20050611, 20:34  #1 
May 2005
2^{2}·3·5 Posts 
Factorization attempt for a c214 regards Odd Perfect Numbers
Hi every one,
Thanks to everyone who helped the factorization for a c163 I posted a couple weeks ago. Before I finish my OPN (9 distinct factors) project, I need to get a complete factorization for a c214, which is a factor of 7^343 1. I am pretty sure c214 is the last roadblock for this project. The completed factorization is 7^343  1 = 7^(7^3)  1 = 2 * 3 * 29 * 4733 * 3529 * 1074473 * 13473433 * 6106505825833677713 * 1373 * 8233 * 49393 * 734021 * 83517610741606021 * 8403170201386002840476080703299123251286617419186485806798706989812597310995759101855982323436346453490295844838291326800248443089057721410790484991729444190401836892041621145614063665607931920955659505589620515021 (c214) I have now completed the 1115 th curve with limit B1=11000000; B2=1100000000 at the 30 digit level on a slow machine utilizing Dario Alpern’s ecm software without luck. Please help and thank you in advance. Regards Joseph E.Z. Chein 
20050611, 20:41  #2 
Dec 2004
13·23 Posts 
What else have you done? P1 to what bounds how about P+1 etc?

20050611, 20:53  #3 
"Nancy"
Aug 2002
Alexandria
2,467 Posts 
I've started ECM with B1=11M.
The SNFS difficulty is 248 with a sextic  not easy, but feasible if a couple of people help sieving. So even if ECM does not get lucky again, we can definitely factor this one. Alex PS. : I've done P1 with B1=10^8 and am currently doing 10^9. Last fiddled with by akruppa on 20050611 at 20:54 
20050611, 22:20  #4 
Feb 2005
1D_{16} Posts 
7^3431 already factored
http://www.loria.fr/%7Ezimmerma/records/c120355 shows that
7^3431 is already factored completely. 214 7, 343 8403170201386002840476080703299123251286617419186485806798706989812597310995759101855982323436346453$ 214 4902958448382913268002484430890577214107904849917294441904018368920416211456140636656079319209556595$ 214 05589620515021 done 1575721793366942921257214180187566081951195327261 Shimoyama 11.08.04 Heikki 
20050612, 04:27  #5 
"Phil"
Sep 2002
Tracktown, U.S.A.
2·13·43 Posts 
http://www.cerias.purdue.edu/homes/ssw/cun/pmain505
also shows this number as completely factored. (Latest version as of 05 May 2005.) Also check http://www.cerias.purdue.edu/homes/ssw/cun/index.html for the latest update. 
20050612, 15:15  #6 
May 2005
60_{10} Posts 
Dear Heikki, Philmoore, Alex and everyone,
Thank you very much for your valuable information. What a pleasure it is to here that c214 has been factored by Shimoyama on 11/08/2004 already. It’s saved me a great deal of time. The completed factorization for c214 is 1575721793366942921257214180187566081951195327261 * p166. Before I close this post, may I ask if you or anyone knows the factorization for c427 = (19^3611)/ (19^191)/ 84216527581 or any factorizations listing of p^n  1, where p is a prime > 12 with high n’s? Please let me know. I just completed the 346th curve for that c427 without luck. It’s time to call it quits. The c427 is much too big for any existing algorithm. Please don’t try. Many thanks. Regards Joseph E.Z. Chein 
20050612, 15:32  #7 
"Nancy"
Aug 2002
Alexandria
2467_{10} Posts 
Prof. Richard Brent's tables list factors of a^n+1 for 12<a<100 and a^n < 10^255. Unfortunately the latter condition excludes 19^3611.
Hisanori Mishima' tables list factors of cyclotomic numbers Phi_n(a) for a<=1000 and eulerphi(n)<=100. Again, the latter condition excludes 19^3611. I don't know of others that collect factorisation of such large a^n1. The c427 is far too large for SNFS, but ECM may have a good chance yet. I'll try a couple of curves. Alex 
20050612, 17:41  #8  
"Mark"
Apr 2003
Between here and the
3·2,081 Posts 
Quote:


20050612, 18:08  #9  
Nov 2003
2^{2}·5·373 Posts 
Quote:
How big is n?? Please note that if p = 1 mod 4, then p^(kp)  1, k odd has an Aurefeullian factorization that might help. Otherwise, Brent's tables contain all that is publicly known. 

20050612, 18:48  #10  
"William"
May 2003
New Haven
4471_{8} Posts 
Quote:
It's also the best source I know for p^{n}1 with p>12 and "large n"  although p>100 tends to have few factors with exponents above 100 and p>1000 tends to have few factors at all. OddPerfect.org has been contributing to these ranges as we prepare our first factors file. Last fiddled with by wblipp on 20050612 at 19:03 

20050612, 19:04  #11  
May 2004
28_{10} Posts 
Quote:
Testing is being continued :) Last fiddled with by Keller on 20050612 at 19:05 

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