The 
th Mills' prime is the prime
number
 |
for a positive integer 
, where 
is Mills' constant and
is the floor
function (Caldwell and Cheng 2005). Under the Riemann
hypothesis, these are the primes obtained by
starting with 
and repeatedly taking the next prime after 
.
The first few 
for 
, 2, ... are 2, 11, 1361, 2521008887,
... (OEIS A051254). The greedy sequence
can be represented more compactly through 
as 
and
 |
Caldwell and Cheng (2005) proved the first 10 terms prime. Later reported extensions include probable primes.
These candidates require primality certificates
before they can be accepted as terms of the greedy prime
number sequence. The reported offsets 
for 
, 2, ... are 3, 30, 6, 80, 12, 450, 894, 3636, 70756, 97220,
66768, 300840, 1623568, 8436308, ... (OEIS A108739).
Batalov and Propper (2024) reported 
and checked the minimality of this offset.
The number lengths of the reported prime and probable prime terms are 1, 2, 4, 10, 29, 85, 254, 762, 2285, 6854, 20562, 61684, 185052, 555154, 1665461, ... (OEIS A224845).
