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The numbers between 89 and 97 are: 90, 91, 92, 93, 94, 95, 96.

All even numbers greater than 2 are composite. All numbers greater than 5 are divisible by 5 are composite. 93 is divisible by 3, so that only leaves 91 as a Prime number.

The composite numbers are 90, 92, 93, 94, 95, 96.

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Q: What are all the composite numbers between 89 and 97?
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