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Abstract
Prime generation via polynomials: Analysis and applications
Author(s): Samrat Singh*This research offers an extensive analysis of a family of prime-generating polynomials Pk(n)=n2−(2k−79)n+[41+(k−39) (k−40)], designed to generate prime numbers for integer values of n up to k where k ∈ {1, 2, . . . , 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.
