Prime numbers with an almost prime reverse
Number Theory
2025-07-11 v2
Abstract
Let be an integer greater than or equal to . For any integer , we denote by the reverse of in base , obtained by reversing the order of the digits of . We establish a Bombieri-Vinogradov type theorem for the set of the reverses of the prime numbers. Combined with sieve methods, this permits us to prove that there exist and such that, for at least primes , the reverse has at most prime factors. Some explicit admissible values of are given.
Cite
@article{arxiv.2506.21642,
title = {Prime numbers with an almost prime reverse},
author = {Cécile Dartyge and Joël Rivat and Cathy Swaenepoel},
journal= {arXiv preprint arXiv:2506.21642},
year = {2025}
}
Comments
Minor corrections and page settings modified. 92 pages