

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:
~~~
644 = 2 × 2 × 7 × 23
645 = 3 × 5 × 43
646 = 2 × 17 × 19.
~~~
Find the first four consecutive integers to have four distinct prime factors. What is the first of these numbers?
