That is correct -- all prime numbers have exactly two factors.
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By definition, a prime number has exactly two factors. So, there are no prime numbers with exactly three factors.
Prime numbers never stop, it is impossible to list them all.
All prime squares have just three factors. Example: 9, 25
All prime numbers have two factors.
All the numbers above 2 that are the squares of odd primes have exactly 3 factors: 1, the odd prime, and the odd prime squared. 4, 9, 25, 49, 81, 121,...