The first two consecutive numbers to have two distinct prime factors are:

$$\begin{align} 14 &= 2 \times 7\\ 15 &= 3 \times 5. \end{align}$$

The first three consecutive numbers to have three distinct prime factors are:

$$\begin{align} 644 &= 2^2 \times 7 \times 23\\ 645 &= 3 \times 5 \times 43\\ 646 &= 2 \times 17 \times 19. \end{align}$$

Find the first four consecutive integers to have four distinct prime factors each. What is the first of these numbers?