Barry Dalgarno

Originally published on 18 September 2014 under the title A Conjecture on the Structure of Random Choice. 

Dedicated to my mother Ruth Dalgarno

       This is a short communication on randomness in relation to the geometry of the prime numbers. The nature of geometric entanglement has been discussed previously (references 1 and 2). Consider the two-dimensional lattice in which the prime interval templates are chosen randomly. There is an infinite set of possible geometric arrangements. Now consider the infinite subset in which the lattice tessellation leaves no discontinuity in the perimeter. When the prime number symmetry equation (see reference 2) is applied to the structure of random choice, the proportionality coefficient (sR) is found to have a value of approximately 2.4  (see reference 3).

As N approaches infinity

References

Ruth Dalgarno - A Life Remembered

https://sites.google.com/view/ruth-dalgarno/home

1. B. Dalgarno (2009). A New Law of Prime Numbers Based on an Infinite Structure of Sequential Triangular Symmetry from Finely-Tuned Geometric Entanglement of the Prime Intervals.

https://sites.google.com/site/geometryoftheprimes/

2. B. Dalgarno (2011). Geometric Entanglement of Prime Number Intervals: An Operation that Reveals the Symmetry Underlying the Distribution of the Primes.

https://sites.google.com/site/geometryoftheprimes/geometric-entanglement-of-prime-number-intervals---an-operation-that-reveals-the-symmetry-underlying-the-distribution-of-the-primes

3. B. Dalgarno (2014). Structure of Random Choice. 

https://sites.google.com/site/geometryoftheprimes/structure-of-random-choice

4. B. Dalgarno (2014). Structure of the Prime Numbers.

https://sites.google.com/site/geometryoftheprimes/structure-of-the-prime-numbers