The Prime Solar System

A mapping of prime numbers onto a solar system is presented. The Prime Solar System (PSS) can be seen as a physical system that is factorising positive integers. Reversely, the factorisation of integers can be seen as a way to compute the location of the PSS planets. Periodicities of the PSS are translated into periodicities of the factorisation of positive integers. This allow:

• the forecast of the next prime number after the integer N form the knowledge of the configuration of the PSS at time N,

• the forecast of voids, that is, the location of regions without prime numbers. Voids of length p_l − 1 starting at p_l# + 1 and ending at pl# + pl are guaranteed to exist for l = 1,2,···,

• the forecast of some factors of large integers from the knowledge of the factors of smaller integers. If n = q mod p_J# is true with q > p_J# then n and q share the same first J primes as factors and as not-factors.