  This paper studies the multiplicative semigroup generated by all rationals of
the form (3n+2)/(2n+1) for nonnegative integers n, together with 1/2. The
subsemigroup of integers in this semigroup is called the wild integer
semigroup, and the wild numbers are the irreducible elements in this
subsemigroup. This paper presents evidence that the wild numbers consist of all
the prime numbers p except 3. The subsemigroup of integers in the
multiplicative semigroup generated by all rationals of the form (3n+2)/(2n+1)
for nonnegative integers n is called the Wooley integer semigroup and its
irreducible elements are called Wooley numbers. This semigroup is shown to be
recursive, and various open problems are formulated about Wooley integers.
