+1310
How many positive integers less than 500 are the product of exactly two distinct (meaning different) primes, each of which is greater than 10?
+128578 Disregard my previous answer, AWSOMEEE...it was total garbage......
The possible prime pairs come from this list : 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | 41 | 43
Notice that 11 is the smallest possible prime used in any pair, so any prime greater than 43 paired with it will produce a product > 500
And...11 can be paired with every prime from 13 to 43....so....that makes 9 integers
And 13 can be paired uniquely with the remaining primes from 17 to 37 ....so....that's 6 more integers
And 17 can be paired uniquely with the remaining primes from 19 to 29...so...that's 3 more integers
And 19 can only be paired uniquely with only one remaining prime, 23 .....so that's 1 more integer
Notice that any other unique pairings of the primes from 23 to 43 produce a product > 500
So.....the number of positive integers matching the given criteria = 9 + 6 + 3 + 1 = 19
