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May 3, 2026Entropy0 citationsOpen Access

The Largest Number Representable in 64 Bits

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JTJohn Tromp

Key Points

  • The aim is to determine the largest value computable by programs constrained to 64-bit registers.
  • Proposed lambda calculus-based Busy Beaver functions
  • Compared advantages over traditional Turing machine-based functions
  • Established a direct relation to Kolmogorov complexity
  • Demonstrated potential for larger outputs than previously established by Turing machines
  • Provided insights into the relationship between lambda calculus and computational complexity
  • Highlighted efficiency improvements in program output generation

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.

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Cite This Study

John Tromp (2026) studied this question.

synapsesocial.com/papers/69f6e6648071d4f1bdfc70a0https://doi.org/10.3390/e28050494
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Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

  1. 1Busy Beaver Function's Non-Computability and Higher-Order Extensions in Turing Oracle Machines — E8 Intelligence Research2026
  2. 2Busy Beaver Function Outpaces All Computable Growth, Defining Arithmetic Knowledge Limits — E8 Intelligence Research2026
  3. 3Busy Beaver Function Outpaces All Computable Growth, Defining Arithmetic Knowledge Limits — E8 Intelligence Research2026
  4. 4Distributed Collaboration Computes Busy Beaver BB(5), Solving 30-Year-Old Problem — E8 Intelligence Research2026
  5. 5The Uncomputable Growth of Busy Beaver Numbers and Their Arithmetical Extension — E8 Intelligence Research2026