+471 How many positive integers less than 500 are the product of exactly two distinct (meaning different) primes, each of which is greater than 10?
+23252 The first prime larger than 10 is 11. The following products of two primes, one of which is 11, are less than 500:
11 x 13, 11 x 17, 11x 19, 11 x 23, 11 x 29, 11 x 31, 11 x 37, 11 x 41, 11 x 43
The next prime number is 17. The following products are less than 500:
13 x 17, 13 x 19, 13 x 23, 13 x 29, 13 x 31, 13 x 37
The next prime is 17:
17 x 19, 17 x 23, 17 x 29
Finally:
19 x 23
+23252 The first prime larger than 10 is 11. The following products of two primes, one of which is 11, are less than 500:
11 x 13, 11 x 17, 11x 19, 11 x 23, 11 x 29, 11 x 31, 11 x 37, 11 x 41, 11 x 43
The next prime number is 17. The following products are less than 500:
13 x 17, 13 x 19, 13 x 23, 13 x 29, 13 x 31, 13 x 37
The next prime is 17:
17 x 19, 17 x 23, 17 x 29
Finally:
19 x 23
