Prime Generation via Polynomials: Analysis and Applications

Samrat Singh

doi:10.20944/preprints202411.0123.v1

Preprint Article Version 1 This version is not peer-reviewed

Version 1 : Received: 1 November 2024 / Approved: 1 November 2024 / Online: 4 November 2024 (09:01:36 CET)

This research offers an extensive analysis of a family of prime-generating polynomials $ P_k(n) = n^2 - (2k - 79)n + [41 + (k - 39)(k - 40)] $, designed to generate prime numbers for integer values of $ n $ up to $ k $ where $ k \in \{1, 2, \ldots, 80\} $. We elaborate on mathematical clarity, consistency in proofs, error bounds, prime repetition analysis, and cryptographic implications. This study provides in-depth inductive proofs, graphical error bounds analysis, prime repetition statistics, and cryptographic security assessments, offering novel insights and future directions for research in number theory and secure prime generation.

primes; polynomials; prime-generation; cryptography

Computer Science and Mathematics, Algebra and Number Theory

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Prime Generation via Polynomials: Analysis and Applications

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