A Formal Conjecture on the Asymptotic Distribution of Primes within Fibonacci Intervals

This paper proposes a novel conjecture regarding the intersection of the Prime counting function, , and the Fibonacci sequence, . While the logarithmic thinning of prime numbers is well-documented via the Prime Number Theorem, and the asymptotic growth rate of the Fibonacci sequence is established by Binet's Formula, the density of primes existing strictly between consecutive Fibonacci milestones has not been unified under a single scaling constant. Based on historical computational models originating in 2008 and verified through modern Python-based empirical analysis up to F40, we conjecture that the ratio of the number of primes in consecutive Fibonacci intervals converges asymptotically to the Golden Ratio,