Problem 73 of Project Euler is the third problem in a row which treats ordering proper fractions. The problem description reads

Consider the fraction,n/d, wherenanddare positive integers. Ifn<dand HCF(n,d)=1, it is called a reduced proper fraction.

If we list the set of reduced proper fractions ford≤ 8 in ascending order of size, we get:

1/8, 1/7, 1/6, 1/5, 1/4, 2/7, 1/3,3/8, 2/5, 3/7, 1/2, 4/7, 3/5, 5/8, 2/3, 5/7, 3/4, 4/5, 5/6, 6/7, 7/8

It can be seen that there are 3 fractions between 1/3 and 1/2.

How many fractions lie between 1/3 and 1/2 in the sorted set of reduced proper fractions ford≤ 12,000?

Note: The upper limit has been changed recently.