Prime numbers have found a wide application in science. Recently use has been made of a 24 prime number spiral that can apparently be linked to the periodicity of atomic matter as well as to structures in the universe. In many of these conjectures as well as proofs such as that of the abc conjecture one starts from prime numbers greater than or equal to 5 (i.e. all prime numbers, except 2 and 3, can be written in the form 6n+-1). Is there a simple reason for this?
http://www.sciencedirect.com/science/article/pii/S1463018404000061
Avoid p=2 if u have quadratic forms. Avoid p=3 if u have elliptic curves. That is the most common reason in an arithmetic situation.
Incidentally the cross of prime numbers as advocated by Plichta is trivial to explain. If
p=24k+a then a cannot be a multiple of 2 or 3 which divide 24. That gives you four forbidden sectors in the spiral...
As a non-mathematician that makes sense to me. It is therefore probable that our speculations in Number Theory and the Periodicity of Matter are also trivial, or wrong.
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