The first two consecutive numbers to have two distinct prime factors are:
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14 = 2 × 7
15 = 3 × 5
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The first three consecutive numbers to have three distinct prime factors are:
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644 = 2 × 2 × 7 × 23
645 = 3 × 5 × 43
646 = 2 × 17 × 19.
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Find the first four consecutive integers to have four distinct prime factors. What is the first of these numbers?