20130214, 16:41  #1  
Nov 2003
2^{2}×5×373 Posts 
What comes after 2^1049+1 ?
Quote:
doing some of the numbers on the wanted list that he put together. 

20130214, 17:24  #2  
"Carlos Pinho"
Oct 2011
Milton Keynes, UK
11620_{8} Posts 
Quote:
Carlos 

20130214, 20:45  #3 
Jul 2003
So Cal
100011010000_{2} Posts 
The next three are 3,745+, 3,706+, 10,770M. Following this the list is open.

20130214, 22:29  #4 
Just call me Henry
"David"
Sep 2007
Liverpool (GMT/BST)
3·5·397 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?

20130215, 19:22  #5  
Jun 2005
lehigh.edu
2^{10} Posts 
Quote:
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 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 20130215 at 19:37 Reason: pending new page 

20130215, 20:16  #6  
Nov 2003
2^{2}×5×373 Posts 
Quote:
He was referring to using 34bit or larger "large primes" in the NFS siever. 

20130215, 20:20  #7  
Basketry That Evening!
"Bunslow the Bold"
Jun 2011
40<A<43 89<O<88
16065_{8} Posts 
Quote:
Are you suggesting, rather, that an snfs record breaker would not be a good test case for a 34 bit lp job? 

20130216, 08:19  #8  
Jun 2005
lehigh.edu
1024_{10} Posts 
Quote:
Factoring says Code:
lpbr: 33 lpba: 33 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. I have P1049 sieving at school, but don't have a .poly anywhere in sight  suppose, if this is all prerecompiling that it's also 33bit. So if the 34bit large prime question is mostly disjoint from the record snfs (and neglecting M1039), the answer is likely that there hasn't been a plausiblysized first case. bdodson Offtopic 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 20130216 at 08:24 Reason: 2nd, even more offtopic remark 

20130216, 10:06  #9 
Just call me Henry
"David"
Sep 2007
Liverpool (GMT/BST)
3×5×397 Posts 
For some reason 2^10891 had stuck in my brain.
Maybe 2^11171 would be interesting. It would increase the largest factored composite quite a bit. Another possibility would be a>200 digit gnfs for which 2^10091 might be a candidate. 
20130216, 17:25  #10 
Nov 2003
2^{2}×5×373 Posts 
This factor was already known and entered into Sam's tables!
Last fiddled with by R.D. Silverman on 20130216 at 17:25 Reason: typo 
20130216, 19:04  #11 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
5·7·277 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 20130216 at 20:24 Reason: P.S. 
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