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

Question

anonymous · Answer

i don't think there is a snap way to do this
list the primes between 10 and 50 and see how many give you products less than 500

anonymous · Answer

ok

valpey · Answer

A useful clue is that since 23^2 is greater than 500, any product of two primes less than 500, each of which is greater than ten has one of the primes between 11 and 19.

anonymous · Answer

11  |  13  |  17  |  19  |  23  |  29  |  31  |  37  |  41  |  43  |  47    

i think this is your list
now you can multiply but $11\times 47$ is too large so only up to 43
you can multiply 11 by the other 9 primes
13 by 7 others because $13\times 41$ is too big, and so on

valpey · Answer

So you just have to solve for 11, 13, 17, and 19. 
11*(11,13,17,19,23,29,31,37,41, or 43)
13*(13,17,19,23,29,31, or 37)
etc.

valpey · Answer

And avoid counting 11*13 and 13*11 etc. separately.

anonymous · Answer

of course i made a mistake because my method counts $13\times 11$ twice

anonymous · Answer

but also they have to be distinct, so don't count $13\times 13$ etc

valpey · Answer

Oh, I missed that part. Yeah, avoid the squares.

anonymous · Answer

i got 23 choices