Number Theory

    

Prime Numbers Density Approximation

Authors: Edward C. Larson

A novel derivation of the density of the distribution of prime numbers is presented, based on a simple frequentist analysis and the smallest scale at which a rigorous upper bound on the frequency holds. An approximating differential equation is derived. It is shown that in the asymptotic limit, the density of primes, pi(x), scales as x / ln x, in accordance with the Prime Number Theorem (PNT). The approach bridges the gap between discrete number theory and continuous differential modeling, offering a mechanistic explanation for the observed thinning of prime density that mirrors the foundational results of classical analysis.

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[v1] 2026-03-01 22:19:46

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