Study about the Pattern of Prime Numbers

Abstract

Prime numbers are fundamental to the most common type of asymmetric encryption used today, namely Diffie-Hellman key exchange, Rivest-Shamir-Adleman cryptosystems, ElGamal Cryptosystem, Elliptic curve cryptosystems, etc.The prime numbers \(p\geq 5\) obey a pattern that can be described by two forms or geometric progressions \(6m+[5,7] \rightarrow m\in \mathbb{z}^+\) or \(6k\pm 1 \rightarrow k\in \mathbb{z}^+\) that facilitates obtaining them sequentially, being possible also to calculate the quantity of primes that are in the geometric progressions \(6k\pm 1 \), fore  \(k\geq 1\) as it is described in this document.