**Prime Number Patterns**

Let's write the prime numbers in base 2 "binary" format. I like to use the convention of least significant digit to the left, so for example the number 11 in binary is 1101, and this simply means..

11=1*(1)+1*(2)+0*(4)+1*(8)

Here are the first 20 prime numbers in binary..

2 01

3 11

5 101

7 111

11 1101

13 1011

17 10001

19 11001

23 11101

29 10111

31 11111

37 101001

41 100101

43 110101

47 111101

53 101011

59 110111

61 101111

67 1100001

71 1110001

Let's try a pattern algorithm. We'll define a replace operator r(n) as "whenever the pattern 01 occurs in the binary representation of n replace it with 101". Here's an interesting thing..

r(2)=5

r(5)=11

r(11)=23

r(23)=47

But the pattern does not continue, because r(47) is not prime.

Of course, this is just a simple example of pattern recognition. If you have access to serious computing power there are many ideas you can test!

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Content written and posted by Ken Abbott abbottsystems@gmail.com