+0  
 
0
78
3
avatar+182 

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?

wiskdls  Apr 29, 2018
 #1
avatar
0

Tried, but didn't work!!. Sorry!.

Guest Apr 29, 2018
edited by Guest  Apr 29, 2018
 #2
avatar
0

Now, let us see what we can do:

There are 999 / 2 =499 numbers that are divisible by 2

There are 999/3 =333 that are divisible by 3. But 166 of them are and are included in 499. But 167 are odd which are not included in 499 above.

So, we have: 499 + 167 =666

We have:999/5=199. But only 100 are odd and end in 5. So, we have:

666 + 100 =766. But, 999/15 =66 half of which are already inculded that end in 5 and are divisible by 3. So, we have: 766 - 33 =733 + 1 itself - 3 primes(2, 3, 5) =731 + 168 primes=899.

So, 999 - 899 = 100 prime-looking numbers under 1,000.

Guest Apr 30, 2018
 #3
avatar
0

Here is another way of looking at this problem, which ends with the same result as figured above:

 

There are 31 primes between 7 and 139 =31[This means that prime numbers from 7 and up can be squared or multiplied by each other to get the desired numbers such as: 7^2, 7*11, 7*13...and so on.

There are 20 primes between 11 and 90=20

There are 16 primes between 13 and 76 =16

There are 10 primes between 17 and 58 =10

There are 8 primes between 19 and 52 =8

There are 6 primes between 23 and 43 =6

There are 2 primes between 29 and 34 =2

There is 1 prime between 31 and 32 =1

That is a total =31 + 20 + 16 + 10 + 8 + 6 + 2 + 1 =94

There is 7^3 for an additional number

There are 7^2*11, 7^2*13, 7^2*17, 7^2*19 = 4 additional numbers.

There is 11^2*7 for 1 additional number.

So, the grand total =94 + 1 + 4 + 1 =100 prime-looking numbers under 1,000.

Guest Apr 30, 2018

6 Online Users

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.