OddPerfect enthusiasts & others: ECM help needed!

[frmky]

Originally Posted by R.D. Silverman

Chasing 3,607- shows a lack of historical perspective.

Argh! Those darn kids today are ruining everything!

Originally Posted by em99010pepe

Done with 40 curves.

Thanks! Only about 15,000 left to go to reach 3*t55!

[R.D. Silverman]

Originally Posted by CRGreathouse

Bob, I'm curious as to why you feel these factorizations are so important. Your arguments (esp. with the OPN crowd) come down to "factoring your numbers isn't important", but I don't really see the intrinsic importance of the Cunningham factorizations either.

Only as an historical matter. It is the longest computational project
in history. Are you aware of some of the pre-electronic computing machines
that were built (and used successfully) for the project?

BTW, Dick Lehmer thought they were important.

[CRGreathouse]

Originally Posted by R.D. Silverman

Only as an historical matter. It is the longest computational project
in history. Are you aware of some of the pre-electronic computing machines
that were built (and used successfully) for the project?

I think I remember two such projects, one from roughly Babbage's time (don't remember if it was his) and another just before the time of electronic computers. A 'loom' and a 'bicycle', perhaps?


It's interesting to me that you would use that explanation in the particular case of OPNs whose existence has been described as the oldest open problem in mathematics. Now I agree that pushing the bounds doesn't bring the project any closer to fruition, but technically neither does factoring 12,269- bring us closer to factoring the Cunninghams.

Originally Posted by R.D. Silverman

BTW, Dick Lehmer thought they were important.

I wonder on what basis. I mean, *I* think they're important -- at one point I wrote a program to do the grunt work of using the tables (find algebraic factors, look up appropriate table entries for composites, etc.). But I can't articulate a reason for that and I was wondering if someone else could.

[R.D. Silverman]

Originally Posted by CRGreathouse

I think I remember two such projects, one from roughly Babbage's time (don't remember if it was his) and another just before the time of electronic computers. A 'loom' and a 'bicycle', perhaps?


It's interesting to me that you would use that explanation in the particular case of OPNs whose existence has been described as the oldest open problem in mathematics. Now I agree that pushing the bounds doesn't bring the project any closer to fruition, but technically neither does factoring 12,269- bring us closer to factoring the Cunninghams.



I wonder on what basis. I mean, *I* think they're important -- at one point I wrote a program to do the grunt work of using the tables (find algebraic factors, look up appropriate table entries for composites, etc.). But I can't articulate a reason for that and I was wondering if someone else could.

Actually, what I would really like to see is for work to be done
on the base 2 tables exclusively. They are the only unfinished
numbers from the 1st edition of the book. Let's finish them off and
move on to doing something else with the CPU time.

I can suggest a number of things:

Looking for elliptic curves of high rank.

Further development in algorithms for computing class numbers/fundamental
units of number fields of degree higher than 2.

Looking for an integer that is both an ordinary pseudoprime and a LL
pseudoprime (with discriminant -5 [The Wagstaff-Pomerance challenge]).
This is a project that is finite in duration and has a definite goal.

Finishing off Seventeen or Bust
This is a project that is finite in duration and has a definite goal.

There is a whole bunch of stuff in R. Guy's "Unsolved Problems in Number Theory" that could be investigated.

[R.D. Silverman]

Originally Posted by R.D. Silverman

Actually, what I would really like to see is for work to be done
on the base 2 tables exclusively. They are the only unfinished
numbers from the 1st edition of the book. Let's finish them off and
move on to doing something else with the CPU time.

I can suggest a number of things:

Looking for elliptic curves of high rank.

Further development in algorithms for computing class numbers/fundamental
units of number fields of degree higher than 2.

Looking for an integer that is both an ordinary pseudoprime and a LL
pseudoprime (with discriminant -5 [The Wagstaff-Pomerance challenge]).
This is a project that is finite in duration and has a definite goal.

Finishing off Seventeen or Bust
This is a project that is finite in duration and has a definite goal.

There is a whole bunch of stuff in R. Guy's "Unsolved Problems in Number Theory" that could be investigated.

BTW, There was a time when Lehmer's sieves were actually held by
the computer museum in Boston. Both his photoelectric sieve and DLS-127
were there. They were not however on display. I personally
protested this to the museum staff, pointing out that they were classic
examples of computing without digital computers. The museum staff was
completely clueless about the machines. Noone, repeat noone knew
what the hardware was, what it had been used for, or even why they had it.
How can a museum function without a curator who knows the history of
the artifacts in the museum???

I understand that the hardware has been returned to Berkeley. It
was quite proper to do so. Does anyone know of its current status?

I got permission to play around with the photoelectric sieve when I was
at MITRE. I borrowed some equipment (a high torque motor, a rubber
belt of the right size, a laser, and a photometer) and actually got the
machine to work. I had to explain to the museum staff how the machine
worked. Of course, they failed to follow my description about modular
arithmetic, quadratic residues, and exclusion moduli. Whether this was
due to my inadequate explanation I will leave for others to decide.....

I will say that the museum staff was hopelessly clueless about the
history of the machines that they had on display, how they were used,
and what they were used for.... I expect the general public to be clueless
about math and computation, but am surprised at the ignorance of the staff.
I would have expected them to know something.

[Andi47]

4 curves at B1=26e7 for benchmarking purpose, no factors.

[xilman]

Originally Posted by R.D. Silverman

How can a museum function without a curator who knows the history of the artifacts in the museum???

I think your expectations are too high.

I doubt that there is a museum worthy of the name anywhere in the planet containing only artefacts which are recognized by the institution's present curators. Every now and again I read news reports of some thingummyajig lying deep in the bowels of a musuem which has escaped attention for a lengthy period of time until re-discovered by someone who knows, or is interested enough to find out, the nature of the object.


Paul

[R.D. Silverman]

Originally Posted by xilman

I think your expectations are too high.

I doubt that there is a museum worthy of the name anywhere in the planet containing only artefacts which are recognized by the institution's present curators. Every now and again I read news reports of some thingummyajig lying deep in the bowels of a musuem which has escaped attention for a lengthy period of time until re-discovered by someone who knows, or is interested enough to find out, the nature of the object.


Paul

Sure. But the museum staff was clueless about MOST of the items that
they had in their possession.

[fivemack]

If you're talking about benchmarking purposes, building gmp-5.0.1 out of the box and ecm-6.3 out of the box against it, and running on the macpro I have at work (2.66GHz i7 Xeon CPUs) one curve at 26e7 takes an hour for Step 1 and 20 minutes for step 2, and sometimes has 1700MB of memory resident.

So I could reasonably run 270 over a weekend (sixty hours, six cores), but no more, and I can't reasonably have a job running in the background on each core because I'd run out of memory. The ECM step is requiring noticeably larger per-CPU resources than the sieving.

[Andi47]

Originally Posted by fivemack

If you're talking about benchmarking purposes, building gmp-5.0.1 out of the box and ecm-6.3 out of the box against it, and running on the macpro I have at work (2.66GHz i7 Xeon CPUs) one curve at 26e7 takes an hour for Step 1 and 20 minutes for step 2, and sometimes has 1700MB of memory resident.

So I could reasonably run 270 over a weekend (sixty hours, six cores), but no more, and I can't reasonably have a job running in the background on each core because I'd run out of memory. The ECM step is requiring noticeably larger per-CPU resources than the sieving.

For me it turned out that it was a quite "dirty" benchmark: I had all 8 threads of my i7 860 @2.8 GHz (Win 7 pro 64 bit) busy (100% each) when I started, but as the other factorization, which I had running, found a factor, 6 threads fell idle somewhere between. Anyway I got these timings (for one of the two threads running (3^607-1)/2 with ecm -maxmem 3000):

GMP-ECM 6.3 [configured with GMP 5.0.1 and --enable-asm-redc] [ECM]
Input number is (3^607-1)/2 (290 digits)
Using B1=260000000, B2=3178559884516, polynomial Dickson(30), sigma=3595759605
Step 1 took 4420818ms
Step 2 took 887053ms
Run 2 out of 2:
Using B1=260000000, B2=3178559884516, polynomial Dickson(30), sigma=1767865861
Step 1 took 3253105ms (54 minutes)
Step 2 took 770691ms (12.8 minutes)

compared to this: ecm-6.2.3 32 bit took 4 hours(!) for step 1.

[em99010pepe]

Andi47 and fivemack,

My timings:

Machine 1 - Core i5 750@3.7GHz

GMP-ECM 6.3 [configured with GMP 5.0.1 and --enable-asm-redc] [ECM]
Input number is (3^607-1)/2 (290 digits)
Using B1=260000000, B2=3178559884516, polynomial Dickson(30), sigma=1725068313
Step 1 took 2554531ms
Step 2 took 603256ms

Machine 2 - Q6600@2.8 GHz

GMP-ECM 6.3 [configured with GMP 5.0.1 and --enable-asm-redc] [ECM]
Input number is (3^607-1)/2 (290 digits)
Using B1=260000000, B2=3178559884516, polynomial Dickson(30), sigma=3536664674
Step 1 took 3383594ms
Step 2 took 880016ms

Funny my Q6600@2.8GHz is almost as fast as your i7 860 @2.8 GHz(Andi47), maybe you should run only 4 threads.

Anyway, I started 800 curves on Machine 1 (100 done so far) and 400 curves on Machine 2 (80 done so far).