### OH MY GOD! DID YOU CREATE MATHEMATICS?

I'm not blaspheming here. This really is amazing. It's a lovely example of mathematics. I read about it today. I never knew it before:
PLAYING WITH PRIME NUMBERSa
The prime numbers below 100 are:
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
I have highlighted some of them. I'll tell you why a bit further on. You might like to try and work it out. It would be hard to guess.
If you divide up the highlighted ones from the others you get two lists of numbers
Bold prime numbers: 2, 5, 13, 17, 29, 37, 41, 53, 61, 73, 89, 97
Shy prime numbers: 3, 7, 11, 19, 23, 31, 43, 47, 59, 67, 71, 79, 83
Do you notice anything about them? The bookb hinted: "Try subtracting each number in the list from it's neighbour". I still didn't get it. I tried subtracting numbers in the different rows. Duh!
THREE IS A VERY NAUGHTY NUMBER
When you subtract the numbers for the first row you get
Bold: 3, 8, 4, 12, 8, 4, 12, 8, 12, 16, 4
and for the second row you get
Shy: 4, 4, 8, 4, 8, 12, 4, 12, 8, 4, 8, 4
I'm sure you've spotted it now. Apart from the naughty 3 at the beginning of the first row, all the numbers are multiples of 4: 1x4, 2x4, 3x4 etc.
And that rule applies to every other number in the sequences that you care to try.
And mathematicians have proved that:
1) Both sequences (both bold and shy prime numbers) go on forever
2) The further you go the closer the ratio of bold to shy gets to 1:1
3) All the numbers (apart from that naughty 3) are multiples of 4. (In fact they are more precise than that)
Oh, I haven’t told you how the prime numbers were divided into bold and shy ones. Simple: Bold ones are sums of two squaresc
2=12+12, 5 = 12+22, 13=22+32, 17=12+42 ...
the others are not.
So why is it that there is a relationship between multiples of four, prime numbers and sums of squares of numbers?
AND HERE IS WHERE WE GET BACK TO GOD
That old God chappy was pretty devious when he was creating the laws of mathematics and he sneaked that one in.
Or did God create the laws of mathematics? Or were they always out there? Please, one of my religious brethren, ask your priest and let us know.
Foot notes:
Just in case you have forgotten / didn't know
a) Prime numbers are whole numbers that cannot be divided by other whole numbers other than 1 and themselves.
b) The book is "I am a Strange Loop" by Douglas Hofstadter. Lent to me by David.
c) A square, in this context, is one whole number multiplied by itself. E.g.
two squared is written 22=2x2=4,
five squared is written 52=5x5=25.
The sum of two squares is what you get when you add two squares together.