## Friday, July 3, 2015

### Prime Numbers

OK, here's the definition of a prime number:

A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number.

In other words, a prime number is a counting number that can't be divided by another number.

So what does this mean?

1. First of all, except for 2, a prime number cannot be an even number. If it was even, 2 would divide into it.
2. Secondly, except for 5, any number that ends in a 5 is not prime. If it ends in 5, 5 would divide into it.
3. Thirdly, if the sum of the digits of a number is 3, 6, or 9, the number is not prime. If the sum of the digits is 3, 6, or 9, 3 divides into it.

So it isn't necessary to check for all the possible divisors to tell if a number is prime or not, just the primes less than the number and up to the square root of the number you're checking. (don't worry about the square root, you'll meet it in a year or two.) So this is the way it works for primes up to 100:

So we can now write down all the prime numbers up to 100. Write down your list and compare it to the answer below:

Answer: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 93, 97
Did you get caught with 91? 7 X 13 = 91