English

Almost prime numbers

Number Theory 2026-03-03 v1

Abstract

We introduce the concept of an almost prime number generalizing a prime number. It turns out that a composite almost prime number must be a Carmichael number, in case it exists. We prove several properties of almost prime numbers and conjecture the infinitude of composite almost primes. In this regards, the latter seems to hold the potential of shading light onto the infinitude of primes with ω(p1)2\omega(p-1)\leq 2.

Keywords

Cite

@article{arxiv.2603.00679,
  title  = {Almost prime numbers},
  author = {Tigran Hakobyan},
  journal= {arXiv preprint arXiv:2603.00679},
  year   = {2026}
}
R2 v1 2026-07-01T10:57:15.965Z