Possible Clues:

• 2, 3, or 5, e.g
• 2 or 3 — but not 4
• 13
• One such as 3, 5, 7, 11, etc
• One with no divisors
• 2, 3 or 5
• Integer divisible only by itself and by 1
• First-rate painkiller one alone can always divide
• Head anesthesiologist?
• One providing amusement