5+ table

[garo]

Size	5	N	+	Diff	Ratio	Comments
291	5	461	+	322.2	0.90	
249	5	463	+	323.6	0.76	
223	5	464	+	324.3	0.68	
290	5	467	+	326.4	0.88	
317	5	472	+	329.9	0.96	
311	5	478	+	334.1	0.93	
224	5	479	+	334.8	0.66	
301	5	488	+	341.0	0.88	
282	5	493	+	344.5	0.81	
303	5	499	+	348.7	0.86	
241	5	500	+	279.5	0.86	/5q
246	5	503	+	351.6	0.75
242	5	505	+	282.4	0.86	/5q
332	5	508	+	355.1	0.94	
355	5	509	+	355.8	1.00	
329	5	512	+	357.9	0.92	
228	5	520	+	290.8	0.78	/5q/13
219	5	523	+	365.6	0.59	/ready for GNFS !!
358	5	524	+	366.3	0.98	
254	5	526	+	367.7	0.69	
314	5	529	+	369.8	0.85	
369	5	538	+	376.0	0.98	
293	5	544	+	380.2	0.77	
263	5	545	+	304.8	0.86	/5q
342	5	547	+	382.3	0.89	
276	5	548	+	383.0	0.72

[akruppa]

4160 curves at B1=44M on each of 5,311+ 5,313+ 5,346+ 5,377+. Adds 3.2074 to p45, 0.5423 to p50 and 0.08289 to p55 for each.

Alex

[geoff]

5,417+ C172 = P80.P92
P80=62312778544931373437312353901828477385743715090139973652675999660403253132274229

This was by SNFS with ggnfs (CVS 20060310) using 28 bit large primes and factor base limits of 20 million each side.

Sieving took 75 GHz days on a mix of P2,P3,P4 CPUs, linear algebra took 15 GHz days on a P4. Peak RAM usage was 895 MB.

[R.D. Silverman]

Originally Posted by geoff

5,417+ C172 = P80.P92
P80=62312778544931373437312353901828477385743715090139973652675999660403253132274229

This was by SNFS with ggnfs (CVS 20060310) using 28 bit large primes and factor base limits of 20 million each side.

Sieving took 75 GHz days on a mix of P2,P3,P4 CPUs, linear algebra took 15 GHz days on a P4. Peak RAM usage was 895 MB.

Will you also do 5,402+ and 5,411+ (both slightly easier)???

[geoff]

I might do 5,411+ when I have finished 7,539L, but I will leave 5,402+ for someone else.

[bdodson]

Originally Posted by garo

Base	Index	Size	11M(45digits)	43M(50digits)	110M(55digits)	260M(60digits)	Decimal

5	382+	C220	0(0.267423)	0(0.0522979)	165(0.00921839)	0(0.00148122)	
5238648350342733743436972033228906610208907657584200427805381061153182854465940691839062000575845546242687790557519403231478906447878227998030723732969894059668289763595474731515301545456690890258829772702342409342092693

This one's fairly early on the 5+ list, looks like 13th or so, depending
upon how current the list is; with 311+ and 313+ in the current
NFSNET queue. So

p49 = 1450381225491210600799800528142580736112755564637,
but the cofactor at C172 is still large (well, under 200-digits, but
it would be one of the larger gnfs's --- there's a c176 Cunningham,
then this would be 3rd?). SNFS difficulty is 267? With .667*267 =
178? Ooh, not good, the c172 might be easier, but not by too much.
I'll finish the t50 on the c172 in a day-or-two, but pending another
smallish factor, this one may be around for a while longer.

-Bruce (ah, an opteron factor, b1=260M; 35 more from c211-c234
that need 1050 curves, 102 down to a last run of 525 curves
for t50.)

[R.D. Silverman]

Originally Posted by bdodson

This one's fairly early on the 5+ list, looks like 13th or so, depending
upon how current the list is; with 311+ and 313+ in the current
NFSNET queue.

I am now doing 5,314+ via SNFS.

[bdodson]

Originally Posted by R.D. Silverman

I am now doing 5,314+ via SNFS.

Just a few hours after the last one, the Opterons picked up
a late-ish p44 = 12963766440395958108028956666113786671783201
from 5, 358+ c233, this time with prime cofactor. I had already
finished 2*t45 before the current pass, so this ought to serve as
a cautionary note about what to expect from ranges where t50
has finished --- maybe a p47 would be a surprise, but there'll be
lots of p48, p49's still left. Speaking of which, the new c172 cofactor
from 5,382+ has passed its t50, without any further factors.

Bruce (OTOH, 525 curves with these p60-limits found this p44 three times;
there are definitively going to be fewer factors < p47 once the 2nd 525
curves needed to t50 finishes on c211-c233. First pass of 525 curves
is now up to 54661560..., just 31 more numbers of the original list of 137
left on the first pass.)

[bdodson]

Originally Posted by bdodson

(snip!)

Bruce (... First pass of 525 curves is now up to 54661560..., just 31 more numbers of the original list of 137 left on the first pass.)

Just 35 numbers from c211-c233 not yet finished with t50, [still] working
on the 2nd pass with 525 curves b1=260M (on the Opterons). 5,416+
C219 gives up a

p55 = 4670727010078891472720277353744610046303535783924992577

leaving a c165. Checking Sam's main list, 416 gives an algebraic factor
of (32), then has a bunch of good-ly sized non-alg factors. In fact,
the product of the 3 listed non-alg with the new p55 has 104-digits,
so 165 for gnfs -vs- 165+104=269 for snfs; which would generically
suggest that the gnfs is easier. Worse, the c165 has passed its test
to p50 (along with the previous c219), and the p55 ecm factor doesn't
bode well for a smaller p5x or p4x.

-Bruce

[geoff]

5,411+ C185 = P55.P61.P70
P55=2110554780135004202099793136762963590324098107950957883
P61=3852735458397598071150011401658661874155403923682368550872409

This was by SNFS (difficulty 192.9) using ggnfs CVS 20060310. Factor base size was 18 million each side, 28 bit large primes.

It took 9 matsolve attempts before Lanczos would converge, I don't know what caused this problem. 2,1926M (SNFS difficulty 193.3) completed using the same parameters with no problems at all.

I will do 5,402+ C152 next.

[geoff]

By SNFS:

5,402+ C152 = P73.P80
P73=3595995025826369977659826406670547615979975895153952282217794900186926613