The Copeland-Erdős constant has decimal expansion 0.23571113171923... (OEIS A033308), obtained by concatenation of the decimal digits of consecutive primes. The successive finite concatenations are 2, 23, 235, 2357, 235711, ... (OEIS A019518), forming one of the Smarandache sequences. The constant's digit sequence is considered as an infinite word by Allouche and Shallit (2003, pp. 299 and 334).
It is therefore given by the formula
 |
where 
is the 
th
prime and 
is the floor function.
Copeland and Erdős (1946) showed that it is a normal number in base 10.
A simply strongly normal number in base 
has the law of the iterated logarithm
fluctuations expected for the number of occurrences of each individual base-
digit. CaptainSude (2026) reported that the Copeland-Erdős
constant is not simply strongly normal in base 10, and hence is not strongly
normal, because the digit 0 violates the required fluctuation
bound. The argument uses Ingham's theorem (Ingham 1937) on gaps
between consecutive primes. The remaining argument
was formalized in Lean conditional on that theorem. CaptainSude (2026) credits GPT-6
Astra with selecting the question, finding the proof, and writing the formalization.
As of Sep. 22, 2026, the Lean development had passed the project's checks, but
independent specialist review had not been reported.
The computed portions of the Champernowne constant continued fraction contain sporadic very large terms. The illustrated initial terms of the Copeland-Erdős constant continued fraction show no comparable large-term behavior.
