Work

Estimating the Number of Primes in Unusual Domains

Year: 2026

Type: article

Abstract: The Prime Number Theorem states that the number of primes in 1, . . . , x, denoted π(x), is approximately x/ln(x) . In this paper, we investigate the distribution of primes for domains other than N. First we look at A d = x: x ≡ 1 (mod d). We give a heuristic argument to form a conjecture on the number of congruence monoid primes in Ad that are ≤ x. We then provide empirical evidence that indicates our conjecture is close but may need some correction. Second, we do similar calculations for the Gaussian Integers. Third, we discuss the difficulty of these types of questions for quadratic extensions of Z.

Source: ACM SIGACT News

DOI: 10.1145/3802807.3802811

Authors: Jonathan Cai, Ryan Diehl, Rohan Sinha, William Gasarch, Ian Kim

Institutions: University of Maryland, College Park, SUNY Morrisville, Morristown High School, Zionsville Community High School, Manhattan High School, Pocatello High School

Language: English

Topic: Analytic Number Theory Research

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7147582691

FWCI:

Cites: 3

Cited by:

Related to: