Here is a complementary counting approach: Note that 2,3,5 are all prime. The next 2 prime numbers are 7 and 11, and the product of them is 77. That is greater than 30, so we just need to subtract off the # of primes that are less than 30 (and 1), other than 2,3,5 . We find the next primes are 7,11,13,17,19,23,29. Thus, we get the answer 30 - (7+1) = 22.
@professionalbronco Yes, that definitely works! It's interesting how both strategies are useful in different cases- Prof. Loh's method is faster when considering larger numbers, but yours is quicker in this case with smaller numbers Nice!