Riemann Zeta Function Zeros for Prime Counting and Spectral Analysis

A computational realization of the Riemann zeta spectrum contains the imaginary parts of the first 2,001,052 non-trivial zeros. This 30.9 MB dataset enables high-precision prime counting, achieving 0.009% relative error at x=10^18, and models black-hole entropy fluctuation spectra. It was created by Jordan Gidman and published in 2026.

Use Cases

• Apply the explicit formula for the prime-counting function π(x) using the 2,001,052 zeros to compute high-precision prime counts.
• Model black-hole entropy fluctuation spectra using the spectral density derived from the Riemann zeta zeros.
• Evaluate eigenvalue-dependent functions in number theory using the diagonal matrix H = diag(t_n) of zeros.
• Cross-validate theoretical number theory results against computational realizations of the first 2 million zeros.

Strengths

• Contains a high-fidelity set of 2,001,052 non-trivial Riemann zeta zeros.
• Demonstrated practical utility with a 0.009% relative error in prime counting at x=10^18.
• Data is openly available under a CC0 license, allowing unrestricted use.

Limitations

• The dataset is specialized for theoretical and computational number theory, limiting general ML applicability.
• Sample data and column structure are not explicitly documented, complicating initial inspection.

Provenance

Source

Zenodo (DOI 10.5281/zenodo.19026613) and GitHub repository.

Collection Method

Computational construction of the Riemann zeta spectrum.

Time Range

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Freshness

Last updated in March 2026.

Geography

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