Least Prime Primitive Roots

2017/09/01 by N. A. Carella, Carella, N. A.
Mathematics · #11A07 (Primary) 11Y16 #11M26 (Secondary) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Finite Group Theory Research #General Mathematics (math.GM)

paper · pdf · doi:10.48550/arxiv.1709.01172

openalex publication_date 2017/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This note presents an upper bound for the least prime primitive roots g^*(p) modulo p, a large prime. The current literature has several estimates of the least prime primitive root g^*(p) modulo a prime p≥ 2 such as g^*(p)≪ p^c, c>2.8. The estimate provided within seems to sharpen this estimate to the smaller estimate g^*(p)≪ p^{5/log log p} uniformly for all large primes p≥ 2.

Citations

• Pólya-Vinogradov and the least quadratic nonresidue

Related

• Topics In Primitive Roots
• The Least Square-free Primitive Root Modulo a Prime
• The least primitive root modulo p²
• Prescribed Primitive Roots And The Least Primes
• The Least Prime Primitive Root and the Shifted Sieve