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March 4th, 2018, 12:30 AM  #1 
Newbie Joined: Mar 2018 From: Bulgaria Posts: 1 Thanks: 0  Give me please some advice on how to solve this problem
We say that a positive integer is quiteprime if it is not divisible by 2, 3, or 5. How many quiteprime positive integers are there less than 100? less than 1000? A positive integer is very quiteprime if it is not divisible by any prime less than 15. How many very quiteprime positive integers are there less than 90000? Without giving an exact answer, can you say approximately how many very quiteprime positive integers are less than 10¹º? less than 10¹ºº?

March 4th, 2018, 08:02 AM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,039 Thanks: 1063 
I suggest determining how many numbers less than 100, 1000, etc ARE divisible by 2, 3, or 5 and subtracting that number from 100, 1000, etc. You should see something of a pattern that let's you estimate the number of them in $10^{10}$ etc. 

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