5^421-1 sieving (reservations closed)

[Andi47]

I just came back to office from holiday and found that my ranges are running much slower than expected.

My range 136-140M is currently done up to q=137377993 - I will keep this one running.

170-174M is done up to q=171450113. Hence running both ranges in parallel uses up approx. 95% of the memory and extremely slows down other applications (like word and excel), I stopped this run and will unreserve the rest of this range. I will upload the relations for 170M to 171.145M today or tomorrow in the evening.

[bsquared]

This past weekend on vacation I found myself driving through Malmo, MN, and couldn't help thinking about this project...

http://maps.google.com/maps?f=q&hl=e...=11&iwloc=addr

[Batalov]

Originally Posted by bsquared

This past weekend on vacation I found myself driving through Malmo, MN, and couldn't help thinking about this project...

...that got me thinking, too. And I realized that in my life I've seen Malmo, apparently... from Kopenhagen, even if barely. And probably better than barely from the plane. And the tunnel-bridge that fooled people in some other thread - by not being the answer to the riddle.

[jasonp]

540k relations from line sieving are uploading now; I'll be able to submit another ~800k tonight or tomorrow.

The line sieving covered |a| <= 4G and b in [1,1200], and required about 20 CPU-days.

Tom, if you still have the scripts that analyzed line sieving relations from 6,383+, could you give a hint how many from this dataset have three large primes, and how many are likely not to be duplicated by the lattice sieving?

I can spare some more CPU time to go farther, but not much farther.

[fivemack]

open A,"< msieve_line_0501_0999.dat";
$novel = 0;
while (<A>)
{
    ($ab,$l,$r) = split ":",$_;
    @left = map hex,(split ",",$l);
    @right = map hex,(split ",",$r);
    $lbig = 0; $rbig = 0; $interesting = 1;
    for $u (@left)
    {
        if ($u > 80000000) {$lbig++;}
    }
    for $u (@right)
    {
        if ($u > 150000000) {$rbig++;}
        if ($u > 50000000 && $u < 350000000) {$interesting = 0;}
    }
    $ct{$lbig.",",$rbig}++;
    $novel += $interesting;
}

print $novel," would not appear in latsieve\n";

for $j (keys %ct)
{
    print $j," ",$ct{$j},"\n";
}

and the results are: 126013 of the 541038 relations would not have been picked up in lattice sieving (IE have no algebraic-side prime between 50M and 350M)

and as for the mix

{rational large primes, algebraic large primes, count}
0,0 7520
0,1 31938
0,2 38522
0,3 18262

1,0 20250
1,1 85531
1,2 101885
1,3 48298

2,0 13527
2,1 56769
2,2 67520
2,3 32277

3,0 1369
3,1 6007
3,2 7528
3,3 3835

I'll update this post when I've got 1-1200. I think we'll be getting about 400k known-non-duplicate relations in a time in which lattice sieving would have got 2.8M raw relations of which perhaps 60% would end up being duplicates.

I'll do another filtering pass at the end of next week, by which time 100-120 and 170-174 ought to be finished: bsquared, should I also wait until your 288-308 range is finished or will that not be until well after the 13th? Expecting ~250M raw relations by then, probably an unusable matrix at the end of September and a not-irredeemable one in mid-October.

The yield at Q=100M (about 1.4Mr/Mq) is very close to the yield at Q=150M, and significantly better than the 1.22Mr/Mq yield at Q=230M. I'm not sure when the diminishing returns from small algebraic factor bases will start kicking in. Should probably run 10k at {40,50,60,70,80}M on a spare core, I'll do that on Monday.

[bsquared]

Originally Posted by fivemack

bsquared, should I also wait until your 288-308 range is finished or will that not be until well after the 13th?

It should be done 110 hrs from now. Uploaded say by next Wednesday evening (the 10th), your time.

[fivemack]

Wow, that's an impressive pace; I guess the cluster upgrade is complete.

[bsquared]

Originally Posted by fivemack

Wow, that's an impressive pace; I guess the cluster upgrade is complete.

It is, but I'm not actually making use of the extra HP. The other 20M ranges I've reserved were tackled with 36 1.4GHz Opteron cores. I'm now using 40 (out of 250 some, most of the rest of which are faster 2 Ghz Opterons). The rest of the cores are queued to obilvion by other people, so I'm thankful to get access to something, at least. And the range would have been ready tomorrow, but for my weekend vacation when I had to leave things idle (but got to see Malmo!).

- ben.

[fivemack]

Originally Posted by Batalov

...that got me thinking, too. And I realized that in my life I've seen Malmo, apparently... from Kopenhagen, even if barely. And probably better than barely from the plane. And the tunnel-bridge that fooled people in some other thread - by not being the answer to the riddle.

I managed to miss both Malmo and the tunnel-bridge; I got into the train in Copenhagen, after a long day visiting museums most of which seemed to be shut, closed my eyes briefly and woke up half an hour beyond Malmo.

I don't recommend long train trips in northern Europe for the scenery; in the Balkans, yes, there are nice mountains all over the place, with bridges, rivers, tunnels and all other manner of scenery, but in the aggregate of about twenty hours from Brussels to Stockholm, the part that happened during daylight could have been an endless repeat of the trip from Cambridge to Peterborough. Flat. Fields. The occasional prosperous-looking market town. More flat. More fields. Sometimes, a cow.

[jasonp]

Originally Posted by fivemack

I'll update this post when I've got 1-1200. I think we'll be getting about 400k known-non-duplicate relations in a time in which lattice sieving would have got 2.8M raw relations of which perhaps 60% would end up being duplicates.

Upload of 940k additional relations just completed. Also, note that relations with three rational large primes would also be missed by the lattice siever (that's a small effect, though).

By your next filtering run I should be able to get you another 400k relations or so.

[fivemack]

Stats from linesieving 1-1200:

1485351 relations. 353914 wouldn't appear in latsieve. The distribution's pretty similar:

0,0 21949
0,1 90519
0,2 106559
0,3 49642

1,0 57967
1,1 238894
1,2 279102
1,3 130241

2,0 37857
2,1 155946
2,2 182481
2,3 84804

3,0 3633
3,1 15716
3,2 19935
3,3 10106