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Perfect square roots are the counting numbers {1, 2, 3, ...} The squares of the perfect square roots are the perfect squares, namely 1² = 1, 2² = 4, 3² = 9, etc.
No - prime numbers are numbers that can only be divided by 1 and itself. 25 and 49 are examples of perfect squares 5*5 = 25 and 7*7=49
There are infinitely many perfect numbers so they cannot all be listed.
There is a one-to-one relationship between even perfect numbers and Mersenne primes. It is unknown whether there are any odd perfect numbers.
Yes. The next perfect numbers are 496 and 8128.