The occurrence of prime numbers revisited

Abstract

Based on an arithmetical and autocatalytic approach, the authors propose a solution for the occurrence of prime numbers. Exact arithmetical calculations are provided for: the closest prime to any given positive integer (or any number of bigger or smaller primes from that integer); the quantity of prime (and composite) numbers between 1 and any positive integer; the quantity of prime (and composite) numbers between any two positive integers.

Keywords

• Occurrence of prime numbers
• Occurrence of composite numbers
• Autocatalysis
• Activator-inhibitor systems