Mills' constant is the least real number 
such that
 |
is prime for every positive integer 
,
where 
is the floor function (Caldwell and Cheng 2005).
Its existence follows from Mills' theorem (Mills
1947). For each 
,
there are uncountably many real numbers 
such that 
is prime for all
positive integers 
(Caldwell and Cheng 2005).
Assuming the Riemann hypothesis, the least constant has the value
 |
(OEIS A051021), and the associated Mills' primes are obtained by starting with 
and taking 
to be the next prime after
(Caldwell and Cheng 2005).
Caldwell and Cheng (2005) computed more than 6850 digits of 
under the Riemann hypothesis.
Larger candidates in the associated sequence have been
reported as probable primes (Batalov and Propper
2024). Such candidates do not establish further digits of 
without primality
certificates and the hypothesis identifying this sequence
with the least constant.
Saito (2025) proved unconditionally that 
is irrational.
