---
title: "On Tables of Random Numbers"
authors:
  - "A. N. Kolmogorov"
year: 1963
venue: "Sankhyā Series A; reprinted Theoretical Computer Science 1998"
arxiv: null
doi: "10.1016/S0304-3975(98)00075-9"
source: "https://doi.org/10.1016/S0304-3975(98)00075-9"
topics:
  - randomness
  - kolmogorov
  - algorithmic-information
seed_rank: 605
seed_batch: "foundations-greats-2026-08-13"
reviewed: "2026-08-13"
pool: "maths-foundations"
relevance_score: 8
lineage: foundations-of-computing
cites:
  - title: "Various techniques used in connection with random digits"
    url: "https://mcnp.lanl.gov/pdf_files/InBook_Computing_1961_Neumann_JohnVonNeumannCollectedWorks_VariousTechniquesUsedinConnectionwithRandomDigits.pdf"
    year: 1951
    arxiv: null
    doi: null
see:
  - "549-various-techniques-used-in-connection-with-random-digits"
---

# On Tables of Random Numbers

## One-sentence takeaway

Kolmogorov asks what it means for a *finite printed table* to be random, and argues that frequency / ensemble accounts do not settle the randomness of an individual sequence.

## Why it matters here

Companion to the 1965 complexity paper: this is the finite-string, engineering-facing side of algorithmic randomness — the right vocabulary for seed tables, hash nonces, and "is this noise texture actually noise?"

## Key ideas

- Classical probability talks about ensembles; a concrete table of digits is a single object.
- Frequency-stability conditions (von Mises style) are necessary but not sufficient for a finite table to deserve the name "random".
- Complexity / incompressibility is already in view as the missing individual-sequence criterion.
- Original: *Sankhyā* Ser. A 25(4), 1963, pp. 369–376; TCS 207(2), 1998 reprint carries the DOI.

## Caveats

## Links

- TCS reprint DOI: [10.1016/S0304-3975(98)00075-9](https://doi.org/10.1016/S0304-3975(98)00075-9)
- JSTOR original: https://www.jstor.org/stable/25049284