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arXiv · 2511.19744

Toda primes

Stephen McKean
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Abstract

A Toda prime of an integer $n$ is an odd prime $p$ such that $4n=(p-1)k$ with $k$ coprime to $p$. We conjecture that every positive integer admits at least two Toda primes. We give a partial proof that every positive integer admits at least one Toda prime. We conclude by discussing connections to denominators of Bernoulli numbers and a generalization of Sophie Germain primes.

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Stephen McKean. 2025-11-24. Toda primes. https://arxiv.org/abs/2511.19744

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