Prime Number Studies
Independent re-derivations, measurements and negative results around the division table
Mohamed Osman · ORCID 0009-0004-5912-999X · independent researcher
Every headline result here already exists in the literature, and each paper says so and names the source.
What the collection offers is a route followed honestly end to end, negative results stated plainly rather than buried,
and a script in code/ that regenerates every number printed.
No claim is made about the Riemann Hypothesis.
Repository ·
DOI 10.5281/zenodo.21638887 ·
The Cell System (the author's other work)
Papers
- A Numerical Study of the Division Table
One elementary table, and the classical mathematics you can see from it
2026-08-02 · PDF - From the Odd Division Table to Prime-Power Towers
A geometric and algebraic reorganization of factorization, stopping before the zeta function
2026-07-28 · PDF - Counting Residue Pairs in a Sieve Cycle, and the Frequency of Prime Gaps
An exact local theorem, and an honest separation of what is proved from what is fitted
2026-07-28 · PDF - A Divisibility-Generated Dynamical Model for Resonances at the Zeros of the Riemann Zeta Function
Construction, exact algebra, and a careful account of what the numerics do and do not certify
2026-07-28 · PDF - Compressing the Division Table into a Single Dynamical Column
Prime clocks, gcd kernels, lag correlations, the von Mangoldt function, and a spectral test
2026-07-28 · PDF - A Probe of the Odd Parity Sector of the CvS Galerkin Matrix
An exact finite identification, an unseeded reconstruction of the zeta ordinates, and a T-scaling measurement
2026-08-13 · PDF
Notes