+2653 A positive integer is called terrific if it has exactly $3$ positive divisors. What is the smallest number of primes that could divide a terrific positive integer?
+1876 In order for a number to be terrific, then it must be divisble by 1, itself, and be a perfect square.
Let's say x is a terrific number.
It has to be divisble by x and 1, and be a perfect square.
\(25\) is a perfect example.
However, let's note that it has to be a perfect square for a prime number, because if the squared number was composite, there would be another divisor.
Thus, the minimum number of primes is \(1\)
So 1 is our answer.
Thanks! :)
