All numbers that are the square of primes have exactly 3 factors.
Squares of prime numbers have exactly three factors.
The squares of all prime numbers above 2 have exactly 3 factors.
A number has exactly three factors if and only if it is the square of a prime number.
By definition, a prime number has exactly two factors. So, there are no prime numbers with exactly three factors.
2 and 3
Squares of prime numbers.
3, 5 and 7
25 and 49
That's an infinite list.