Number Theory

    

A Lucas-Lehmer Type Primality Test for Numbers of the Form 4p^n-1

Authors: Predrag Terzić

We present a new, specific primality test for numbers of the form N = 4p^n - 1, where p is an odd prime and n > 0. The test is a generalization of the Lucas-Lehmer test for Mersenne numbers and relies on a sequence defined by Dickson polynomials. We prove that, under a certain condition, N is prime if and only if the n-th term of a specific sequence is congruent to zero modulo N. This provides a deterministic primality test for this family of numbers.

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[v1] 2025-06-02 19:37:53

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