Status 5,31[13][+-]

[xilman]

Originally Posted by xilman

Something seems to be wrong with that file, though I know not what.

The prototypical version on my achine is fine, though with a different MD5 hash. It must have been corrupted when uploaded.

A corrected one is now on my website.


Paul

[R.D. Silverman]

Originally Posted by fatphil

Bob - are these Phi_n(3,2) ones all *sieve jobs, or are they still in ECM territory? (Is there a table of candidates/stati?)

Phil

I missed seeing this question.

All of these numbers are being done with SNFS. There are currently
8 left. One has been sieved (3,2,391-) and one is being sieved (3,2,367-).

[R.D. Silverman]

Originally Posted by Wacky

Just a note to keep everyone informed.

We are making progress!

Because of a number of factors, the least of which being "a real job", the NFSNet effort has somewhat degenerated into a "hard core" of participants.
Two of our contributors are each doing about 1/3 of the sieving. The rest of us make up the other 1/3.

We have completed sieving on 5,311- and 5,311+. We are about 3/4 finished with the estimated sieving on 5,313- and should finish it this week (unless I then find that my estimates were too low). On a couple of my personal machines, I am now starting a survey sieving in 5,313+ in order to better estimate to total requirement. I expect to start switching other sievers to this project at the end of the week. It should take about a month if the preliminary estimates are correct and the level of participation remains unchanged.


Richard

Any news?

I have finished sieving both 6,281- and 5,329-. The LA failed on
my first attempt for 6,281-. I ran some memory diags which turned up
nothing and am trying again. It should finish in 4 days.

5,329- is filtered and waiting for 6,281- to finish before I do the LA.

These will be my last two Cunningham numbers for a while. I no longer
have access to sufficient resources.

[Wacky]

Originally Posted by Wacky

Two of our contributors are each doing about 1/3 of the sieving. The rest of us make up the other 1/3.
We have completed sieving on 5,311- and 5,311+. We are about 3/4 finished with the estimated sieving on 5,313- and should finish it this week (unless I then find that my estimates were too low). On a couple of my personal machines, I am now starting a survey sieving in 5,313+ in order to better estimate to total requirement. I expect to start switching other sievers to this project at the end of the week. It should take about a month if the preliminary estimates are correct and the level of participation remains unchanged.

My guess is that we will finish sieving on 5,313+ by Thanksgiving. Hopefully Paul will have found time to figure out a reasonable "next" project by that time.

On the "back end":
I have run into a serious "glitch" on by G5 system. I have been getting unreproducible results and other internal errors that indicate that I either have a hardware problem, or have hit some OS constraint that is causing bad results.
None of the other programs that I run seem to have any problems.

On 5,311-, I estimate that we can build a matrix slightly greater than 5M.
However, the above mentioned errors have prevented me from completing that task.

On 5,311+, after transferring the data to another machine, I did succeed in building a matrix that has 4727789 rows, matrix weight of 258403863, and occupies 1.4GB. I project that I will complete the Block Lanczos solution of it on November 30.

Richard

We have temporarily lost the resources from one of those contributors. But I anticipate that those resources will return in a month, or so. As a result, we did not complete the sieving for 5,313+ by Thanksgiving, but should have it done in another week to 10 days. We are currently at 87% for my extimated sieving.

Given the slow progress of my LA resources, I also decided to do a bit more sieving on the (sieving) "completed" projects in the hopes of reducing the matrix size, and thus the time required to solve them.

The LA for 5,311+ is right on schedule. I have completed 4695107 of the 4727789 iterations and expect it to finish later today.

We have selected 10,229+ for the "next" project and the extremely limited survey sieving that I have completed confirms Paul's estimates of required sieving.

In an effort to try to harness additional computers, I have done some experimentation with a scheme to get the siever to run in a Condor environment. This may also lead to the ability to reintroduce "off line" participation. However, unless someone wants to do a lot of hand-holding, we are not there yet.

[xilman]

Originally Posted by Wacky

The LA for 5,311+ is right on schedule. I have completed 4695107 of the 4727789 iterations and expect it to finish later today.

My main machine is due to complete a 5.1M matrix in four days time. At that point it becomes available to perform the LA for a NFSNET factorization.

Paul

[R.D. Silverman]

Originally Posted by xilman

My main machine is due to complete a 5.1M matrix in four days time. At that point it becomes available to perform the LA for a NFSNET factorization.

Paul

If the LA for 6,281- fails again, I may ask you to do it. I would
send the data via CD.

It depends whether I can scrounge up a different machine.

[xilman]

Originally Posted by R.D. Silverman

If the LA for 6,281- fails again, I may ask you to do it. I would send the data via CD.

Pas de problème.

Originally Posted by R.D. Silverman

It depends whether I can scrounge up a different machine.

Good luck!

Paul

[Wacky]

End of processing for dependency 3.

Factorization completed after 6882.37 seconds, at Thu Nov 30 17:53:56 2006
Original number had 159 digits:
150650548844352814472034553603725365278060147080078718886994332064798998676174032863553350168785846893529217000119086372273707058271765344885514708578781094447
Probable prime factor 1 has 74 digits:
13132762900451821968706840158108829466847315743095478589617724372773046827
Probable prime factor 2 has 86 digits:
11471352219354375576867856155746425346416263800209213701608739475620813560935030594061

[R.D. Silverman]

Originally Posted by xilman

Pas de problème.
Good luck!

Paul

The LA ran OK this time.

We have an interesting phenomenon: TWO ECM near misses on the same
number. 6,281- split unexpectantly into 3 factors.

6,281- C162 = p50.p53.p61

p50 = 11762786832623811560644277958387970995125858157407
p53 = 28717354535597728468537227064151476862005971007351781
p61 = 1543716606774880990775734941009568252713968653903070066195497

The LA for 5,329- is now in progress.

[bdodson]

Originally Posted by R.D. Silverman

We have an interesting phenomenon: TWO ECM near misses on ...

6,281- C162 = p50.p53.p61

Since a full t50 worth of Lehigh curves ran on this number, I'd count
that as nearly two full ecm misses. The only slight quibble is that
t50 = finding a known p50 to prob 62% [at which point, optimal
computing use is to switch for looking for p55s]. That still leaves
a 38% chance that a known/expected p50 SHOULD be left, and
even 2*t50 leaves the prob at 1-1/(e^2) = .86466 (oops, 1/e gives
63.21%, not 62%), so still 13.5% of a p50 being left.

So if a pool of 100 numbers starts with 8 p50's, say all with p45's
and smaller removed, and we've found seven of them, the last one
ought to be left for finding by snfs so long as there are other pools
of near-term sieving candidates that haven't gotten t50 tests.

As I've been saying elsewhere, I'd be happy to have a pool of the
31st to 131st easiest snfs numbers to run a 2nd t50 on (the 1st
to 30th presumably being easy enough to run to leave that last
1/8 p50, if I recall Bob's earlier comment correctly).

-Bruce

[xilman]

The linear algebra is now well past the 50% mark. I hope to have factors some time next week, probably Monday or Tuesday.

Paul