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Old 2020-08-17, 13:18   #5
Dr Sardonicus
 
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Feb 2017
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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 self-referencing, 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

\frac{3\;\pm\;\sqrt{5}}{2}\;=\(\;\frac{1\;\pm\;\sqrt{5}}{2}\)^{2}

so, taking x = y^(p/2), we have

x \; = \; \(\frac{1\;\pm\;\sqrt{5}}{2}\)^{p}
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