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2017: A Prime Year

January 24, 2017
By Robert and Libby Strong and Richard Pollack - SMART Science , OVParent

Have you noticed that there are different kinds of whole numbers? All positive whole numbers easily can be divided into "odd" (numbers whose last right digit is 1, 3, 5, 7 or 9) and "even" (numbers that end in 0, 2, 4, 6 or 8). There are other kinds of ways to group positive whole numbers into what are called "prime" and "composite" numbers.

(Note: Zero (0) and one (1) are special case whole numbers. They don't fit the definitions of the prime and composite.)

A positive whole number is considered a prime number if it is greater than 1 and can be divided by only 1 and itself. Examples of prime numbers in order from smallest to 30 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.

Composite numbers are those positive whole numbers greater than 1 that are not prime numbers. Examples of composite numbers in order from smallest to 30 are: 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30. You will notice that if you combine the above sets of prime and composite numbers, you include all positive whole numbers between 2 and 30. This pattern continues as far as we have checked, and we believe this continues to infinity.

There are some interesting things to notice about prime numbers. The first thing to notice is all prime numbers are odd numbers, except for the number 2.

Activity #1: Twin Primes

Challenge

Look closely at the short list of prime numbers. You may notice that the prime numbers often differ by only two, Examples are: 3, 5 or 5, 7 or 11, 13 or 17, 19. These are called twin prime numbers. See how many twin prime numbers there are between 2 and 100.

To do this:

On a sheet of paper, write out all the numbers from 2 to 100.

Circle all the prime numbers.

Now circle all the twin primes.

Look for any patterns in prime numbers and twin primes.

People have been looking for other patterns within prime numbers for hundreds of years. See if you can find any patterns for yourself.

Activity #2: Goldbach's

Conjecture

The German mathematician Christian Goldbach came up with another pattern in whole positive numbers that you can check. Goldbach's Conjecture states that every even whole number greater than 2 is the sum of two prime numbers.

Use the sheet of paper where you wrote out all the numbers from 2 to 100.

Pick any even number on the list and write it down.

Look for two prime numbers (note: these can be the same number) that, when added together, will make the even number you picked.

Do you think the Goldbach Conjecture will continue forever to infinity? Discuss this with your friends and family.

So, you may ask, what does the year 2017 have to do with all this prime number talk? It turns out that the number 2017 is a prime number. The number 2017 is only divisible by the numbers 1 and 2017.

Don't take our word for it - check it for yourself!

Libby and Robert Strong and Richard Pollack work with the SMART-Center, a hands-on science outreach and education organization in the northern Ohio Valley, the headquarters of which is located at the SMART Centre Market, 30 22nd St., Wheeling.

 
 

 

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