24 is composite.
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The composite numbers between 21 and 31 are: 21 22 24 25 26 27 28 30
7, 31, 103 All three are prime numbers and not composite numbers.
The they are.
The eight composite numbers between 31 and 41 are 32, 33, 34, 35, 36, 38, 39, and 40.
At least one of them is, so the answer to the question is yes.