A 120-State Binary Turing Machine Equivalent to the Riemann Hypothesis

Joseph M. Shunia

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arXiv · 2609.30306

A 120-State Binary Turing Machine Equivalent to the Riemann Hypothesis

Joseph M. Shunia

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Abstract

We construct an explicit deterministic one-tape, two-symbol Turing machine with 120 working states whose blank-tape computation halts if and only if the Riemann hypothesis is false. The machine uses the same binary blank-tape model and state-counting convention as the widely cited 744-state Matiyasevich-O'Rear-Aaronson construction. The reduction from 744 to 120 working states removes 624 states, or 83.87%. Subject to independent end-to-end verification, our machine is a new state-count record for the Riemann hypothesis.

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Joseph M. Shunia. 2026-09-23. A 120-State Binary Turing Machine Equivalent to the Riemann Hypothesis. https://arxiv.org/abs/2609.30306

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