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An Explicit Result for the Sum of Two Almost Primes

Adrian Dudek, Lachlan Dunn

Abstract

We show that every $N \geq 2$ can be written as the sum of positive integers $a$ and $b$ where $Ω(ab) \leq 21$. The result is obtained through the direct application of an explicit lower bound Selberg sieve along with some computation and optimisation.

An Explicit Result for the Sum of Two Almost Primes

Abstract

We show that every can be written as the sum of positive integers and where . The result is obtained through the direct application of an explicit lower bound Selberg sieve along with some computation and optimisation.
Paper Structure (4 sections, 8 theorems, 37 equations)

This paper contains 4 sections, 8 theorems, 37 equations.

Table of Contents

  1. Introduction
  2. Preliminary Lemmas
  3. Proof of Theorem \ref{['maintheorem']}
  4. Acknowledgements

Key Result

Theorem 1.1

Every even integer $N \geq 4$ can be written as the sum of a prime and a number $r$ such that $\Omega(r) \leq 395$.

Theorems & Definitions (13)

  • Theorem 1.1
  • Theorem 1.2
  • Theorem 1.3
  • Lemma 2.1
  • proof
  • Lemma 2.2
  • proof
  • Lemma 2.3
  • proof
  • Lemma 3.1
  • ...and 3 more