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Checking if a Number from 1-100 is Prime

Date: 09/06/2008 at 16:41:34
From: Brooke
Subject: what is an easy way to determine if a number is prime

What is an easy way to determine if a number is prime?  
example: Write the number 100 as the sum of two prime numbers. 

For me it is difficult to determine whether or not a number is prime. 
I can but it takes a while.  I want to know a simpler way than trying
to multiply a bunch of numbers together.  Well some are obvious but if
I'm going from 1-100 I need an easy way.

Date: 09/06/2008 at 19:53:45
From: Doctor Rick
Subject: Re: what is an easy way to determine if a number is prime

Hi, Brooke.

There isn't a really easy way, but you can write your own list of 
prime numbers less than 100 without much trouble (if you can't look 
up the list, as in our FAQ).  I'll give you some pointers, because it 
will turn out to be useful every now and then to know the primes 
under 100.

If a number can't be divided by any prime number less than or equal 
to the square root of the number, then it is prime.  (If you don't 
know this, we can discuss it further!)  This is a big help, because 
it means that we can find all the primes under 100 by checking for 
divisibility by the primes 2, 3, 5, and 7.  The next prime, 11, is 
greater than the square root of 100 (namely, 10).

This immediately rules out all numbers ending in an even digit except 
2 (because they are divisible by 2), and all numbers ending in 0 or 5 
except 5 itself (because they are divisible by 5).  All other primes 
less than 100 must end in 1, 3, 7, or 9.

A number is divisible by 3 if the sum of its digits is divisible by 
3. That's easy to check for two-digit numbers.  Among the numbers in 
the 50s, for example, this eliminates 51, 54, and 57.  We already 
knew 54 was out, but now our list is down to 53 and 59.  You should 
know your 7-times table and realize that neither of these numbers is 
on it, so they are both prime.  If you've learned up through 7 times 
12, then you don't need to actually do a division until you get past 
84.  That's not bad!

Going through the numbers from 2 through 99 in order, I can construct 
the list of primes fairly quickly.  You'll find that the more you do 
this, the more you'll start recognizing primes in this range.  I mess 
up once in a while, such as thinking that 91 is prime--so I still 
have to check my list by doing the division by 7.  Most of the work, 
though, as I said, is pretty quick.

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

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