Models of Prime-Like Sequences Generated by Least Element Sieve Operations Like the Sieve of Eratosthenes

TL;DR

This paper proposes alternative models for prime-like sequences generated by sieve operations, aiming to explain key randomness properties of prime numbers and related conjectures.

Contribution

It introduces new models of sieve-generated sequences to analyze prime number properties and conjectures.

Findings

Models provide insights into twin prime conjecture

Models help explain the Riemann hypothesis implications

Potential to unify understanding of prime distribution

Abstract

We suggest other models of sieve generated sequences like the Sieve of Eratosthenes to explain randomness properties of the prime numbers, like the twin prime conjecture, the lim sup conjecture, the Riemann conjecture, and the prime number theorem.