Call a polynomial P prime covering if for every prime p, there exists an integer n for which p divides P(n). Determine the number of ordered triples of integers (a, b, c), with 1 \leq a<b<c \leq 25, for which P(x)=\left(x^{2}-a\right)\left(x^{2}-b\right)\left(x^{2}-c\right) is prime-covering.