Number Theory

    

Distribution of Artificial Prime Numbers in the Fibonacci Sequence and Their Relation to the Counting Function

Authors: Jose Acevedo Jimenez

This paper introduces the concept of artificial primes, defined within a specific subset SSS of positive integers greater than one. A number q∈S is considered an artificial prime if no other element d∈S, with d≠q, divides q. Focusing on the subset of Fibonacci numbers greater than 1, we analyze the behavior of artificial primes in this sequence. Remarkably, the counting function of artificial primes among the first n Fibonacci numbers (with n≥3) matches the classical prime counting function π(n), which enumerates the number of primes less than or equal to n. This correspondence highlights a surprising structural parallel between classical prime distribution and internal divisibility properties within recursive numerical sequences.

Comments: 6 Pages.

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[v1] 2025-04-11 18:30:49

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