Fractal

I found the pattern of prime numbers, but I know that it is almost the same with sieve of Eratosthenes.

When you see odd numbers, there is symmetry and you can find sieve of Eratosthenes.

	3	5	7	9	11
3	9	15	21	27	33
5	15	25	35	45	55
7	21	35	49	63	77
9	27	45	63	81	99
11	33	55	77	99	121

I mean x=(3,5,7,9,11) y=(3,5,7,9,11).
Therefore, you can see z=x*y and z=x+Σ2x or z=y+Σ2y. 9=3*3 and 9=3+2*3,15=3*5 and 15=3+4*3 or 15=5*3 and 15=5+2*5, 21=3*7 and 21=3+6*3 or 21=7*3 and 21=7+2*7・・・・.
z is not prime numbers, so x'=(3,5,7,11) y'=(3,5,7,11).

However, when you add 2, the symmetry is broken.

	3	5	7	9	11
2	6	10	14	18	22
3	9	15	21	27	33
5	15	25	35	45	55
7	21	35	49	63	77
9	27	45	63	81	99
11	33	55	77	99	121

x=(3,5,7,9,11) y=(2,3,5,7,9,11) z=x*y and z=x+Σ2x or z=y+Σ2y
x' and y' are prime numbers. x'=(3,5,7,11) y'=(2,3,5,7,11)

Therefore,

when you can see z=x*y and z=x+Σ2x or z=y+Σ2y, z is not prime numbers.

This would be the infinite pattern.