mersenneforum.org What comes after 2^1049+1 ?
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2013-02-14, 16:41   #1
R.D. Silverman

Nov 2003

22×5×373 Posts
What comes after 2^1049+1 ?

Quote:
 Originally Posted by pinhodecarlos Last 16e Lattice Sieve application wu received is at ~q=521M (goal to 1000M) Last 16e Lattice Sieve V5 application wu received is at ~q=1304M (goal to unknown, then backwards from 1000M until meet 16e in the middle)
What number is next?? I suggest that we should honor John Selfridge by
doing some of the numbers on the wanted list that he put together.

2013-02-14, 17:24   #2
pinhodecarlos

"Carlos Pinho"
Oct 2011
Milton Keynes, UK

3·1,663 Posts

Quote:
 Originally Posted by R.D. Silverman What number is next?? I suggest that we should honor John Selfridge by doing some of the numbers on the wanted list that he put together.
Ask Greg. I am just trying to update on several team forums the progress of the 2,1049+ sieve so that people can be happy. As you know people run for the stats and a little bit more of information for the ones who run NFS@Home is important and appealing.

Carlos

 2013-02-14, 20:45 #3 frmky     Jul 2003 So Cal 32·13·19 Posts The next three are 3,745+, 3,706+, 10,770M. Following this the list is open.
 2013-02-14, 22:29 #4 henryzz Just call me Henry     "David" Sep 2007 Cambridge (GMT/BST) 593710 Posts I vote for a >33 bit large prime number at some point soon. The siever's will need recompiling but there is no reason for the check. What is the snfs record currently?
2013-02-15, 19:22   #5
bdodson

Jun 2005
lehigh.edu

210 Posts

Quote:
 Originally Posted by henryzz I vote for a >33 bit large prime number at some point soon. The siever's will need recompiling but there is no reason for the check. What is the snfs record currently?
Sam's Champions page has
Code:
Special number field sieve by SNFS difficulty:
6132	C320	2,1061-	NFS@Home
5501	C307	2,1039-	K.Aoki+J.Franke+T.Kleinjung+A.K.Lenstra+D.A.Osvik
6064	C299	2,1031-	NFS@Home
with 2,1039- having been the first snfs with difficulty above kilo-bit. M1061
was the long standing Challenge number; perhaps you might recall nfs@Home
breaking the record snfs? -bdodson

[Notice that the next page would list 2,1037- c289 in 3rd place, unless 2, 1049+ finishes
first and bumps 1039- Greg lists 316.1 for the decimal version, looks like 1039 comes in at 312.7]

Last fiddled with by bdodson on 2013-02-15 at 19:37 Reason: pending new page

2013-02-15, 20:16   #6
R.D. Silverman

Nov 2003

22×5×373 Posts

Quote:
 Originally Posted by bdodson Sam's Champions page has Code: Special number field sieve by SNFS difficulty: 6132 C320 2,1061- NFS@Home 5501 C307 2,1039- K.Aoki+J.Franke+T.Kleinjung+A.K.Lenstra+D.A.Osvik 6064 C299 2,1031- NFS@Home with 2,1039- having been the first snfs with difficulty above kilo-bit. M1061 was the long standing Challenge number; perhaps you might recall nfs@Home breaking the record snfs? -bdodson [Notice that the next page would list 2,1037- c289 in 3rd place, unless 2, 1049+ finishes first and bumps 1039- Greg lists 316.1 for the decimal version, looks like 1039 comes in at 312.7]
Henry was clearly not stating what he meant very clearly.

He was referring to using 34-bit or larger "large primes" in the NFS siever.

2013-02-15, 20:20   #7
Dubslow

"Bunslow the Bold"
Jun 2011
40<A<43 -89<O<-88

1C3516 Posts

Quote:
 Originally Posted by R.D. Silverman Henry was clearly not stating what he meant very clearly. He was referring to using 34-bit or larger "large primes" in the NFS siever.
"What is the snfs record currently?" seems pretty clear to me.

Are you suggesting, rather, that an snfs record breaker would not be a good test case for a 34 bit lp job?

2013-02-16, 08:19   #8
bdodson

Jun 2005
lehigh.edu

210 Posts

Quote:
 Originally Posted by Dubslow "What is the snfs record currently?" seems pretty clear to me. Are you suggesting, rather, that an snfs record breaker would not be a good test case for a 34 bit lp job?
Thanks for the clarification(s). For M1061 the .poly posted over on
Factoring says
Code:
lpbr: 33
lpba: 33
The M1039 post says
Code:
large primes:

We accepted large primes up to 2^38, but the parameters were
optimised for large primes up to 2^36. Most jobs attempted to
split cofactors up to 2^105 (both sides), only doing the most
promising candidates.
but that may not count for public ggnfs and public postprocessing.

I have P1049 sieving at school, but don't have a .poly anywhere
in sight --- suppose, if this is all pre-recompiling that it's also
33-bit. So if the 34-bit large prime question is mostly disjoint
from the record snfs (and neglecting M1039), the answer is likely
that there hasn't been a plausibly-sized first case. -bdodson

Off-topic factoring report: PaulZ seems to be away for a few days,
so perhaps I could announce 11, 337+ C331 = p66*p2xx, Dodson/ECMNET.
Given the difficulty of p65 tests, someone is lucky not to have found
this p66 by a Very difficult snfs!

Likewise, I'm just getting started with the new C158 cofactor of
2, 2146L with Serge's .poly (reserved, Batalov+Dodson).

Last fiddled with by bdodson on 2013-02-16 at 08:24 Reason: 2nd, even more off-topic remark

 2013-02-16, 10:06 #9 henryzz Just call me Henry     "David" Sep 2007 Cambridge (GMT/BST) 3·1,979 Posts For some reason 2^1089-1 had stuck in my brain. Maybe 2^1117-1 would be interesting. It would increase the largest factored composite quite a bit. Another possibility would be a>200 digit gnfs for which 2^1009-1 might be a candidate.
2013-02-16, 17:25   #10
R.D. Silverman

Nov 2003

22·5·373 Posts

Quote:
 Originally Posted by bdodson Off-topic factoring report: PaulZ seems to be away for a few days, so perhaps I could announce 11, 337+ C331 = p66*p2xx, Dodson/ECMNET. Given the difficulty of p65 tests, someone is lucky not to have found this p66 by a Very difficult snfs!
This factor was already known and entered into Sam's tables!

Last fiddled with by R.D. Silverman on 2013-02-16 at 17:25 Reason: typo

 2013-02-16, 19:04 #11 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 100101100010002 Posts This is interesting: 1. It was still in ECMNET's composite tables (and the date.cgi lists it as new) 2. Sam's tables indeed have the factorization (but only since summer of 2012; I have earlier pmain page snapshots) 3. There's no previous report of this factorization. By timing, it should have been on page124 Since the largest ECMers are Bruce and Sam, it appears that Sam found it probably in August 2012 (see the datastamp in "More information" on the p66), inserted it into main tables but not in the factor pages. P.S. Ah, this belonged to the recent extension. Most likely, this happened when Sam merged his 11+ (301 to 350) from xtend pages into main pages but did not update Paul on the factors found over his last couple of weeks. I will download ECMNET's Cunningham input list and check it against Sam's main tables to avoid more duplicated effort. (Sam or Paul should have done it!) P.P.S. Seems to be a rare glitch. There are a few more entries that are still in the ECMNET's list: Code: 217 2 1175 + 331 11 337 + 289 2 1037 - Last fiddled with by Batalov on 2013-02-16 at 20:24 Reason: P.S.