No.
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imaginary numbers. but no, not really.
Square numbers can't be prime. They have too many factors.
No, there are no prime numbers that are also square numbers. Prime numbers are only divisible by 1 and themselves, while square numbers have integer square roots. Since the square root of a prime number is not an integer, a prime number cannot be a square number.
negative always
No, square numbers greater than 1 have more than two factors.