Primitive Roots In Short Intervals

2018/06/01 by N. A. Carella, Carella, N. A.
Computer Science · Mathematics · #11A07 (Primary) #11N37 (Secondary) #Analytic Number Theory Research #Coding theory and cryptography #FOS: Mathematics #General Mathematics (math.GM) #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.1806.01150

openalex publication_date 2018/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let p≥ 2 be a large prime, and let N≫ ( log p)^1+ε. This note proves the existence of primitive roots in the short interval [M,M+N], where M ≥ 2 is a fixed number, and ε>0 is a small number. In particular, the least primitive root g(p)= O ((log p)^1+ε ), and the least prime primitive root g^*(p)= O ((log p)^1+ε ) unconditionally.

Citations

• Approximate formulas for some functions of prime numbers
• The Difference Between Consecutive Primes

Related

• Topics In Primitive Roots
• Prescribed Primitive Roots And The Least Primes
• Small Prime Primitive Roots in Arithmetic Progressions
• Least Prime Primitive Roots
• Configurations Of Consecutive Primitive Roots