Have you ever eaten prime rib? Maybe you’ve lucked into a prime parking spot near the front of the store? Have you ever primed a pump? What about priming the walls before painting them?

As you can see, the word “prime” has many uses and meanings. When referring to numbers, though, prime has a special definition. A prime number is a whole number greater than 1 that can only be divided equally by itself and 1. In other words, prime numbers have only themselves and 1 as factors.

Any number may be made by multiplying two or more other numbers together. The numbers you multiply together are called factors of the final number. For prime numbers, their only factors are themselves and 1.

Let’s take a look at the numbers 1 through 10 as examples:

  • 1: not a prime number by definition
  • 2: can only be divided by 2 and 1, so 2 is prime
  • 3: can only be divided by 3 and 1, so 3 is prime
  • 4: can be divided by 4, 2 and 1, so 4 is not prime
  • 5: can only be divided by 5 and 1, so 5 is prime
  • 6: can be divided by 6, 3, 2 and 1, so 6 is not prime
  • 7: can only be divided by 7 and 1, so 7 is prime
  • 8: can be divided by 8, 4, 2 and 1, so 8 is not prime
  • 9: can be divided by 9, 3 and 1, so 9 is not prime
  • 10: can be divided by 10, 5, 2 and 1, so 10 is not prime

Numbers that are not prime numbers are called composite numbers. You may have noticed that every even number greater than 2 is a composite number. This is because every even number greater than 2 is divisible by 2, so they cannot be primes. Thus, 2 is the only even prime number!

Here is a list of the 25 prime numbers between 1 and 100:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97

Although some experts believe that the ancient Egyptians knew about prime numbers, it was the ancient Greeks who first studied prime numbers in depth. In fact, it was Greek mathematician Euclid who proved that an infinite number of prime numbers exists. So that list of prime numbers above just keeps going and going

Mathematicians consider prime numbers to be the “building blocks” of all numbers. According to the fundamental theorem of arithmetic, every positive whole number greater than 1 can be written as a unique product of one or more prime numbers.

If you’re wondering about the largest prime number found to date, it’s pretty big! In 2008, a group of people used the combined computing power of hundreds of computers to discover a prime number that has approximately 13 million digits!

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    • Thanks for stopping by Wonderopolis today, Think Alot (we know that’s not your real name, but it lets everyone know you like to WONDER about things)! We’re glad to have you as a new friend! :-)

  1. I know that a prime number has two factors (one and itself) and composite number has more than two factors. I learned this in math class!
    :D

    • Thanks for sharing your background knowledge about prime numbers, Julie! You are a super smart Wonder Friend! We’re glad you stopped by this Wonder of the Day®! :-)

    • Not to worry, RodMan, sometimes it takes some time to grasp the idea of prime numbers. We Wonder if you can take a look at the Wonder again and help us understand where you’re confused. We are more than excited to help our AWESOME Wonder Friends, like you! We can’t wait to do some more math WONDERing with you soon! :)

  2. It’s so neat to see so many diferent ways of thinking about numbers. I think prime numbers is defenftly my favorite subject.

    • Thanks for sharing your SUPER comment, Audrey 4-b! We are glad that you liked WONDERing about prime numbers with us today– it’s so much fun to hang out with a great Wonder Friend like you! :)

  3. I remember when we were learning prime and composite numbers they were fun and easy, and I just wanted to say to all the little kids I think you may have a good time learning them too!!!

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Have you ever wondered…

  • What is a prime number?
  • How many prime numbers are there?
  • What is the largest known prime number?

Wonder Gallery

black and white numbers_shutterstock_25821664hhVimeo Video

Try It Out

Grab 2, 3, 5, or even 7 friends and family members to help you explore one or more of the following prime activities!

  • Ready to Be a Prime Number Hunter? Just print out a 100 Chart, grab some markers, and get ready to do some fancy cipherin’! As you hunt, circle the prime numbers and cross out the composite numbers. You’ll probably begin to see some shortcuts that you can take. For example, you know that 2 is the only even prime number, so you can cross out all the other even numbers. You also know that 3 is a prime number, so you can cross out all the multiples of 3: 6, 9, 12, 15 and so on. As you do this with each prime number you find, you’ll quickly narrow down the list of numbers to just the primes.
  • The shortcut you discovered in the first activity above was actually discovered by ancient Greek mathematician Eratosthenes. He developed a simple algorithm for finding all the prime numbers up to a specific whole number. His famous algorithm is called the Sieve of Eratosthenes. If you want, you can check out an interactive version of the Sieve of Eratosthenes online!
  • Up for a challenge? Jump online to check out Math Forum: Prime Numbers. You’ll go beyond simple prime number definition to learn about both Euclid’s theory of prime numbers (which has been proven) and Goldbach’s Conjecture (which hasn’t). 

Still Wondering

Visit Illuminations to play a fun, interactive Factor Game that will exercise your ability to determine the factors of a number!

 

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