Number Theory

    

Artificial Prime Numbers in the Fibonacci Sequence: A Structural Approach

Authors: Jose Acevedo Jimenez

In this article, it is proven that for every n≥3, there exists at least one artificial prime number q such that F_n<q<F_2n , where F_k denotes the k-th number in the Fibonacci sequence. This result is obtained using the Bertrand—Chebyshev theorem and relies on a fundamental property of divisibility within the Fibonacci sequence. Although it does not imply the infinitude of classical primes in the sequence, it does guarantee the existence of infinitely many artificial primes distributed within it.

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[v1] 2025-04-16 01:52:04

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