Posted by **David** on Friday, April 2, 2010 at 12:47pm.

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

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.

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