Copeland-Erdős Constant is Normal

Theorem

The Copeland-Erdős constant, whose decimal expansion is formed by concatenating the prime numbers in ascending order:

$0 \cdotp 23571 \, 11317 \, 1923 \ldots$

is normal with respect to base $10$.


Proof


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Sources

  • 1946: A.H. Copeland and P. Erdős: Note on Normal Numbers (Bull. Amer. Math. Soc. Vol. 52: pp. 857 – 860)
  • 1983: François Le Lionnais and Jean Brette: Les Nombres Remarquables ... (previous) ... (next): $0,23571 11317 1923 \ldots$
  • 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Copeland-Erdős number
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