Distinct primes factors
The first two consecutive numbers to have two distinct prime factors are:
\[ 14 = 2 × 7\\\\ 15 = 3 × 5 \]
The first three consecutive numbers to have three distinct prime factors are:
\[ \begin{align} 644 &= 2^2 × 7 × 23\\ 645 &= 3 × 5 × 43\\ 646 &= 2 × 17 × 19. \end{align} \]
Find the first four consecutive integers to have four distinct prime factors each. What is the first of these numbers?