AUSTRIAN-POLISH 1989 Problem 3

Find all natural numbers $N$ (in decimal system) with the following properties: (i) $N =\overline{aabb}$ , where $\overline{aab}$ and $\overline{abb}$ are primes, (ii) $N = P_1P_2P_3$ , where $P_k (k = 1,2,3)$ is a prime consisting of $k$ (decimal) digits.