July 18th, 2014, 09:38 AM  #1 
Member Joined: Nov 2012 From: Germany Posts: 59 Thanks: 0  Another prime theory
First the facts: a is element of IN a^3+(a1)^3=(2a1)*(a^2a+1) x=a^3+(a1)^3 y=(2a1) z=(a^2a+1) x=y*z Ok, now my new theory: If (x1)/3 or (x+1)3 is element of IN, then x have one primefactor in the form of y or z! It is similar to: If the cross sum of x is completely divisible by 9, then it is the only case were x have none primefactor in the form of y or z! To see what i mean you can watch the table.. Have fun with prime research^^ 
July 18th, 2014, 10:13 AM  #2 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 937 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms 
What is IN? Is this the integers $\mathbb{Z}$, the positive integers $\mathbb{Z}^+$, the natural numbers $\mathbb{N}=\{0,1,\ldots\}$, or something else? It seems that you are saying: If a^3+(a1)^3 is not divisible by 3, then either 2a1 or a^2a+1 is prime. Is this correct? 
July 18th, 2014, 12:54 PM  #3 
Member Joined: Nov 2012 From: Germany Posts: 59 Thanks: 0 
IN is the natural numbers. yes or lets say If a or a+1 is divisible by 3, then either 2a1 or a^2a+1 is prime. But i found to much composites, often when y is divisible by 5, also when y is p^k Maybe just luck in a small research But this is interesting: When log((a^2a+1)+1)=log(z+1) is element of IN, then log(z+1) is an Mersenne exponent. There are Mersenne Primes z for a={2;3;6;91;...} Last edited by PerAA; July 18th, 2014 at 01:16 PM. 
July 19th, 2014, 05:45 PM  #4 
Senior Member Joined: Aug 2008 From: Blacksburg VA USA Posts: 338 Thanks: 4 Math Focus: primes of course 
strike the log from both sides, it's irrelevant. Check your claim, I don't think 91 works.

July 19th, 2014, 05:49 PM  #5  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 937 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Quote:
Is this for any integers a and z? What is the base of the logarithm?  

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