The prime-counting concatenation constant is formed by concatenating the decimal digits of consecutive values of the prime
counting function for , 2, ..., which gives the terms 0, 01, 012, 0122, 01223,
012233, 0122334, .... Interpreting the limiting sequence as the decimal digits of
a constant gives
Using a method of Szüsz and Volkmann (1994), Campbell (2024) proved that Cramér conjecture on prime
gaps implies the normality of in any integer base
for , with each written in that base.
Campbell, J. M. "The Prime-Counting Copeland-Erdős Constant." Acta Math. Hungar.173, 101-111, 2024. https://doi.org/10.1007/s10474-024-01437-8.Sloane,
N. J. A. Sequence A366033 in "The
On-Line Encyclopedia of Integer Sequences."Szüsz, P. and Volkmann,
B. "A Combinatorial Method for Constructing Normal Numbers." Forum Math.6,
399-414, 1994.
for 
, 2, ..., which gives the terms 0, 01, 012, 0122, 01223,
012233, 0122334, .... Interpreting the limiting sequence as the decimal digits of
a constant gives
in any integer base
for 
, with each 
written in that base.
