20060411, 18:07  #23  
Bamboozled!
May 2003
Down not across
2^{2}·41·61 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
89 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  
Nov 2003
3·2,473 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  
Nov 2003
1110011111011_{2} 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
5,717 Posts 
Quote:


20060412, 16:23  #32  
Nov 2003
3·2,473 Posts 
Quote:
Which factor? 

20060412, 17:49  #33 
Jul 2005
2×193 Posts 
400 (16,80) 19995617469086942401.C134
19995617469086942401 = 4388625601 x 4556236801 
Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
New phi for homogeneous Cunningham numbers  wpolly  Factoring  26  20160729 04:34 
Mathematics of Cunningham Numbers (3rd ed., 2002, A.M.S.)  Xyzzy  Cunningham Tables  42  20140402 18:31 
Don't know how to work on Cunningham numbers.  jasong  GMPECM  6  20060630 08:51 
Doing Cunningham numbers but messed up.  jasong  Factoring  1  20060403 17:18 
Need help factoring Cunningham numbers  jasong  Factoring  27  20060321 02:47 