The prime constant is the real number whose binary expansion is obtained by concatenating the values of the characteristic function of the primes, defined by
 |
(1)
|
For 
, 2, ..., this function
has values 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, ... (OEIS A010051). Interpreting these values as successive
binary digits gives
 |  |  |
(2)
|
 |  |  |
(3)
|
 |  |  |
(4)
|
 |  |  |
(5)
|
(OEIS A051006), where 
is the 
th prime number.
The continued fraction is [0, 2, 2, 2, 3, 12, 131, 1, ...] (OEIS A051007). It has high-water marks of 0, 2, 3, 12, 131, 169, ... (OEIS A102878), occurring at positions 0, 1, 4, 5, 6, 20, 31, 54, ... (OEIS A103313).
