The Largest Number Representable in 64 Bits

We investigate how large an output can be computed by programs fitting inside a single register, using languages not designed for generating large outputs. We propose lambda calculus-based Busy Beaver functions that offer various advantages over the existing Turing machine-based ones, including a direct relation to Kolmogorov complexity.

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Publication Details

Journal
Entropy
Published
2026-04-26
DOI
https://doi.org/10.3390/e28050494
Primary Topic
Computability, Logic, AI Algorithms
Type
article
Field-Weighted Citation Impact
0.00
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article

The Largest Number Representable in 64 Bits

John Tromp
Entropy
Computability, Logic, AI Algorithms
article

The Largest Number Representable in 64 Bits

John Tromp
article en

Abstract

We investigate how large an output can be computed by programs fitting inside a single register, using languages not designed for generating large outputs. We propose lambda calculus-based Busy Beaver functions that offer various advantages over the existing Turing machine-based ones, including a direct relation to Kolmogorov complexity.

EntropyVol. 28(5)
National Health Care Institute (NL)
Openalex Percentile: Top 4%
Computability, Logic, AI Algorithms
DOIOpen Access PDFOpenAlex
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The Largest Number Representable in 64 Bits — John Tromp · Entropy (2026) | TGRS Research Map | TGRS