Contributing to Cunningham Project

[R.D. Silverman]

Originally Posted by sweety439

but 12^319 > 10^323, so 10^323-1 should be factored first

Also Phi_319(12) > Phi_323(10)

12^319-1 has an algebraic factor. We are not factoring 12^319-1, we are factoring (12^319-1)/(12^29-1) ~12^290 ~ C313.

The resulting polynomial is reciprocal, so we can do this number with a quintic.
However, quintic polynomials for numbers this size result in matrices that are
significantly larger than those for numbers of similar
size done with sextics. Greg is LA constrained right now, so he skipped 12^319-1
for the time being. He did C314, C315, C316 C317 and is now working on C318's
via 3^667-1 etc.

Greg may indeed do R323 before he does 12^319-1. I think he will. R323 might well be
done by a reciprocal octic to take advantage of the algebraic factor 10^19-1. Whether
the octic would be easier than the obvious sextic might be an interesting experiment.


It might also be interesting to see if a septic would be any better. I think a septic
will be slightly better in general for numbers of this size.

Let's do a "back of the envelope" look at the norms. Take (10^6, 10^6) == (a,b) as a
'typical lattice point'.

For a sextic, an algebraic norm is ~ a^6 ~ 10^36 and a
linear norm is ~ b * (10^324/6) ~ 10^60. For a septic an anorm is ~a^7 ~ 10^42
and a linear norm is b *(10^322/7) ~ 10^52. The norms are closer for the
septic and their product is slightly smaller. A septic seems slightly superior.
For the reciprocal octic an anorm is a^8 ~ 10^48 and a linear norm is b * (10^38) ~ 10^44 which seems even better still.

Note that one also needs to adjust these estimates by the special-q. The estimates
also ignore the effect of variance on the norms. Since we want smooth numbers
we are more concerned with the tails of the distributions of the norms rather than
the means. However, it does give a quick comparison.

NFS works best when the norms are as nearly equal as possible, other things
being equal.

This very rough estimate is based on the assumption that (10^6, 10^6) is a
typical lattice point. Adjust the analysis if this assumption is not a good enough
estimate. I do now know what sieve areas the lasievef siever uses.

Noone has been calling for him to do 12^319-1.

It is possible that Greg missed the reciprocal octic for R323. He will get to it.

Doing R323 seems to be a compulsion with you.

[frmky]

Originally Posted by R.D. Silverman

12,293+ just set a new record for largest penultimate factor.

Wow. I've been so busy I didn't even notice. Yay!

[frmky]

Originally Posted by R.D. Silverman

It is nice to hear that Universities are still going!

Greg, do you know of anyone offering a first course (on-line) in string theory?
I'd love to take one. Or a course in quantum field theory? I did get to take
a course in relativistic quantum mech from Ed Purcell when I was an undergrad.
[45 years ago, however!] It was a small fun class; he was a superb teacher.

I'm not sure if I have the needed pre-reqs.
My differential geometry background is minimal, so I may need to take that first.
Basic tensor analysis is not a problem.

Sorry, but I don't. I took a QFT course 20 years ago from Alfred Shapere at U. Kentucky, who was a student of Frank Wilczek. Haven't looked at it since I'm afraid. The closest I've come to string theory is attending a couple of talks by Ed Witten, of which I understood very little.

[R.D. Silverman]

Originally Posted by R.D. Silverman

<snip>

Greg may indeed do R323 before he does 12^319-1. I think he will. R323 might well be
done by a reciprocal octic to take advantage of the algebraic factor 10^19-1. Whether
the octic would be easier than the obvious sextic might be an interesting experiment.


It might also be interesting to see if a septic would be any better. I think a septic
will be slightly better in general for numbers of this size.

Let's do a "back of the envelope" look at the norms. Take (10^6, 10^6) == (a,b) as a
'typical lattice point'.

For a sextic, an algebraic norm is ~ a^6 ~ 10^36 and a
linear norm is ~ b * (10^324/6) ~ 10^60. For a septic an anorm is ~a^7 ~ 10^42
and a linear norm is b *(10^322/7) ~ 10^52. The norms are closer for the
septic and their product is slightly smaller. A septic seems slightly superior.
For the reciprocal octic an anorm is a^8 ~ 10^48 and a linear norm is b * (10^38) ~ 10^44 which seems even better still.


.

I'd like to hear ideas from others about what I wrote just above. It seems that
a degree 7 polynomial would be better (than degree 6) for Greg to use moving forward
for numbers that NFS@Home is about to undertake.

[wreck]

Originally Posted by R.D. Silverman

I'd like to hear ideas from others about what I wrote just above. It seems that
a degree 7 polynomial would be better (than degree 6) for Greg to use moving forward
for numbers that NFS@Home is about to undertake.

I test the speed 4 years ago, the result shows deg 7 is much slower than deg 6.
deg 6 need 102 CPU years to collect 1200M raw relations, while deg 7 need 182 CPU years on an i3 CPU.
I attach the poly and test files.

[R.D. Silverman]

Originally Posted by wreck

I test the speed 4 years ago, the result shows deg 7 is much slower than deg 6.
deg 6 need 102 CPU years to collect 1200M raw relations, while deg 7 need 182 CPU years on an i3 CPU.
I attach the poly and test files.

One needs to change the factor base sizes moving from d = 6 to 7. Increase the
algebraic and decrease the linear.

[R.D. Silverman]

Originally Posted by R.D. Silverman

One needs to change the factor base sizes moving from d = 6 to 7. Increase the
algebraic and decrease the linear.

Note also that one should (likely) apply special q to the algebraic side instead of
rational side.

[wreck]

I guess you mean increase alim and decrease rlim, use option -a.
But I test again with these changes, the situation is the same.
When I use alim=800M rlim =200M -a, and binary lasieve5_f compiled, it need 100 CPU years to collect 1200M raw relations on an i7 CPU;
While use alim=rlim =400M,-r with the same binary and processor,it need 40 CPU years to collect 1200M raw relations.
Though I don't know why,it is a little strange.

[Max0526]

Originally Posted by wreck

There are some special effort at repunit number (10^n - 1).

Kurt Team (Bo Chen, Wenjie Fang, Alfred Eichhorn, Danilo Nitsche, Kurt Beschorner, et al. ) aim at factoring

these number use snfs and gnfs, until last year we have polish most number snfs less than 300 and gnfs less than 200.

Now we are factoring snfs less than 310 and gnfs less than 210.

10,337- gnfs 202 is within our reach, I have suggest the team to factoring this number after the relation collect of

10^459 - 1, a snfs 306 number. In principle, we could factor this gnfs 202 with 12 months.

If Kurt and other members accept my suggestion, we will send Sam an email to reserve this number.

Yousuke Koide concentrates at 10^n+1, where n is between 400 and 800, using method ecm and nfs.

It would better if the duplicate effort could avoid.

If you still want to factor this number, we will not select this number as our next target.

I found 3,748+ c204 is also less than 210, perhaps you could factoring this number, I and Kurt have

no interest to this number.


Best regards,

Bo Chen

Dear forumites,
Kurt Beschorner's team (http://kurtbeschorner.de/) is days away from cracking R459/C221 by SNFS and 40% in the GNFS sieving for R1740M/C204. Slowly but surely we are selecting our next repunit cofactor to work on. One of the candidates is R337/C202.
If nobody is actively working on this number, could we please reserve it for Kurt's team?
Since the discussion in late February 2020 (see wreck's message above), did anybody try to polyselect for this C202?
I ran CADO with standard parameters for a day and found a mediocre baseline poly (2.39e-15), the 2018 record belongs to fivemack (3.665e-15).
If nobody minds our reservation, we would really appreciate your help in polyselecting, especially on the msieve side.
I will run CADO with improved parameters and spin up all good candidates as always.
Please let us know, here or via PM.
Stay safe,
Max

[VBCurtis]

Fine with me- we're not in a big hurry to grab a 201-202 for a 15e/home-CADO hybrid.
I wager there's less than 10% chance anymore of msieve finding a winning poly for a composite at 200+ digits. I can do a little CADO poly select, but not a ton- if Kurt's group wants firepower, please reserve a range of c5 values (admin/admax) for them, and some of us will add our efforts in nonoverlapping ranges. Might not be worth their time to coordinate, though.

[Max0526]

Originally Posted by VBCurtis

Fine with me- we're not in a big hurry to grab a 201-202 for a 15e/home-CADO hybrid.
I wager there's less than 10% chance anymore of msieve finding a winning poly for a composite at 200+ digits. I can do a little CADO poly select, but not a ton- if Kurt's group wants firepower, please reserve a range of c5 values (admin/admax) for them, and some of us will add our efforts in nonoverlapping ranges. Might not be worth their time to coordinate, though.

Thank you, VBCurtis!
Kurt cracked R459 in the morning: http://kurtbeschorner.de/
Gimarel found an exceptional poly for R337/C202: https://mersenneforum.org/showpost.p...postcount=1930
And I started the spinup process: https://mersenneforum.org/showpost.p...postcount=1931