Given relatively prime integers a(1) ,..., a(n), the Frobenius number g(a(1) ,..., a(n)) is defined as the largest integer which cannot be expressed as x(1)a(1)+ . . . + x(n)a(n) with x(i) nonnegative integers. In this paper, we give the Frobenius number of primitive Pythagorean triples: g(m(2) - n(2), 2mn, m(2) + n(2)) - (m - 1)(m(2) - n(2)) + (m - 1)(2mn) - (m(2) + n(2))