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 95 prime numbers less than 500. How many prime-looking numbers are there less than 500?

Among $$1, 2, \ldots, 499$$, count those divisible by none of 2, 3, 5 by inclusion-exclusion, using $$\lfloor \frac{499}{2} \rfloor = 249$$, $$\lfloor \frac{499}{3} \rfloor = 166$$, $$\lfloor \frac{499}{5} \rfloor = 99$$, $$\lfloor \frac{499}{6} \rfloor = 83$$, $$\lfloor \frac{499}{10} \rfloor = 49$$, $$\lfloor \frac{499}{15} \rfloor = 33$$ and $$\lfloor \frac{499}{30} \rfloor = 16$$. This gives $$499 - 249 - 166 - 99 + 83 + 49 + 33 - 16 = 134$$ numbers. These consist of the number 1, the $$95 - 3 = 92$$ primes other than 2, 3, 5, and the prime-looking numbers. Hence there are $$134 - 1 - 92 = 41$$ prime-looking numbers less than 500.