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Problem 47

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Distinct primes factors

The first two consecutive numbers to have two distinct prime factors are:
$$
\begin{aligned}
14 &= 2 × 7 \\
15 &= 3 × 5
\end{aligned}
$$

The first three consecutive numbers to have three distinct prime factors are:
$$
\begin{aligned}
644 &= 2^2 × 7 × 23 \\
645 &= 3 × 5 × 43 \\
646 &= 2 × 17 × 19
\end{aligned}
$$

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

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不同的质因数

首次出现连续两个数均有两个不同的质因数是在：
$$
\begin{aligned}
14 &= 2 × 7 \\
15 &= 3 × 5
\end{aligned}
$$

首次出现连续三个数均有三个不同的质因数是在：
$$
\begin{aligned}
644 &= 2^2 × 7 × 23 \\
645 &= 3 × 5 × 43 \\
646 &= 2 × 17 × 19
\end{aligned}
$$

首次出现连续四个数均有四个不同的质因数时，其中的第一个数是多少？

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