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Prime Numbers: 20-30

Date: 01/31/97 at 17:55:32
From: John Stephany
Subject: prime numbers

Dear Dr. Math,

What are the prime numbers 20 through 30? My mom can't help me.

Thank you,

Date: 01/31/97 at 18:48:10
From: Doctor Wilkinson
Subject: Re: prime numbers

First of all, you need to be sure you understand what prime numbers 
are.  In fact, if you understand that, you should be able to do this 
problem without any difficulty.

A prime number is a whole number which is not the product of smaller
numbers.  For example, 14 is not a prime number, becaues it is 
2 times 7. But 3 is a prime number, because the only smaller numbers 
are 1 and 2, and 3 is not 1 times 1 or 1 times 2 or 2 times 2.

To see if a number is prime, all you need to do is try the numbers 
smaller than it and bigger than 1 and divide them into your number.  
If this ever comes out even, then your number isn't prime.  Otherwise, 
it is.

For example take 15.  If you try dividing it by 2, it doesn't come out
even.  But if you try 3, it does.  15 is 3 times 5.  So it's not a 

Now let's look at 17.  If you try dividing it by 2, it doesn't come 
out even.  If you try 3, that doesn't come out even either.  Neither 
does 4, and neither does 5.  

Now you could go ahead and try 6, 7, 8, and so on.  But if you noticed 
when you tried 5, you got a quotient of 3 and a remainder of 2. Now if 
you try something bigger, you're going to get a smaller quotient. So
if it was going to come out even, it would already have come out even 
when you tried the smaller number, and at this point you can quit, 
because you now know that 17 is prime.

Do you think you can do this for the numbers from 20 to 30?  To get 
you started, I'll point out that 20, 22, 24, 26, 28, and 30 are all 
evenly divisible by 2, so none of them is prime.

-Doctor Wilkinson,  The Math Forum
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Associated Topics:
Elementary Prime Numbers
Middle School Prime Numbers

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