Note : Whenever you use a formula, please detail in sentences exactly how/why it works for your particular solution (merely plugging values into a formula does not by itself demonstrate understanding). Proving a more general case of the formula(e) is another valid strategy.

1. Call a number "prime-looking" if it is composite but not divisible by 2, 3, or 5. The three smallest prime-looking numbers are 49, 77, and 91. There are 168 prime numbers less than 1000. How many prime-looking numbers are there less than 1000?