The Prime Cuboctahedron – Order from Chaos

The Prime Cuboctohedron

“…despite their simple definition and role as the building blocks of the natural numbers, the prime numbers grow like weeds among the natural numbers, seeming to obey no other law than that of chance, and nobody can predict where the next one will sprout.”  -Don Zagier 1975

There is structure to the prime numbers. Divine order from apparent chaos. Prime numbers, or numbers that are divisible by only themselves and one, don’t grow like weeds among the other numbers. A very simple pattern emerges when the numbers are laid out in multiples of six.

The cuboctahedron, or vector equilibrium, is the most simple geometric form that is in balance with the space it occupies, in perfect equilibrium on all sides. Organizing numbers one to infinity in a radial pattern on its twelve points creates a 2-Dimensional cross emerging from the most harmonious 3-Dimensional form. All prime numbers greater than three reside on this plane of existence. This esoteric numerical gnosis shatters contemporary cosmogonic beliefs and notions that the universe is random.  There is order and intelligence in nature. Our Universe is not random and product of time and luck. Contrary to materialistic and reductionistic ideologies about the cosmos and our place in it, this knowledge suggests there exists an intelligent architect of our reality.

Statements by famous Mathematicians on Prime numbers:

“Mathematicians have tried in vain to discover some order in the sequence of Primes and we have reason to believe that it is a mystery into which the mind will never penetrate” -Leonhard Euler, 1707-1783

“No branch of number theory is more saturated with mystery than the study of prime numbers: those exasperating, unruly integers that refuse to be divided evenly by any integers except themselves and 1.” M. Gardner -1964

“…there is no apparent reason why one number is prime and another not. To the contrary, upon looking at these numbers one has the feeling of being in the presence of one of the inexplicable secrets of creation.” – D. Zagier -1977

“It will be another million years, at least, before we understand the Primes” – Paul Erdos, 1998
How can so much of the formal and systematic edifice of mathematics, the science of pattern and rule and order per se, rest on such a patternless, unruly, and disorderly foundation? Or how can numbers regulate so many aspects of our physical world and let us predict some of them when they themselves are so unpredictable and appear to be governed by nothing but chance?” H. Peter Aleff -2011

For more on prime numbers see the work of Anthony Morris and his Numerical Universe.

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