20060411, 18:07  #23  
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across
2·5,791 Posts 
Quote:
Given a^n \pm b^n == 0 mod N, divide by b^n to get (a/b)^n \pm 1 == 0 mod N. You've now got exactly the same form as for the regular Cunningham tables. Purists can witter on about multiplicative inverses and whether they exist mod N. Such purists will also realize that if the inverse can't be found by the extended GCD algorithm a factorization of N is at hand anyway. Paul 

20060411, 20:00  #24 
Sep 2005
UGent
74_{8} Posts 
Bob, would you mind if I also put a copy online at my page http://cage.ugent.be/~jdemeyer/cunningham/?

20060412, 07:19  #25 
Apr 2006
2×53 Posts 
The factors of the C98 from 3^3492^349 are:
4168235213414369860712355318929423366202629 (pp43) 6054961803389403532431183517420804533418860819773628313 (pp55) 
20060412, 08:16  #26  
Oct 2004
Austria
2·17·73 Posts 
Quote:
Edit: Primo certifies both factors as prime within a split second Last fiddled with by Andi47 on 20060412 at 08:20 

20060412, 10:37  #27  
"Bob Silverman"
Nov 2003
North of Boston
1110101001000_{2} Posts 
Quote:
Go right ahead. 

20060412, 12:16  #28 
Oct 2004
Austria
2×17×73 Posts 
Done 648 curves on 3^379+2^379 using GMPECM at B1=1e6 and B2=default, no factor found. Together with Silverman's ~300 curves this should have finished the 35 digit range.
(P.S.: This should read 379 (1) 5.C181 ;) ) Now running a some curves with B1=3e6 at this number. I have also done 300 curves on the C144 of 3^3952^395, no factor found. Last fiddled with by Andi47 on 20060412 at 12:20 
20060412, 12:46  #29  
"Bob Silverman"
Nov 2003
North of Boston
1D48_{16} Posts 
Quote:
I follow the Cunningham format: N (a,b,c...) means that 3^N + 2^N has the algebraic factors 3^a + 2^a, 3^b + 2^b, etc. So 379 (1) C181 means that 3^379 + 2^379 has the algebraic factor of 3^1 + 2^1. 5 is an algebraic factor. Algebraic factors do not get directly listed. The exponents for the algebraic factors are listed inside the parentheses. 

20060412, 15:42  #30 
Jul 2005
2·193 Posts 
Ah, I did wonder. Knowledge gained and all of that...

20060412, 15:56  #31  
"Mark"
Apr 2003
Between here and the
15253_{8} Posts 
Quote:


20060412, 16:23  #32  
"Bob Silverman"
Nov 2003
North of Boston
1D48_{16} Posts 
Quote:
Which factor? 

20060412, 17:49  #33 
Jul 2005
110000010_{2} Posts 
400 (16,80) 19995617469086942401.C134
19995617469086942401 = 4388625601 x 4556236801 
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