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

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

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

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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