Multidegrees of tame automorphisms with one prime number

Let 3 <= d(1) <= d(2) <= d(3) be integers. We show the following results: (1) If d(2) is a prime number and d(1)/gcd(d(1), d(3)) not equal 2, then (d(1), d(2), d(3)) is a multidegree of a tame automorphism if and only if d(1) = d(2) or d(3) is an element of d(1)N + d(2)N; (2) If d(3) is a prime number and gcd(d(1), d(2)) = 1, then (d(1), d(2), d(3)) is a multidegree of a tame automorphism if and only if d(3) is an element of d(1)N + d(2)N. We also show that the condition d(1)/gcd(d(1), d(3)) not equal 2 in (1) cannot be removed.