Rare Occurneces with Prime Numbers?

What is the the most symmetrical and function of Prime numbers that Math has yet to explain?
First let me get into some elementary mathematics first.
ab=ba correct? This is symmetry
a=1
b=2
1*2=2*1
Ok let’s complicate it a little.
a=2
b=3
a*2b=b*2a
2*2(3)=3*2(2)
12=12
Weird but true...
Now for the truly weird.
a* (b+b)= b* (a+a)
a=2
b=3
2*(3+3)=3*(2+2)
12=12
Now this works for every set of numbers but lets get to pure symmetry.....
What set of numbers, when placed in this formula will give complete symmetry? In where the two numbers and their sums (a+a) and (b+b) will be symmetrical forwards and backwards?
Would it matter if I said that is a very important Prime number! In actuality it is only one Prime number. Does any one know what it is?
You guessed it.....13!
Let’s try it.
We will take 13 and then read it backwards, 31.
These are both prime numbers!
Ok, so now let’s pluck them into the formula.
a=13
b=31
13*(31+31)=31*(13+13)
Now that looks cool, right!
Ok let’s take it a step further...
13*(62)=31*(26)
Did you see it!!!! Read the complete equation backwards......
13*62=26*31
Complete symmetry using 13.....But wait....This is all happening because of a summation of 13 and it’s reverse. In which both are primes and their summation is not. So could it be? Could the product of the equation be a sum of two prime numbers?
That it is....
806/2= 403 where 403 is a prime number.
Pretty weird eh?
13 is seriously a special number in nature and life. My higher self taught me this in one night, in which I have never seen it before. If anyone has ever seen this before please let me know where.
Now why is 13 important?
I would love to have some feedback on this. I currently have a String Theory or more over an M-theory in where 13 is the number of dimensions in reality not 11. And when you use it in the formula of 12+1 you come to startling conclusions.....
Let me know all...
Love light and hugs..
Joshua