On Telhcirid's theorem on arithmetic progressions

TL;DR

This paper investigates the distribution of reversed primes in arithmetic progressions, proving their infinitude under certain conditions and establishing an effective Siegel--Walfisz type result with improved bounds.

Contribution

It introduces the concept of reversed primes and proves their infinitude in arithmetic progressions, providing an effective distribution result with enhanced bounds over classical methods.

Findings

Reversed primes are infinite in certain arithmetic progressions.

An effective distribution theorem for reversed primes is established.

The results improve bounds compared to classical prime distribution theorems.

Abstract

In this paper, we study the distribution of the digital reverses of prime numbers, which we call the "reversed primes". We prove the infinitude of reversed primes in any arithmetic progression satisfying straightforward necessary conditions provided the base is sufficiently large. We indeed prove an effective Siegel--Walfisz type result for reversed primes, which has a larger admissible level of modulus than the classical case.