  It is well known that the arithmetic nature of Mills' prime-representing
constant is uncertain: we do not know if Mills' constant is a rational or
irrational number. In the case of other prime-representing constants,
irrationality can be proved, but it is not known whether these constants are
algebraic or transcendental numbers. By using Liouville or Roth's theorems
about approximation by rationals, we find a couple of prime-representing
constants that can be proved to be transcendental numbers.
