Is it true that among any 24 consecutive integers, all larger than 5, there always exists a number which has at least three (not necessarily distinct) prime factors?

As an example, 12 has three prime factors: 2, 2, 3.

true
false

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We will show, that a much stronger statement is true:

"Amongst any 8 positive consecutive integers, there is at least one, which has at least three (not necessarily distinct) prime factors."

It is easy to see, that amongst 8 consecutive integers, there is exactly one, which is divisible by 8. Since 8 (= 2×2×2) itself has 3 prime factors, therefore this number has at least 3 prime factors.

Hence, our answer should be:

$\boxed { \text { TRUE } }$