Consider the concatenation of the 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's conjecture on prime gaps implies the normality of
in a given base for .
Campbell, J. M. "The Prime-Counting Copeland-Erdős Constant." Acta Math. Hungar. 2024.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 a given base 
for 
.
