From everything I am reading, a proper skyline diffuser must have a it's number of wells be one less than a prime number. For example, 156 wells, which is 1 less than the prime number 157.
And further, each dimension must have a number of wells that is not divisible by the same number that the other dimension is divisible by. For example, 12x13, since neither number is divisible by the same numbers (12 is divisible by 2 and 2 and 3, but 13 is only divisible by 13). Of course, based on this, the dimension ratio of a proper skyline diffuser is not square, but some form of unusual rectangle.
Yet all the diffusers I see for sale and DIY in pictures are all 12x12 wells or 18x18 wells, etc. They don't seem to follow the math at all.
I'm hoping to use 1"x1" wells, and a 12"x13" diffuser is too small for me. I was thinking between 18" and 24" wide, and between 18" and 70" tall.
So ... I started crunching numbers. But I'm having a hard time of it. If I choose a large prime number (300+) and find what it minus 1 is divisible by, all of the good dimensions are divisible by each other. If I avoid this by multiplying two prime numbers by each other and adding one, the resulting number never turns out to be a prime.
First, does it really make a difference to use prime numbers for this?
Second, if it is important, why does everyone else just build them to common dimensions?
Third, is there a formula for discovering these prime numbers that do turn out better for diffusers?
Fourth, do you know of a list of diffuser dimensions that are mathematically good? I would imagine 12x13 would be on that list, but I want a bigger one.
Thanks!
