20210611, 07:25  #210 
(loop (#_fork))
Feb 2006
Cambridge, England
2^{2}·3^{2}·179 Posts 
May I take the C209 S210 from (5,8) on line 88?

20210611, 09:33  #211 
"Ed Hall"
Dec 2009
Adirondack Mtns
2^{4}·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. 
20210611, 12:34  #212 
"Max"
Jun 2016
Toronto
38A_{16} 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 = 8.65288632e17  (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 = 9.26201191e17 < higher score 
20210611, 13:24  #213 
"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.

20210611, 13:53  #214 
"Ed Hall"
Dec 2009
Adirondack Mtns
2^{4}·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. 
20210611, 16:07  #215 
Jan 2012
Toronto, Canada
95_{10} Posts 
c146 GNFS for (5, 10) should be done tomorrow, reserving (6,8) c148 for GNFS

20210611, 17:04  #216 
"Max"
Jun 2016
Toronto
2·3·151 Posts 

20210611, 17:19  #217 
"Max"
Jun 2016
Toronto
1110001010_{2} Posts 

20210611, 17:59  #218 
"Max"
Jun 2016
Toronto
1110001010_{2} 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 a5a8 soon. Last fiddled with by Max0526 on 20210611 at 18:02 
20210611, 19:39  #219 
If I May
"Chris Halsall"
Sep 2002
Barbados
2^{6}·157 Posts 

20210611, 21:27  #220  
"Max"
Jun 2016
Toronto
1612_{8} Posts 
a5a8 formulas with an example
Quote:
Code:
### a1 = a from the Magma script ### > a1 := 1106273959150699304135127106363386120968812205980268960573631929106481/126098023634219809899835084852688502789500914867461314423771553552960; > s := a1; > a5 := 6*(2*s^214*s+28+sqrt(4*s^466*s^3+383*s^2924*s+784))/s; > a6 := 180/a5; > a7 := 12*(a515)/(a512); > a8 := 15*(a512)/(a515); Code:
a5 := 700645316548417658401985828694234244401797260158210592496450279693521/10786963307681811764114618362962601770038791026484251295375326612440 a6 := 1941653395382726117540631305333268318606982384767165233167558790239200/700645316548417658401985828694234244401797260158210592496450279693521 a7 := 6466090403198285783283198638997542614214584737131361876789844566083052/571201756856235917232610408338683023161331767840399576951946360344241 a8 := 8568026352843538758489156125080245347419976517605993654279195405163615/538840866933190481940266553249795217851215394760946823065820380506921 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 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 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 = 9.26201191e17 < 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 = 8.65288632e17 < second poly by score 

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