  Given a finite set of primes $S$ and a $m$-tuple $(a_1,\dots,a_m)$ of
positive, distinct integers we call the $m$-tuple $S$-Diophantine, if for each
$1\leq i < j\leq m$ the quantity $a_ia_j+1$ has prime divisors coming only from
the set $S$. For a given set $S$ we give a practical algorithm to find all
$S$-Diophantine quadruples, provided that $|S|=3$.
