Let’s agree to say that a positive integer is prime-like if it is not divisible by 2, 3, or 5. How

Question

many prime-like positive integers are there less than 100? less than 1000? A positive integer
is very prime-like if it is not divisible by any prime less than 15. How many very primelike
positive integers are there less than 90000? Without giving an exact answer, can you
say approximately how many very prime-like positive integers are less than 1010? less than
10100? Explain your reasoning as carefully as you can.