Research Projects

This project aims to study the size of the set of all primes with a bad primitive root and develop faster algorithms for searching for such roots. The objectives include assuming Artin's conjecture, heuristically finding the asymptotic growth rate of P_a, studying the infinitude and density of primes with at least one bad primitive root, constructing faster algorithms to list such primes, studying the relationship between Wieferich primes and primes with bad primitive roots, and studying the properties of bad primitive roots to develop a cryptographic system based on primitive roots.