Teaching Prime Numbers a Different Way
Let's consider the positive integers greater than 1, that is 2,3,4,5,..
Suppose we are given the first integer 2 and asked to make all other integers using only the multiply operation.
We soon run into trouble because 2*2=4 and we have no way to make 3.
OK, we just add 3 to our set of given numbers g, so g={2,3}
Can we make 4? Yes, 2*2=4
Can we make 5? No, all our tries fail, so we add 5 to our set of given number g={2,3,5}
Can we make 6? Yes, 2*3=6
Can we make 7? No, all our tries fail, so we add 7 to our given numbers g={2,3,5,7}
Can we make 8? Yes, 2*2*2=8
Can we make 9? Yes, 3*3=9
Can we make 10? Yes, 2*5=10
Can we make 11? No, all our tries fail, so we add it to the set g={2,3,5,7,11}
Can we make 12? Yes, 2*2*3=12
Can we make 13? No, so add it to the set g={2,3,5,7,11,13}
Can we make 14? Yes, 2*7=14
Can we make 15? Yes, 3*5=15
Can we make 16? Yes, 2*2*2*2=16
What is the set g that we are generating by this process? It's the set of prime numbers! This is simply another way to explain prime numbers.
It's a nice demonstration because it shows how prime numbers generate all numbers using only the multiply operation. You can also see that as g gets bigger we can obviously generate more numbers from it, so prime numbers become less and less frequent.
Content written and posted by Ken Abbott abbottsystems@gmail.com
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