Number Theory

    

Prime Number Generation Without Factorization: A Hyperbola-Based Algorithm

Authors: Jayme Mendes

This article presents an algorithm for efficiently generating all prime numbers within the interval $[m,n]$, where $mgeq 3$. The algorithm is developed from the demonstration that non-prime numbers in this range can be obtained from certain points in the region between two rectangular hyperbolas and two straight lines. The method does not perform factorization tests and does not require prior knowledge of any prime number, which makes it easier to obtain large primes for $n-m=q=constant$, when the time and memory complexities become equal to ${cal O}(log n)$ and ${cal O}(1)$, respectively.

Comments: 10 Pages.

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Submission history

[v1] 2025-04-14 19:31:11
[v2] 2025-04-22 12:11:40

Unique-IP document downloads: 325 times

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