reassuringly consistent

total yield: 44, q=70000213 (1.65068 sec/rel)

(there is one useful prime in that range, 0x42c1de7 = 70000103, above which are precisely two ideals)

[Mini-Geek]

How much harder would it be to break the SNFS record (M1039) than M941? Candidates might be M1051 (22-bit factor known, 1030-bit cofactor) or M1061 (no factors known).

[jasonp]

for 1000+ bit numbers you'd need large primes > 32 bits, which msieve cannot currently handle. You would also need > 2^32 relations, which msieve also cannot currently handle (though that's easier to fix).