36
Average = (24+32+38+31+61+35+31)/7
= 252/7
= 36
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37
31 is a prime number, but 24 and 35 are not.
If by between you mean strictly between (not including 23 or 35), the answer is 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, and 34.
24 is divisible by 2 and 35 is divisible by 5. 31 has only two factors: 1 and itself. 31 is the prime number.
At least one of them is, so the answer to the question is yes.