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No. To be prime it has to be divisible only by itself and one. That means that no numbers multiply to be it. The only possible exception is one. In the math world it may have been decided whether or not one is a Prime number, but that is debatable and I'm not aware of the answer. If 1 was considered a prime number, then it would be the only prime square.

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Q: Can a prime number also be a square number?
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