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April 18, 2026Open Access

A Spectral Scaling Law for Partial Sums of Primes

Key Points

To establish a predictive spectral law for the summatory function of primes, Ψ(K).
Proposes a scaling law C(K) ∼ K3/2 √ln K for prime sums.
Introduces new mathematical framework for predicting prime fluctuations.
Establishes the first predictive model for prime summatory function.
Enables predictions of prime sums without knowing individual primes.

Abstract

This foundational manuscript, submitted for peer review on April 04, 2026, establishes a breakthrough in number theory by proposing a predictive spectral law for the summatory function of primes Ψ(K). For the first time, it introduces the scaling C(K) ∼ K3/2 √ln K, allowing for the prediction of prime sums fluctuations without prior knowledge of individual primes. This work serves as the precursor to the MokraBela Spectral Project, providing the physical-mathematical basis for the energy flux constants S and λ Legal Note & Priority Claim: This manuscript was originally submitted to the International Journal of Number Theory (IJNT) on April 04, 2026. This DOI establishes the global priority of the initial spectral discovery. .

A Spectral Scaling Law for Partial Sums of Primes

Key Points

Abstract

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