P
Prime OS
2025 Analytic Number Theory

Prime Calculation OS &
State-of-the-Art Benchmarks

Moving beyond the inequalities of conventional explicit formulae. Introducing the Finite Closure approach.

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A. Fog vs. Window

Conventional methods rely on bounding the "infinite tail" of the zeta zeros with inequalities ($|\psi(x)-x| < \epsilon$).

Prime OS applies the Yukawa Window to mathematically suppress contributions outside the target interval, enabling a "finite closure" state.

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Legacy: Noise from infinite tail persists

B. Research Map 2025

A comparative analysis of the current state-of-the-art benchmarks versus the structural paradigm shift offered by Prime OS.

📉

Conventional Benchmarks

Structural Limit

🚀

Prime OS Breakthrough

Paradigm Shift
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C. References

Primary sources supporting the report (2020–2025).
Click ID to highlight.