On a Deterministic Property of the Category of $k$-almost Primes: A Deterministic Structure Based on a Linear Function for Redefining the $k$-almost Primes ($\exists n\in \mathrm{N}$, $1\le k\le n$) in Certain Intervals

Abstract

In this paper based on a sort of linear function, a deterministic and simple algorithm with an algebraic structure is presented for calculating all (and only) $k$-almost primes ($where$ $\exists n\in \mathrm{N}$, $1\le k\le n$) in certain interval. A theorem has been proven showing a new deterministic property of the category of $k$-almost primes. Through a linear function that we obtain, an equivalent redefinition of the $k$-almost primes with an algebraic characteristic is identified. Moreover, as an outcome of our function's property some relations which contain new information about the $k$-almost primes (including primes) are presented.

10 pages. Accepted and presented article in the 11th ANTS, Korea, 2014. The 11th ANTS is one of international satellite conferences of ICM 2014: The 27th International Congress of Mathematicians, Korea. (Expanded version)

References in corpus (2)

• Factorising numbers with a Bose-Einstein condensate
• A function to calculate all relative prime numbers up to the product of the first n primes