Prime-counting Concatenation Constant
Alternate name
Definition
Consider the concatenation of the digits of consecutive values of the prime counting function π(n) for n = 1, 2, ..., which gives the terms 0, 01, 012, 0122, 01223, 012233, 0122334, .... Interpreting the limiting sequence as the decimal digits of a constant gives C_PCCC = 0.01223344445566667788889999991010111... (OEIS A366033). Using a method of Szüsz and Volkmann, Campbell proved that Cramér's conjecture on prime gaps implies the normality of 0.a_1 a_2 ... in a given base b>=2 for a_n = π(n).
