  The existence of infinitely many consecutive prime triples $p_n$, $ p_{n+1}$,
and $p_{n+2}$ as $n \to \infty$, is sufficient to prove that the Catalan
constant $\beta(2)=0.9159655941\ldots $ is an irrational number. This note
provides the detailed analysis. Moreover, the numerical data suggests that the
irrationality measure is $\mu(\beta(2))=2$, the same as almost every irrational
real numbers.
