Definition of "two primes"

[user4370]

Dear GregMat team,

I was redoing some gregmat questions and a stumbled upon this question (image):

In the solution, it is said that only 111 can be expressed as a product of two primes, since it can be written as 37*3.

However, I cannot understand why 333 and 999 do not satisfy that condition; they could be written like 373^2 and 37^3, respectively- hence using the same two primes. Is it because 37, 3, 3 are considered three primes, even though the 3’s are equal to each other and you are “only” using 37 and 3?

Thanks in advance!

[Jovyn]

Hello,

Yes, since the question explicitly states only ‘2’ prime numbers can be used in the multiplication to get the number.

For this reason, even though you might be using the same prime number twice, it accounts to using 3 numbers in total for the product part.

So hence, only 111 (37*3) is the correct answer.

Thank you