The no. of solutions of the equation $$xy(x + y) = 2010$$, where $$x$$ and $$y$$ denote positive prime numbers, is______

$$2010 = 2 \times 3 \times 5 \times 67$$. If $$x = 2$$, then $$y(y + 2) = 1005$$, but $$29 \times 31 = 899$$ and $$31 \times 33 = 1023$$, so no prime works (and the same holds with $$y = 2$$). If both are odd primes, then $$xy \cdot \frac{x + y}{2} = 1005 = 3 \times 5 \times 67$$, and checking the possible pairs $$(3, 5)$$, $$(3, 67)$$, $$(5, 67)$$ and equal primes gives no solution. So there are 0 solutions.