How many positive integers less than 500 are the product of exactly two distinct (meaning different) primes, each of which is greater than 10?

Mr.Owl
Oct 31, 2017

#1**+2 **

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

geno3141
Oct 31, 2017

#1**+2 **

Best Answer

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

geno3141
Oct 31, 2017