On finding a lead to the Prime Number paradox

[Dubbelosix]

In my studies to find the premise behind why prime numbers existed (and I really do think I'm onto something) I ended up from a calculation that gave me a number of 256, and after some online studying, this number is really important. I learned, that the number is vital in computers. First of all, the number is exactly (256 = 2*2*2*2*2*2*2*2 =2^8.) This is the same as (256 = [2^4]^2 = 16^2). The number 256 is not itself a prime number, and the logarithm (log_16 [256] =2) exactly. In computer algorithm, a byte represents exactly 256 different values precisely and a computer containing 8 bytes can store any value between 0 and 255 parts. It's important because it represents a common base for the units inside the computer. Pretty interesting from a numberphile point of view.

Further, 256 is a 'composite number' in numerical analysis. All the prime numbers before 256 are the following 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, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251.

With this aside, what did I find? I decided from a general rule to find any obvious patterns in prime numbers, and started off by analysing the multiplication table. The one that stared obvious to me was the 9x multiplication table because it's order of numbers are symmetric, ie. 18, 27, 36, 54, 63, 72, 81, the order of these numbers when you take away their values, such as 1-8 = -7, for the next, we get 2-7 = -5 then 3-6 =-3 and finally 4-5 =-1, and continuing the process, the signs flip giving 3, 5 and 7 once again. This a prime rule, since 3, 5 and 7 are all prime numbers just above the prime number of 2. Equally, ignoring the signs, but only cautiously, 75311357 which is known as a palindrome in numerics, that which spells the same forward as it would backwards. There appears to be, if we take the 1 +1 as the factor of 2, a general rule for at least the first four prime numbers arising from the 9x table, which is extraordinarily simple!

Edited April 4, 2021 by Dubbelosix