Number Theory

    

A Deterministic Polynomial-Time Primality Test Based on Binomial Coefficient Divisibility

Authors: Mar Detic

This paper describes a deterministic primality test based on thedivisibility properties of binomial coefficients modulo a candidate integer n. The test checks the condition nk≡ 0 (mod n) for all k inthe range 1 ≤ k ≤ ⌊log2 n⌋. This criterion is a direct consequence ofthe polynomial identity (x + 1)n ≡ xn + 1 (mod n), which holds ifand only if n is prime. The algorithm uses an efficient recurrence relation, achieves a time complexity of Oe(log3 n), and correctly identifiescomposite numbers, including Carmichael numbers.

Comments: 3 Pages.

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Submission history

[v1] 2024-12-02 02:58:17
[v2] 2024-12-09 21:32:45
[v3] 2025-01-02 21:31:44
[v4] 2025-08-02 00:19:03
[v5] 2025-08-30 10:31:05

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