English

An Explicit Result for the Sum of Two Almost Primes

Number Theory 2026-05-12 v3

Abstract

We show that every N2N \geq 2 can be written as the sum of positive integers aa and bb where Ω(ab)40\Omega(ab) \leq 40. The result is obtained through the direct application of an explicit lower bound Selberg sieve along with some computation and optimisation.

Keywords

Cite

@article{arxiv.2602.22720,
  title  = {An Explicit Result for the Sum of Two Almost Primes},
  author = {Adrian Dudek and Lachlan Dunn},
  journal= {arXiv preprint arXiv:2602.22720},
  year   = {2026}
}

Comments

9 pages