20080720, 16:19  #34  
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across
26337_{8} Posts 
Quote:
Quote:
Paul 

20080720, 17:07  #35  
Jul 2003
So Cal
2469_{10} Posts 
Quote:
Greg 

20080725, 09:35  #36  
Noodles
"Mr. Tuch"
Dec 2007
Chennai, India
1257_{10} Posts 
Quote:
No hopes for degree 4. Substituting x = y + (1/y) in x^{8}, so it gives up which is clearly being at degree 8. Other terms will have their appropriate degrees. So, when substituted, the whole algebraic polynomial will be of degree 8 only. And the linear polynomial becomes more cumbersome, in this form, with 10^{25}(y+(1/y))  (10^{50}+1) 

20080725, 10:04  #37 
(loop (#_fork))
Feb 2006
Cambridge, England
2×7×461 Posts 
Hi Raman.
The calculation of M should be modulo the number you're trying to factor  ie 10^25 N = (10^50+1) mod cofactor. But as xilman pointed out you just fill in the numerator and denominator in the Y0 and Y1 fields. The idea of substituting y+1/y is to take advantage of the symmetry of the octic; you write {octic} = x^4 * quartic(x+1/x) for some suitablychosen quartic, and the 10^50+1 and 10^25 are from (x + 1/x) written as (x^2+1)/x. 
20080725, 11:16  #38  
"Bob Silverman"
Nov 2003
North of Boston
5^{2}·13·23 Posts 
Quote:
results in a homomorphism of its splitting field, sending a root r of the polynomial to 1/r. Thus, if the coefficients of the polynomial are the same when reversed, we can replace the polynomial with one whose roots are r + 1/r and get an isomorphic field. 

20080917, 17:10  #39  
Jun 2005
lehigh.edu
2^{10} Posts 
Quote:
file, and the indices 271, 301 and 393 are not in the 7/08 appendix C. That leaves 18, with the NFSNET number 7,319 sieved. with the matrix running; and 7,313 a C/D number, also sieved, with matrix running. Bruce 

20090918, 18:23  #40  
Jun 2005
lehigh.edu
2^{10} Posts 
count/recount
Quote:
in the first post. There should be 15, with Code:
7 277 C201 done 7 311 C225 first 7 313 C248 done 7 323 C241 second, &etc. four base2's and two each for 3, 5, 6, 7, 10, 11 and 12, so 4+2*7 = 18) this one is the one that's gone the longest without a new factor report? No reserved numbers, either; with 311 on the more wanted list. Bruce Off Topic PS: from the old pages on Sam's site, the cover letter for page 80 (from 1998) lists a bunch of the tables as having been extended Quote:
seems to have been an update 2.C. There was also an update 2.E, followed the the 3rd edition of the tables, Sept 2001. I don't see any update 3.*'s; so suppose that it's unclear whether dropping one of the table below five entries would trigger an update and extension, or we might have some more time to clear an entire table (most likely 3 perhaps). 

20091221, 07:53  #41 
Nov 2008
2×3^{3}×43 Posts 
In the DB, someone has entered the (previously unknown) factor of 7,391:
p57 = 478566296656273815311438559010751123205277732759848440243 with a p187 cofactor. However, it can be found nowhere else  at least the forum and Sam's page don't mention it, and Google doesn't return any results for it. I expect the finder will come forward soon, but anyway, that's one "impossible" out of the way. Last fiddled with by 10metreh on 20091221 at 07:56 
20091221, 08:05  #42  
Noodles
"Mr. Tuch"
Dec 2007
Chennai, India
2351_{8} Posts 
Quote:


20091221, 08:27  #43 
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across
3×7×547 Posts 

20100128, 20:57  #44 
"Bob Silverman"
Nov 2003
North of Boston
7475_{10} Posts 
LA Failure?
Did the LA for 7,311 fail?

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