John Grieve: Points of Symmetry: Grieve's Twin Prime Conjecture    
 Points of Symmetry: Grieve's Twin Prime Conjecture0 comments
22 Feb 2010 @ 18:29, by John Grieve

Points of Symmetry

My twin prime conjecture of August 2008 implied the idea that among primes, and particularly twin primes, there was some sort of symmetry. I have referred to this as "Points of Symmetry", and used it to understand why there are always at least two pairs of twin primes between consecutive primes squared.

This is my first effort at demonstrating these points of symmetry and suggesting a general formula. The high correspondance of primes in these examples suggests an almost perfect symmetry.

If N is an odd prime square it and divide it by 2 and round down to the even number. For example, 7 squared is 49 and when we divide by 2 we get 24.5 which we round down to 24.

24 =11 13
24 =7 17
24 =5 19

Another simple example will show the potential of this formula:

11 squared =121 which divided by 2 = 60.5 which rounds down to 60

60=53 7
60=47 13
60=43 17
60=41 19
60=37 23
60=31 29

There are obvious links here between the twin prime conjecture and Goldbach's problem and if you use a Goldbach calculator to find the number of pairs of primes that combine you will find that numbers generated by my formula give an exceptionally high number of pairs.

For example 420 gives 30 pairs, which is remarkably high. 420 =29 squared/2 rounded down.

I will leave you to investigate further.


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