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

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

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

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

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