Factoring for a publication

[charybdis]

Originally Posted by bur

And both Y0 and Y1 are positive, I think I once read this shouldn't be the case, is that correct?

In many standard cases of SNFS we have Y1 = 1 and Y0 negative. If your number N can be represented as a polynomial (usually deg 4-6) evaluated at an integer m - say, N = 4m^5 - 2m^2 + 37 - then that polynomial is the algebraic polynomial, and for the rational polynomial we will have Y1 = 1, Y0 = -m, as we need m to be a root of both polynomials mod N. But there's no need for Y0 and Y1 to have different signs in general.

Originally Posted by charybdis

Planning to run t45 on (6,-8) c179 and (5,-8) c209, as well as t50 on the remaining composites from (7,-8) and (8,-7).

All done, no more factors.

[Max0526]

Originally Posted by bsquared

Thanks! Sorry I missed that.

The 4 possible polys scores I see are:

a1 Murphy = 1.533000e-11
a2 Murphy = 9.510000e-12
a3 Murphy = 1.335000e-11
a4 Murphy = 1.274000e-11

So the first one is the best.

I have been getting the rational coefficient variations by plugging the following into wolfram alpha, where obviously the a1 changes based on the magma output:

a1 = -31163499011003626601359716776483379457194762910/15539382401903125112142699946841259192950669329; a2=7*(a1-4)/(2*a1-7); a3 = 14/a1; a4 = 2*(2*a1-7)/(a1-4)

I saved the a1-a4 calculations right in the shared Magma script for copy-pasting. Change [9, 8] into the point you would need.

m := [9, 8]; // edit the plot point here
a:=rt(m[1]*gen[3]+m[2]*gen[4]);
// a1 := -31163499011003626601359716776483379457194762910/15539382401903125112142699946841259192950669329
a1:=a;
"a1 =", a1; //" "; // uncomment this to get Y0 and Y1 for the SNFS poly, if necessary
a2 :=7*(a1-4)/(2*a1-7);
"a2 =", a2;
a3 := 14/a1;
"a3 =", a3;
a4 := 2*(2*a1-7)/(a1-4);
"a4 =", a4; " ";

a1 = -31163499011003626601359716776483379457194762910/15539382401903125112142699946841259192950669329
a2 = 653247200330312889349513615946938913602982081582/171102674835329128987718333180855573265044211123
a3 = -108775676813321875784998899627888814350654685303/15581749505501813300679858388241689728597381455
a4 = 171102674835329128987718333180855573265044211123/46660514309308063524965258281924208114498720113

Checking your scores now.

EDIT: effectively the same scores provided by cownoise.com

(9, 8) c158 / snfs188 --> poly 1
n: 65450905747953132329287628843212925588466942908707926747521851453432385566465577084163919043429825490519033179336453712931411833277467544260317417144700707839
# a1 = -31163499011003626601359716776483379457194762910/15539382401903125112142699946841259192950669329
Y0: 31163499011003626601359716776483379457194762910
Y1: 15539382401903125112142699946841259192950669329

# poly x^4 - 6*x^3 + 17*x^2 - 84*x + 196
c0: 1
c1: -6
c2: 17
c3: -84
c4: 196

skew: 3.10892
# E = 1.53716677e-11 <-- best poly

---------------------------------------------

(9, 8) c158 / snfs188 --> poly 2
n: 65450905747953132329287628843212925588466942908707926747521851453432385566465577084163919043429825490519033179336453712931411833277467544260317417144700707839
# a2 = 653247200330312889349513615946938913602982081582/171102674835329128987718333180855573265044211123
Y0: -653247200330312889349513615946938913602982081582
Y1: 171102674835329128987718333180855573265044211123

# poly x^4 - 6*x^3 + 17*x^2 - 84*x + 196
c0: 1
c1: -6
c2: 17
c3: -84
c4: 196

skew: 3.76937
# E = 9.51040349e-12

---------------------------------------------

(9, 8) c158 / snfs188 --> poly 3
n: 65450905747953132329287628843212925588466942908707926747521851453432385566465577084163919043429825490519033179336453712931411833277467544260317417144700707839
# a3 = -108775676813321875784998899627888814350654685303/15581749505501813300679858388241689728597381455
Y0: 108775676813321875784998899627888814350654685303
Y1: 15581749505501813300679858388241689728597381455

# poly x^4 - 6*x^3 + 17*x^2 - 84*x + 196
c0: 1
c1: -6
c2: 17
c3: -84
c4: 196

skew: 4.50460
# E = 1.33863784e-11

---------------------------------------------

(9, 8) c158 / snfs188 --> poly 4
n: 65450905747953132329287628843212925588466942908707926747521851453432385566465577084163919043429825490519033179336453712931411833277467544260317417144700707839
# a4 = 171102674835329128987718333180855573265044211123/46660514309308063524965258281924208114498720113
Y0: -171102674835329128987718333180855573265044211123
Y1: 46660514309308063524965258281924208114498720113

# poly x^4 - 6*x^3 + 17*x^2 - 84*x + 196
c0: 1
c1: -6
c2: 17
c3: -84
c4: 196

skew: 3.71423
# E = 1.27390093e-11

[Max0526]

Originally Posted by charybdis

Planning to run t45 on (6,-8) c179 and (5,-8) c209, as well as t50 on the remaining composites from (7,-8) and (8,-7).
All done, no more factors.

All done, no more factors.

Updated. Huge thank you!

[bsquared]

Originally Posted by Max0526

EDIT: effectively the same scores provided by cownoise.com

The small differences I guess are due to the different skews that cownoise comes up with. But the algebraic poly is the same in all cases and therefore (c0 / c4) ^ (1 / 4) should also be the same, which I find to be (196 / 1) ^ (1 / 4) = 3.741. Anyone know how the different skew values are calculated?

[VBCurtis]

Originally Posted by bsquared

Anyone know how the different skew values are calculated?

My understanding is that cownoise iterates around the theoretically-derived skew until it finds a local max for E-score.

[Max0526]

Originally Posted by bsquared

Thanks! Sorry I missed that.

The 4 possible polys scores I see are:

a1 Murphy = 1.533000e-11
a2 Murphy = 9.510000e-12
a3 Murphy = 1.335000e-11
a4 Murphy = 1.274000e-11

So the first one is the best.

I have been getting the rational coefficient variations by plugging the following into wolfram alpha, where obviously the a1 changes based on the magma output:

a1 = -31163499011003626601359716776483379457194762910/15539382401903125112142699946841259192950669329; a2=7*(a1-4)/(2*a1-7); a3 = 14/a1; a4 = 2*(2*a1-7)/(a1-4)

Have you started the processing already?
I just figured out four more possible values for a --> a5-a8. The formulas might be more complicated. I am posting four more polys. Maybe some will be better.

EDIT: Four more SNFS polys for a5-a8, the last one is second best in the set of 8.

Hold on, ignore for now, I am still checking them...

[Max0526]

Originally Posted by Max0526

I saved the a1-a4 calculations right in the shared Magma script for copy-pasting. Change [9, 8] into the point you would need.

m := [9, 8]; // edit the plot point here
a:=rt(m[1]*gen[3]+m[2]*gen[4]);
// a1 := -31163499011003626601359716776483379457194762910/15539382401903125112142699946841259192950669329
a1:=a;
"a1 =", a1; //" "; // uncomment this to get Y0 and Y1 for the SNFS poly, if necessary
a2 :=7*(a1-4)/(2*a1-7);
"a2 =", a2;
a3 := 14/a1;
"a3 =", a3;
a4 := 2*(2*a1-7)/(a1-4);
"a4 =", a4; " ";

a1 = -31163499011003626601359716776483379457194762910/15539382401903125112142699946841259192950669329
a2 = 653247200330312889349513615946938913602982081582/171102674835329128987718333180855573265044211123
a3 = -108775676813321875784998899627888814350654685303/15581749505501813300679858388241689728597381455
a4 = 171102674835329128987718333180855573265044211123/46660514309308063524965258281924208114498720113

Checking your scores now.

EDIT: effectively the same scores provided by cownoise.com

(9, 8) c158 / snfs188 --> poly 1
n: 65450905747953132329287628843212925588466942908707926747521851453432385566465577084163919043429825490519033179336453712931411833277467544260317417144700707839
# a1 = -31163499011003626601359716776483379457194762910/15539382401903125112142699946841259192950669329
Y0: 31163499011003626601359716776483379457194762910
Y1: 15539382401903125112142699946841259192950669329

# poly x^4 - 6*x^3 + 17*x^2 - 84*x + 196
c0: 1
c1: -6
c2: 17
c3: -84
c4: 196

skew: 3.10892
# E = 1.53716677e-11 <-- best poly
...

All algebraic polys here should be

c4: 1
c3: -6
c2: 17
c1: -84
c0: 196

All skews and E scores are correct. Sorry for the confusion.

[bsquared]

Thanks for the new polys... if the methods to generate a5 thru a8 apply in general then I'm interested to see the formulas.

I've started sieving line 105 already, should be done when I wake up tomorrow.

[richs]

Originally Posted by richs

I'm working on line (5, -9).

Actually I should have written line 126, (5, -9). C110 and C131 are fully factored. ECM underway on C251.

[EdH]

Something's not right! Line 143 c124 survived an overzealous amount of ECM and then crashed CADO-NFS GNFS!:

Info:Linear Algebra: mksol: N=8195 ; ETA (N=9000): Wed Jun  9 09:53:46 2021 [0.022 s/iter] 
Warning:Command: Process with PID 615364 finished with return code 2 
Error:Linear Algebra: Program run on server failed with exit code 2

On another front, both the c217 and c228 have survived better than t45 ECM.

A question: On the wraithx.net site, do I read the t as the 50-50 point or the top of the knee for the success curve?

My three top ECM values for the c217:

7488 @ 43e6 
3324 @ 11e6 
2350 @ 3e6

For the c228:

10000 @ 43e6 
3324 @ 11e6 
2350 @ 3e6

It will not be until tomorrow, but I WILL factor the c124!!

[swishzzz]

Originally Posted by EdH

A question: On the wraithx.net site, do I read the t as the 50-50 point or the top of the knee for the success curve?

I think generally tn means that the collection of curves run has about a 1-1/e (about 63%) chance of finding a factor of n digits if one were to exist, so that would mean the point on the graph where success probability is closest to 63%.