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To determine which of the given numbers is prime, we need to check whether each number has exactly two distinct positive divisors: 1 and itself.
- 27: The divisors are 1, 3, 9, and 27. (Not prime)
- 54: The divisors are 1, 2, 3, 6, 9, 18, and 54. (Not prime)
- 69: The divisors are 1, 3, 23, and 69. (Not prime)
- 95: The divisors are 1, 5, 19, and 95. (Not prime)
- 97: The only divisors are 1 and 97. (Prime)
The only prime number among the choices is 97 (Choice E).