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arXiv · 2610.02550

The Prime Wavelet Tree: Compressing the Carmichael Numbers

Ankur Gupta·Jonathan Webster·Sylvia Webster
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Abstract

We present two number-theoretic compression techniques. The first is \textit{local}, and compresses individual numbers. The second is \textit{global}, and compresses the entire set of numbers using a \textit{prime wavelet tree}, which is a data structure of independent interest. Our techniques apply to any set of numbers satisfying a Korselt-like criterion. We demonstrate our compression techniques using the recently completed tabulation of all $308{,}279{,}939$ Carmichael numbers less than $10^{24}$ that occupies $18.4$ gigabytes as text. When combined with standard compression techniques and a heuristic choice of divisors, the resulting file is $588.7$ megabytes ($31.2$ times smaller than the text file). The initial $80$-bit numbers now use about $15.3$ bits.

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Ankur Gupta, Jonathan Webster, Sylvia Webster. 2026-10-01. The Prime Wavelet Tree: Compressing the Carmichael Numbers. https://arxiv.org/abs/2610.02550

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