20050918, 10:13  #45  
Feb 2004
France
3^{2}·103 Posts 
Quote:
Saouter used the Pocklington's theorem, with where . Necessity: If there exists a k satisfying Pocklington's conditions, then the prime divisors p_i of F_n,3 have the form , and multiplying p_1 and p_2 prime divisors of F_n,2 leads to a contradiction, and F_n,2 is prime. If one uses the same way for F_n,3 numbers , candidate factors of F_n,3 should have the form. And, using the same idea than Saouter, it only seems able to prove that if a Pรฉpin test does exist for F_n,3 numbers, it can only help to prove that F_n,3 has less than 4 factors, which is not a contradiction and does not help to prove F_n,3 is prime. Prime divisors p_i of F_n,3 seem to have the form . F_0,5 = 31 = 1+2*3*5 F_1,5 = 1082401 = 601 * 1801 601 = 1 + 2^3*3*5^2 1801 = 1 + 2^3*3^2*5^2 F_2,5 = (1+2^4*3*5^3*41*...)*(1+2^4*3^2*5^3*41*...) Can we mix Pocklington's theorem with the real form of factors of F_n,3 numbers and build a contradiction ? Any idea ? Tony Last fiddled with by T.Rex on 20050918 at 10:27 

20050918, 14:10  #46 
Aug 2002
Buenos Aires, Argentina
1,423 Posts 
I've just uploaded the new version of the page with the missing factor found by Saouter.

20050918, 15:07  #48  
Jan 2005
D_{16} Posts 
Apology for asking the question.
Quote:
At least I did not have to resort to cursing to express myself. Please, in the future do not respond to my questions if you must curse to express yourself. Carlos 

20050918, 20:20  #49  
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across
10101110001011_{2} Posts 
Quote:
My response was to Alex Kruppa's posting, not yours. Review the posting history and you will find that I quoted his words. The phrase "stating the bleeding obvious" is mildly ironic and contains no perjorative connotations in English (i.e. the language spoken in England). I've no idea whether it exists in American or other variants of English. Alex clearly understood it. Paul 

20051008, 11:48  #50 
Aug 2002
Buenos Aires, Argentina
1,423 Posts 
I've written a program to compute factors of . In only two days I found many new factors that you can see in my Factors of Modified Fermat Numbers page.
I'm optimizing the program and once it is ready for "public consumption" I will post it at the same page. 
20051008, 16:45  #51 
Feb 2004
France
3^{2}·103 Posts 
"Feneralized Fermat Numbers"
I've had an email discussion with Dr Cosgrave. He is very busy with his students, so he cannot spend too much time searching his papers. Maybe later.
Nevertheless, he said that he did not find a new prime "Generalized Fermat Number" (GFN): . He studied many values of n and r. On his site, there is a paper (Fermat 6) that explains the story. His colleague Wilfrid Keller could provide more information later. Alpertron, I'm interested in your program for finding factors of numbers. Can it be extended to any GFN ? Tony 
20051008, 17:23  #52  
Aug 2002
Buenos Aires, Argentina
1,423 Posts 
Quote:


20051010, 00:12  #53 
Aug 2002
Buenos Aires, Argentina
1,423 Posts 
I've just uplodaded it to my Web server. You can download it by going to the bottom of:
http://www.alpertron.com.ar/MODFERM.HTM Please let me know if there are errors. 
20051010, 09:16  #54  
Banned
"Luigi"
Aug 2002
Team Italia
2·41·59 Posts 
Quote:
Luigi 

20051010, 17:04  #55  
Feb 2004
France
3^{2}×103 Posts 
In ASM ! Bravo !
Quote:
I've also done a quick experiment with icc/Linux and it says: icc genferm.c o genferm lm genferm.c(12): error: invalid combination of type specifiers typedef long long __int64; ^ compilation aborted for genferm.c (code 2) Seems icc does not like this. But, is icc useful there ? Tony 

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