I discovered this by accident, when trying to create a formula that generates prime numbers (an impossible task, I know).
But, I find it very interesting that you take any prime number 5 and greater, then you square it and subtract 1, dividing it by 3 always results in a whole integer.
5 x 5 = 25 - 1 = 24 / 3 = 8
11 x 11 = 121 - 1 = 120 / 3 = 40
The result is always a whole number, regardless of how high the prime number is.
Can someone explain why this is so, mathematically? This does not seem possible (to me). And if this is really true, why can I find nothing written about it?
I have never heard of this theorem before, and nothing is mentioned on Wikipedia or other sources. But perhaps this could be a helpful in reducing 33% of the possibilities when trying to find or prove large prime numbers, computationally.
UPDATE: someone commented that the resulting number is divisible by 24 , not just 3