mersenneforum.org Factoring for a publication
 Register FAQ Search Today's Posts Mark Forums Read

 2021-06-11, 07:25 #210 fivemack (loop (#_fork))     Feb 2006 Cambridge, England 22·32·179 Posts May I take the C209 S210 from (5,-8) on line 88?
 2021-06-11, 09:33 #211 EdH     "Ed Hall" Dec 2009 Adirondack Mtns 24·257 Posts Line 140 (7,10): the c219 let a couple small factors slip out to leave a c184, which has now been ECM'd to t50. Just a note, that I'm not running any NFS on the larger composites that I've ECM'd in the tables ATM, so they are free to be booked by others.
 2021-06-11, 12:34 #212 Max0526   "Max" Jun 2016 Toronto 38A16 Posts tough corner (8, -8) @fivemack Regarding your comments in the sheet on the highest difficulty SNFS degree 4 job ever run at the forum (8, -8) http://factordb.com/index.php?id=1100000002598203189 c229/snfs275.5, c253/snfs275.2 (t45 done on both) I am happy to say that (at least) c253 could be represented by 8 (not just 4) different SNFS polys. I got 6 explicitly so far and still working on the other 2 (next level math is involved). The two best I know are below. If anything better comes up, I'll update. The formulas are coming too. Code: (8, -8) c253 / snfs276 --> poly 1 n: 8804520161676131700982540766264320490679194033982281399896425294638109453150751678880580616975539504041811224827523553098748730672460054169092839796707517989930320213119027214444156828381573746656945529005366269066529760620006615774307975893498163091241 # a = 1106273959150699304135127106363386120968812205980268960573631929106481/126098023634219809899835084852688502789500914867461314423771553552960 Y0: -1106273959150699304135127106363386120968812205980268960573631929106481 Y1: 126098023634219809899835084852688502789500914867461314423771553552960 # poly 2*x^4 - 30*x^3 + 169*x^2 - 420*x + 196*2 c0: 392 c1: -420 c2: 169 c3: -30 c4: 2 skew: 4.97043 # E = 8.65288632e-17 ------------------------------------------ (8, -8) c253 / snfs276 --> poly 5 n: 8804520161676131700982540766264320490679194033982281399896425294638109453150751678880580616975539504041811224827523553098748730672460054169092839796707517989930320213119027214444156828381573746656945529005366269066529760620006615774307975893498163091241 a = 700645316548417658401985828694234244401797260158210592496450279693521/10786963307681811764114618362962601770038791026484251295375326612440 Y0: -700645316548417658401985828694234244401797260158210592496450279693521 Y1: 10786963307681811764114618362962601770038791026484251295375326612440 # poly x^4 - 24*x^3 + 288*x^2 - 4320*x + 32400 <-- a different poly here c0: 32400 c1: -4320 c2: 288 c3: -24 c4: 1 skew: 21.08616 # E = 9.26201191e-17 <-- higher score
 2021-06-11, 13:24 #213 bsquared     "Ben" Feb 2007 3·1,193 Posts I will work on line 128 (3,-9) next. At difficulty 221 and 222 both should be doable by SNFS if it comes to that.
 2021-06-11, 13:53 #214 EdH     "Ed Hall" Dec 2009 Adirondack Mtns 24·257 Posts Line 161 (10, -8): I'll factor the smaller ones and ECM the larger ones a bit. All other composites that I have ECM'd should no longer be booked to me.
 2021-06-11, 16:07 #215 swishzzz   Jan 2012 Toronto, Canada 9510 Posts c146 GNFS for (5, 10) should be done tomorrow, reserving (6,-8) c148 for GNFS
2021-06-11, 17:04   #216
Max0526

"Max"
Jun 2016
Toronto

2·3·151 Posts

Quote:
 Originally Posted by fivemack Line 99 done (c139 split as p54 x p85 in 3h20m wall-time on 28-thread Skylake)
This one patches a stretch of 23 lines in a row in stage 9!
Thank you!

2021-06-11, 17:19   #217
Max0526

"Max"
Jun 2016
Toronto

11100010102 Posts

Quote:
 Originally Posted by EdH Line 161 (10, -8): I'll factor the smaller ones and ECM the larger ones a bit. All other composites that I have ECM'd should no longer be booked to me.
Thank you, EdH!
You are only on line 161 (10, -8) in the sheet now.

 2021-06-11, 17:59 #218 Max0526   "Max" Jun 2016 Toronto 11100010102 Posts 8 SNFS polys From now on, 8 polys are available for some of the composites. If you are ready to start SNFS on your booked number, please let me know. I will write instructions (and code) on creating SNFS polys for a5-a8 soon. Last fiddled with by Max0526 on 2021-06-11 at 18:02
2021-06-11, 19:39   #219
chalsall
If I May

"Chris Halsall"
Sep 2002

26·157 Posts

Quote:
 Originally Posted by Max0526 I will write instructions (and code) on creating SNFS polys for a5-a8 soon.
Cool.

Just to share, I only had a little bit of understanding of what you guys are doing.

But clearly, it was sane, based on who was playing...

2021-06-11, 21:27   #220
Max0526

"Max"
Jun 2016
Toronto

16128 Posts
a5-a8 formulas with an example

Quote:
 Originally Posted by Max0526 From now on, 8 polys are available for some of the composites. If you are ready to start SNFS on your booked number, please let me know. I will write instructions (and code) on creating SNFS polys for a5-a8 soon.
I use point (8, -8) as an example. The simplest explicit formulas for a5, a6, a7, a8 are obtained like this:
Code:
### a1 = a from the Magma script ###

> a1 := 1106273959150699304135127106363386120968812205980268960573631929106481/126098023634219809899835084852688502789500914867461314423771553552960;
> s := a1;
> a5 := 6*(2*s^2-14*s+28+sqrt(4*s^4-66*s^3+383*s^2-924*s+784))/s;
> a6 := 180/a5;
> a7 := 12*(a5-15)/(a5-12);
> a8 := 15*(a5-12)/(a5-15);
Code:
a5 := 700645316548417658401985828694234244401797260158210592496450279693521/10786963307681811764114618362962601770038791026484251295375326612440
a6 := 1941653395382726117540631305333268318606982384767165233167558790239200/700645316548417658401985828694234244401797260158210592496450279693521
a7 := 6466090403198285783283198638997542614214584737131361876789844566083052/571201756856235917232610408338683023161331767840399576951946360344241
a8 := 8568026352843538758489156125080245347419976517605993654279195405163615/538840866933190481940266553249795217851215394760946823065820380506921
It is only possible to create usable quartic SNFS polys 5-8, if the composite to factor [in this case, c253 from line 85 point (8, -8)] is a cofactor of the evaluated numerator of one of the following three polynomials:
Code:
### when x = a5, or x = a6, or x = a7, or x = a8,
### c253 from line 85 point (8, -8) is a cofactor of the second one

x^4 - 96*x^3 + 2232*x^2 - 17280*x + 32400
x^4 - 24*x^3 + 288*x^2 - 4320*x + 32400
x^4 + 192*x^3 - 5544*x^2 + 34560*x + 32400
c253 from http://factordb.com/index.php?id=1100000002598204946
evaluated numerator N, 276 digits, is in FactorbDB http://factordb.com/index.php?id=1100000002598203499
Code:
> c253 := 8804520161676131700982540766264320490679194033982281399896425294638109453150751678880580616975539504041811224827523553098748730672460054169092839796707517989930320213119027214444156828381573746656945529005366269066529760620006615774307975893498163091241:
> x := a5;
> N := numer(x^4 - 24*x^3 + 288*x^2 - 4320*x + 32400);
> "N/c253=",N/c253;
Code:
N := 8804520161676131700982540766264320490679194033982281399896425294638109453150751678880580616975539504041811224827523553098748730672460054169092839796707517989930320213119027214444156828381573746656945529005366269066529760620006615774307975893498163091241
"N/c253=", 18744110927863956358681
All 8 SNFS polys are attached in a text file. The E scores range almost twice. The first poly (for a1) is second best, and the best by the E score is poly 5 (for a5) from the 5-8 set, so all this black belt level math was not in vain.
Code:
(8, -8) c253 / snfs276 --> poly 5
n: 8804520161676131700982540766264320490679194033982281399896425294638109453150751678880580616975539504041811224827523553098748730672460054169092839796707517989930320213119027214444156828381573746656945529005366269066529760620006615774307975893498163091241
a = 700645316548417658401985828694234244401797260158210592496450279693521/10786963307681811764114618362962601770038791026484251295375326612440
Y0: -700645316548417658401985828694234244401797260158210592496450279693521
Y1: 10786963307681811764114618362962601770038791026484251295375326612440
# poly x^4 - 24*x^3 + 288*x^2 - 4320*x + 32400
c0: 32400
c1: -4320
c2: 288
c3: -24
c4: 1
skew: 21.08616
# E = 9.26201191e-17 <-- best poly by score
---------------------------------
(8, -8) c253 / snfs276 --> poly 1
n: 8804520161676131700982540766264320490679194033982281399896425294638109453150751678880580616975539504041811224827523553098748730672460054169092839796707517989930320213119027214444156828381573746656945529005366269066529760620006615774307975893498163091241
# a = 1106273959150699304135127106363386120968812205980268960573631929106481/126098023634219809899835084852688502789500914867461314423771553552960
Y0: -1106273959150699304135127106363386120968812205980268960573631929106481
Y1: 126098023634219809899835084852688502789500914867461314423771553552960
# 2*x^4 - 30*x^3 + 169*x^2 - 420*x + 196*2
c0: 392
c1: -420
c2: 169
c3: -30
c4: 2
skew: 4.97043
# E = 8.65288632e-17 <-- second poly by score
Now I start thinking about coding some artificial opportunistic spin on all of them. Need to find original Murphy's formulas to calculate the E score (saw it in one of the CADO-NFS Shi Bai's papers). Everything there depends on the skew, but we know the predicted SNFS skew value. Also, they are huge because CADO-NFS team polyselected for degree 6, for us c5 = c6 = 0, and they will be shorter.
Attached Files
 c253.polys.txt (5.9 KB, 29 views)

 Similar Threads Thread Thread Starter Forum Replies Last Post baih Miscellaneous Math 9 2020-09-21 07:11 xx005fs GPU Computing 3 2018-10-27 14:49

All times are UTC. The time now is 14:37.

Sun Dec 5 14:37:37 UTC 2021 up 135 days, 9:06, 2 users, load averages: 1.00, 1.09, 1.10