Prescribed Primitive Roots And The Least Primes
N. A. Carella

TL;DR
This paper investigates the distribution of primes for which a fixed integer is a primitive root, providing bounds close to a long-standing conjecture and proving the existence of small such primes.
Contribution
It establishes the existence of small primes where a fixed integer is a primitive root, approximating the conjectured upper bounds.
Findings
Proves the existence of small primes p where q is a primitive root.
Provides bounds p (\u221a) ( ext{log} x)^c, close to conjectured bounds.
Advances understanding of primitive roots and prime distribution.
Abstract
Let be a fixed integer, and let be a large number. The least prime number such that is a primitive root modulo is conjectured to be where . This note proves the existence of small primes , where is a constant, a close approximation to the conjectured upper bound.
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Taxonomy
TopicsAnalytic Number Theory Research · Mathematics and Applications · Algebraic Geometry and Number Theory
