Least Prime Primitive Roots
N. A. Carella

TL;DR
This paper establishes a sharper upper bound for the least prime primitive root modulo a large prime, improving previous estimates and providing a more precise understanding of primitive roots' distribution.
Contribution
It introduces a new upper bound for the least prime primitive root, refining existing estimates to a smaller, more accurate bound for large primes.
Findings
New upper bound: $g^*(p) \\ll p^{5/\\log \\log p}$ for large primes
Improves upon previous bounds like $g^*(p) \\ll p^c, c>2.8$
Results hold uniformly for all sufficiently large primes
Abstract
This note presents an upper bound for the least prime primitive roots modulo , a large prime. The current literature has several estimates of the least prime primitive root modulo a prime such as . The estimate provided within seems to sharpen this estimate to the smaller estimate uniformly for all large primes .
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAnalytic Number Theory Research · Algebraic Geometry and Number Theory · Finite Group Theory Research
