A composite is a number containing at least two prime factors. For example, $15 = 3 \times 5$; $9 = 3 \times 3$; $12 = 2 \times 2 \times 3$.

There are ten composites below thirty containing precisely two, not necessarily distinct, prime factors: $4, 6, 9, 10, 14, 15, 21, 22, 25, 26$.

How many composite integers, $n \lt 3 \times 2^N$, have precisely two, not necessarily distinct, prime factors?