2LM Table - Page 17

Batalov · 2009-12-14, 07:15

Hey, I was just trying to use what I've learned from the Global Warming modelling thread!

R.D. Silverman · 2009-12-14, 19:47

Quote:

Originally Posted by frmky

NFS@Home is getting into some harder numbers, so unless participation picks up significantly output will be slowing down for a bit. OTOH, we were just added to the DC Vault, so participation may pick up.

The 1st four 2LM holes are still relatively small (SNFS difficulty less than 260).
[at least by NFS@HOME standards; certainly not small according to the
amount of hardware that I have available]

Perhaps you might consider some of the "smaller but needed" numbers via
GNFS?

frmky · 2009-12-14, 20:11

Quote:

Originally Posted by R.D. Silverman

Perhaps you might consider some of the "smaller but needed" numbers via
GNFS?

The smaller but needed numbers are on the edge of being too small, but they could be knocked out quickly. For now, though, I have reserved all base-2 odd below 900 bits. Following that, we're taking a brief detour to do EM43, then back to the new wanted list (which actually contains only 11 unreserved numbers, not counting smaller but needed) and the 2LM's to 1800.

Greg

10metreh · 2009-12-23, 08:36

2,2074M:

p73 = 2379087623493826349515745289386828551177970787122205156170504291507059373
p87 = 699542895279776505639833525842426286778648665708138990137122334064416327166982767750281

10metreh · 2010-01-07, 20:12

2,2186L has a factor

p55 = 7382602259305831427170481228432877375865567099206873553

found by PaulZ. 2nd on the top 10 for 2010.

frmky · 2010-01-31, 01:13

NFS@Home has completed 2,1714M using GNFS. The factors were found on the sixth square root attempt. The log is attached.

Code:

prp64 factor: 1318415567213047203957952355470806576099575135763692557207429133
prp105 factor: 469511786868882962896230777843610545810641617638747418724266905318153966403658231404227868665642108361057

jasonp · 2010-01-31, 01:49

That's a pretty snazzy polynomial; did you use the GPU code to find it?

Raman · 2010-01-31, 04:20

prp64 factor = 2227660455354501880387798727738² + 36241593454326714762231020842067²
prp105 factor =
12281609984761459819640668440041899913807031571535409² + 17851438122770125368066144819389350841629933528916576²
What is the best algorithm in use for decomposing an arbitrary prime number of the form 1 (mod 4) into sum of two squares? Note that the representation is unique!

(I can use google search to find out algorithm, if available. The reason that I have posted about that is for sharing up with you only, for you to create interest within this topic only.)
No, that it is not available anywhere online at all.

frmky · 2010-01-31, 05:52

Quote:

Originally Posted by jasonp

That's a pretty snazzy polynomial; did you use the GPU code to find it?

Yes, in fact I did use the GPU code to find it. Here's the actually E:
# norm 1.476015e-16 alpha -8.373280 e 3.434e-13

wblipp · 2010-01-31, 10:06

Quote:

Originally Posted by Raman

pWhat is the best algorithm in use for decomposing an arbitrary prime number of the form 1 (mod 4) into sum of two squares?

I suggest following the descriptions and code from Dario Alpern's applet at

http://www.alpertron.com.ar/ECM.HTM

After factoring, the applet expresses numbers as the sum of the smallest number of squares possible (never more than 4).

FactorEyes · 2010-02-01, 05:44

Quote:

Originally Posted by Raman

What is the best algorithm in use for decomposing an arbitrary prime number of the form 1 (mod 4) into sum of two squares? Note that the representation is unique!

I don't know if it's necessarily the best, but the Cornacchia algorithm is laid out in Crandall & Pomerance, and it's online in several places.

2010-01-31, 04:20	#184
Raman Noodles "Mr. Tuch" Dec 2007 Chennai, India 4E9₁₆ Posts	prp64 factor = 2227660455354501880387798727738² + 36241593454326714762231020842067² prp105 factor = 12281609984761459819640668440041899913807031571535409² + 17851438122770125368066144819389350841629933528916576² What is the best algorithm in use for decomposing an arbitrary prime number of the form 1 (mod 4) into sum of two squares? Note that the representation is unique! (I can use google search to find out algorithm, if available. The reason that I have posted about that is for sharing up with you only, for you to create interest within this topic only.) No, that it is not available anywhere online at all. Last fiddled with by Raman on 2010-01-31 at 04:41

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2009-12-14, 07:15	#177
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 9488₁₀ Posts	Hey, I was just trying to use what I've learned from the Global Warming modelling thread!

2009-12-23, 08:36	#180
10metreh Nov 2008 2×3³×43 Posts	2,2074M: p73 = 2379087623493826349515745289386828551177970787122205156170504291507059373 p87 = 699542895279776505639833525842426286778648665708138990137122334064416327166982767750281

2010-01-07, 20:12	#181
10metreh Nov 2008 912₁₆ Posts	2,2186L has a factor p55 = 7382602259305831427170481228432877375865567099206873553 found by PaulZ. 2nd on the top 10 for 2010.

2010-01-31, 01:49	#183
jasonp Tribal Bullet Oct 2004 3·1,181 Posts	That's a pretty snazzy polynomial; did you use the GPU code to find it?