Genetic Properties of Integers and their Applications

Abstract

The paper first makes an overview on the genetic properties of the odd integers by summarizing tens of theorems that have been proved in literatures, and then presents several new theorems related with the genetic properties and with the divisor's distribution of a composite odd integer. Based on the theorems, the paper also proposes a guideline of designing parallel algorithm to factorize an odd integer. Numerical experiments show the genetic property is helpful for solving the hard problem of integer factorization.