Mills' constant can be defined as the least 
such that
 |
is prime for all positive integers 
(Caldwell and Cheng 2005).
The first few 
for 
, 2, ... are 2, 11, 1361, 2521008887,
... (OEIS A051254). They can be represented
more compactly through 
as 
and
 |
Caldwell and Cheng (2005) calculated the first 10 Mills primes. 13 are known as of Jul. 2013, with the firth few 
for 
, 2, ... being 3, 30, 6, 80, 12, 450, 894, 3636, 70756, 97220,
66768, 300840, ... (OEIS A108739). 
is not known, but it is known that 
(E. Weisstein, Aug. 13, 2013).
The integer lengths of the Mills' primes are 1, 2, 4, 10, 29, 85, 254, 762, 2285, 6854, 20562, 61684, 185052, ... (OEIS A224845).
