Primes with small primitive roots
Abstract
Let δ ( p ) tend to zero arbitrarily slowly as p → ∞ . We exhibit an explicit set 𝒮 of primes p , defined in terms of simple functions of the prime factors of p - 1 , for which the least primitive root of p is ≤ p 1 / 4 - δ ( p ) for all p ∈ 𝒮 , where # { p ≤ x : p ∈ 𝒮 } ∼ π ( x ) as x → ∞ .
Fields of Study & Subjects
History and Theory of Mathematics
Analytic Number Theory Research
Mathematics and Applications
Publication details
- Journal / source
- Journal de Théorie des Nombres de Bordeaux
- Volume
- 38
- Issue
- 1
- Pages
- 71–89
- Publication date
- 24 April 2026
- Language
- EN