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?
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