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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 = 2² × 7 × 23 645 = 3 × 5 × 43 646 = 2 × 17 × 19.

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

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 = 2² × 7 × 23
• 645 = 3 × 5 × 43
• 646 = 2 × 17 × 19.

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

The correct answer is 134043. I used some sort of memoization to work out the problem but the performance is still pretty bad: 5.4–5.5 seconds. The trick in this question here is that the prime factors can actually be on some power which if evaluated doesn't result in a prime number but if the base is prime it's fine: e.g., 2² = 4.

The correct answer is :

134043.

I used some sort of memoization to work out the problem but the performance is still pretty bad: 5.4–5.5 seconds. The trick in this question here is that the prime factors can actually be on some power which if evaluated doesn't result in a prime number but if the base is prime it's fine: e.g., 2² = 4.