I suggest trying this out on your own, even if you don't think prime numbers are interesting, give it a shot. You don't even need to know if 101 is s a prime number or not.

All prime numbers greater than 3 are multiples of 6 + or -1.

You can do 6's. just write them out with enough space to write some number in between. Like this: 5 6 7 11 12 13 17 18 19 23 24 25 29 30 31 35 36 37 ... just keep going if you can to 100 or 150. but if you can make your rows begin with 5, 35, 65. 95 and so on. Go high enough to make it challenging. The even numbers should all line up so you can cross them out, and the 2 columns of 5, but we'll come back to those.

This contains all the prime numbers to whatever number that you went to, but of course all of those aren't prime numbers. Let's weed those out. 5's are easy to eliminate but let's use another way that will show the process of this sieve.

Take 7 and multiply it times 6 which gives you 42. Starting with the prime number 7, keep adding 42 till you reach the amount you went to with your 6's. Like this 7 49 91 133 175 217 ... You can cross these off of your list

Do the process with 11. 11 x 6 is 66. So add 66 to 11 and each following number. 11 77 143 209 ...

Now for 13. 13 x 6 + 78. So add 78 to 13 and keep adding.

On paper, when you write these out and use those numbers in your first column for each row of numbers. That column other than the first number, the prime number, is a column of elimination. It matches with the composite (non- prime) numbers on the list.

But there is more. As you noticed with 5, there are two columns of numbers you can eliminate, a 2 for 1 deal. the other number is the square of the prime number. That happens for every prime number that falls in the sequence of 5 11 17 23 29 35 41 47 53 and so on

What is also cool is that rather than adding all those numbers, 6 times the prime number to the prime number, they are actually multiples of the prime number: 1 7 13 19 25 31 37 43 49 55 61.

Do those 2 sequences look familiar? Put them together and you have 5 7 11 13 17 19 23 25 29 31 35 37 41 43 47 49.

All of the numbers identify the numbers on the list that don't belong, and show a fascinating order to prime numbers.

I have done this up to 2000 and it has not missed identifying each composite number on the list.

I hope you enjoyed this.

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