solution: If an integer has at least two different prime factors, say, $p$ and $q$, then it must have at least four positive divisors: $1$, $p$, $q$, and $pq$. So, for a number to have exactly three positive divisors, it must be a power of a single prime number. The positive divisors of $p^n$ are $1,p,p^2,p^3,\cdots,p^{n-1},p^n$. Therefore, $p^n$ has $n+1$ different positive divisors, and the only positive integers with exactly three positive divisors are the squares of prime numbers.
  
  The five smallest such integers are, in ascending order, $2^2$, $3^2$, $5^2$, $7^2$, and $11^2$. The fifth number listed is $11^2=\boxed{121}$.
prompt.content: <|im_start|>system
  You are a helpful assistant.<|im_end|>
  <|im_start|>user
  When the positive integers with exactly three positive divisors are listed in ascending order, what is the fifth number listed?
  Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
  <|im_start|>assistant
  
prompt.role: user
extra_info.answer: 121
extra_info.question: When the positive integers with exactly three positive divisors are listed in ascending order, what is the fifth number listed?
extra_info.split: test