This
magnum opus does not begin well.
Quote:
The function that generates those two prime numbers is:
dn/dx = x^(4/p)  3x^(2/p) + 1
Where n is the derivative of order n and p is the distance in units of the separation that we want to find.

So, "n" is selfreferencing, and the symbol p is used to denote the
separation, or distance between two primes, rather than a prime number.
It continues into the demonstrably false:
Quote:
The relationship between this function and the Lucas numbers is that in the undifferentiated function
x^(4/p)  3x^(2/p) + 1 it's zeros are the Lucas numbers.
For example x^(4/7)  3x^(2/7) + 1 = 0
One of its zeros is 29 which is the 7th number of Lucas

Er, no. Substituting 29 for x in the given expression gives 0.00198416, approximately.
The zeros of y^2  3*y + 1 are
so, taking x = y^(p/2), we have