20050714, 16:32  #1 
Nov 2003
2^{2}·5·373 Posts 
Project proposal?
I will agree with the statement:
"Knowing if M_p 2 is also prime" is somewhat interesting. However, I would like to observe that in the current stateoftheart in factoring, that trying to factor M_p 2 is HOPELESS, except for the smallest p. The level of effort spent so far has not been unreasonable. (IMO). However, I think spending yet more time is unlikely to lead to success(es). Allow me to instead suggest an alternative project which does have some hope of success: Extending the Cunningham project to 'homogeneous form', i.e. numbers of the form A^n  B^n with (A,B) = 1, B>1. [Cunningham is just B = 1] I have already done some modest work in this area. I have completed the following: ("Base x to y" means that I have completed A^n  B^n for A = x and all B < A up to exponent y with (A,B) = 1) Base 3 to 330 Base 4 to 256 Base 5 to 225 Base 6 to 195 Base 7 to 165 Base 8 to 155 Base 9 to 135 Base 10 to 130 Base 11 to 130 Base 12 to 120 I will make these results available to anyone who asks. I don't post them here; the current tables are ~600Kbytes total. Perhaps some of you might like to extend these? Such an effort would be achievable. I am also cross posting this to the ''twin prime' discussion. 
20050715, 13:43  #2 
Sep 2002
1226_{8} Posts 
What does (A,B)=1 mean in the context of your project proposal ?
For the first item on the list Base 3 to 330 does it evaluate to 3^0  0^0 3^0  0^1 ... 3^0  0^329 3^0  0^330 3^1  1^0 ... 3^1  1^330 ... 3^330  2^0 ... 3^330  2^330 If the preceding is incorrect, then please show the correct evaluation. 
20050715, 14:03  #3 
Aug 2002
Buenos Aires, Argentina
2^{2}×3×5×23 Posts 
It appears that he wants to factor:
3^2  2^2 3^3  2^3 3^4  2^4 ... 3^330  2^330 4^2  2^2 ... 4^256  2^256 4^2  3^2 ... 4^256  3^256 where the exponents are the same. In that case there are forms of Aurifeuillan factorizations that help factor many of these numbers. There is a publication of Richard Brent about these Aurifeuillian factorizations. 
20050715, 14:05  #4  
Nov 2003
2^{2}×5×373 Posts 
Quote:
I wrote: numbers of the form A^n  B^n with (A,B) = 1, B>1. [Cunningham is just B = 1] (A,B) = 1 is standard, numbertheoretic notation. (x,y) is the GCD of x and y. And since I clearly wrote A^n  B^n, I do not understand why you are suggesting putting different exponents on A and B. And since I also clearly wrote B > 1, I do not understand why you are putting B=0. Was my writing unclear???? BTW, I have also done A^n + B^n to the same limits. 

20050715, 14:06  #5 
Aug 2002
Buenos Aires, Argentina
2^{2}·3·5·23 Posts 
It appears that I made a mistake.
4^2  2^2 ... 4^256  2^256 should not be included because (A,B)>1. They are already factored in the Cunningham project. 
20050716, 23:47  #6 
Sep 2002
1010010110_{2} Posts 
Thank you for the explanation.
Last fiddled with by dsouza123 on 20050716 at 23:49 
20050719, 05:05  #7 
Jun 2003
2^{2}×61 Posts 
approximately how big are the numbers that would still need factoring in this 'project'?

Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
PhD Research Proposal  pinhodecarlos  Soap Box  2  20120818 22:01 
Proposal for a new subsubforum  Orgasmic Troll  Miscellaneous Math  3  20081202 18:47 
Proposal for new subforum  ewmayer  Miscellaneous Math  49  20051010 23:25 
Proposal: "Math for beginners" subforum  Mystwalker  Math  18  20050530 03:53 
A Proposal for searching Recurrence Series Primes  Erasmus  Factoring  3  20040514 09:26 