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July 18th, 2014, 08:38 AM   #1
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Another prime theory

First the facts:

a is element of IN

a^3+(a-1)^3=(2a-1)*(a^2-a+1)

x=a^3+(a-1)^3
y=(2a-1)
z=(a^2-a+1)

x=y*z

Ok, now my new theory:

If (x-1)/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^^
Attached Images xyz-prime-method.PNG (3.1 KB, 1 views) xyz-prime-table.jpg (21.6 KB, 4 views) July 18th, 2014, 09:13 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+(a-1)^3 is not divisible by 3, then either 2a-1 or a^2-a+1 is prime. Is this correct? July 18th, 2014, 11:54 AM #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 2a-1 or a^2-a+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^2-a+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 12:16 PM. July 19th, 2014, 04:45 PM #4 Senior Member   Joined: Aug 2008 From: Blacksburg VA USA Posts: 346 Thanks: 6 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, 04:49 PM   #5
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Quote:
 Originally Posted by PerAA IN is the natural numbers. yes or lets say If a or a+1 is divisible by 3, then either 2a-1 or a^2-a+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
Indeed. The conjecture fails infinitely often, indeed on a subset of the naturals with density 1.

Quote:
 Originally Posted by PerAA When log((a^2-a+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;...}
Is this for any integers a and z? What is the base of the logarithm? Tags prime, theory Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post PerAA Number Theory 4 March 3rd, 2013 06:52 AM PerAA Number Theory 2 November 11th, 2012 05:34 AM PerAA Number Theory 9 November 10th, 2012 04:35 AM ibougueye Number Theory 8 February 7th, 2012 03:33 PM frankJ Number Theory 11 May 4th, 2009 03:10 PM

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