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: 938 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: 343 Thanks: 5 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: 938 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?  

Tags 
prime, theory 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
prime algorithm theory and paralells to pascall  PerAA  Number Theory  4  March 3rd, 2013 07:52 AM 
prime fibonacci algorithm theory  PerAA  Number Theory  2  November 11th, 2012 06:34 AM 
prime algorithm theory  PerAA  Number Theory  9  November 10th, 2012 05:35 AM 
Additive theory of number and prime twins numbers  ibougueye  Number Theory  8  February 7th, 2012 04:33 PM 
Prime GCD Theory Proof  frankJ  Number Theory  11  May 4th, 2009 04:10 PM 