This is the post I posted yesterday. It is relevant to Mathematica because it cannot be solved without it. Review the Mathematica code and help me find how to determine the error of the 2 equations! _______________________________________________________________________________-
There is a problem with error. That is the decimal I am adding to the right side of the equation. It should be 0.299
but for a number in the trillions the error is 0.33. I dont understand why it isnt working. This is what we need to be working on.
The truth is this equation is too valuable to abandon. Obviously a computer algorithm could test different errors. I just wanted to make the math equation pure. That is having no guesses just a perfect equation that solves for PNP.
I have posted this to my Backers and 2 message boards. I post not so the equations are stolen, but more minds will solve this.
Yes I cheated with the 11 digit example. I know that putting a number into the equation without the error creates imaginary numbers. However the error can be graphed for error as opposed to the difference of the left equation minus the right side of the equation. This should give a relatively easy and good estimate as to the error that the equations fall in.
So far not perfect but I am working with it. On the bottom equation I took the error the known 0.28 and put it in and a real number 941 appears. Place the original PNP and put 941 in for x and subtract the left equation from the right and the error is found.
I know this solution of the error is not mathematically perfect, but remember it started as a pattern and with the assistance of a computer estimating the error should be possible. I know for a 256 bit number this sounds cumbersome. However I would say that graphing y = ((PNP^4/x + 2* (PNP^2 * x^2) + x^5) / PNP^3) - ((PNP^2/x) + x^2)/PNP
PNP = 3163007
NSolve[((PNP^4/x + 2* (PNP^2 * x^2) + x^5) / PNP^3)== ((PNP^2/x)+x^2)/PNP + 0.287159517,x]
3163007
{{x->10766.8 +18673. I},{x->10766.8 -18673. I},{x->-21533.6},{x->-953.082},{x->953.}}
The equation below shows how to solve the error which is 0.287
PNP = 3163007
NSolve[((PNP^4/x + 2* (PNP^2 * x^2) + x^5) / PNP^3)== ((PNP^2/x)+x^2)/PNP + 0.28,x]
3163007
{{x->10767.00553406246` +18672.685351161595` I},{x->10767.00553406246` -18672.685351161595` I},{x->-21533.93266812111`},{x->-941.1247294994954`},{x->941.0463294956866`}}
The error of 0.28 is a starting point. Each side of the NSolve equation. These equations equal the Prime product within this error. I know it isnt exact yet, but I am working on it.
x = 941
PNP = 3163007
((PNP^4/x + 2* (PNP^2 * x^2) + x^5) / PNP^3) - ((PNP^2/x) + x^2)/PNP
941
3163007
8859632789683911270/31644661843413961343
N[8859632789683911270/31644661843413961343,11]
0.27997242737
_________________________________________________________________________________________________- ____________________________________________________________________________________________________
PNP = 85
x = 5
y = sqrt ((PNP*y\[Dash]x^2)/x)
y = ((PNP^2/x) + x^2)/PNP
y = ((PNP^4/x + 2* (PNP^2 * x^2) + x^5) / PNP^3)
85
5
$RecursionLimit::reclim: Recursion depth of 1024 exceeded. >>
Hold[425 sqrt y \[Dash]]
294/17
N[y, 11]
17.593323835
N[y, 11]
17.593323835
PNP = 85
x = 5
((PNP^4/x + 2* (PNP^2 * x^2) + x^5) / PNP^3) - ((PNP^2/x) + x^2)/PNP
85
5
1470/4913
N[1470/4913, 11]
0.29920618767
PNP = 605054707
NSolve[((PNP^4/x + 2* (PNP^2 * x^2) + x^5) /
PNP^3) == ((PNP^2/x) + x^2)/PNP +
0.29920618766537756971300630979035212701, x]
605054707
{{x -> 357642.060612364370036337217772965000 +
619600.276496119708382454094550208609 I}, {x ->
357642.060612364370036337217772965000 -
619600.276496119708382454094550208609 I}, {x -> \
-715284.031700385975080353264491082027}, {x -> \
-13455.01084271186475677779496348851204}, {x ->
13454.92131836909976445662390864053977}}
PNP = 605054707
x = 13454.9213
(((PNP^2/x) + x^2)/PNP )
((PNP^4/x + 2* (PNP^2 * x^2) + x^5) / PNP^3)
(PNP/x - (((PNP^2/x) + x^2)/
PNP )) + ( ((PNP^4/x + 2* (PNP^2 * x^2) + x^5) / PNP^3) - PNP/x)
605054707
13454.9
44969.3
44969.6
0.299206
PNP = 605054707
NSolve[((PNP^4/x + 2* (PNP^2 * x^2) + x^5) /
PNP^3) - .6 == ((PNP^2/x) + x^2)/PNP - 0.299206186842639, x]
605054707
{{x -> 357642. + 619601. I}, {x ->
357642. - 619601. I}, {x -> -715284.}, {x -> -13490.7}, {x ->
13490.6}}
PNP = 605054707
x = 13490.6
(((PNP^2/x) + x^2)/PNP )
((PNP^4/x + 2* (PNP^2 * x^2) + x^5) / PNP^3)
PNP/x
(PNP/x - (((PNP^2/x) + x^2)/
PNP )) + ( ((PNP^4/x + 2* (PNP^2 * x^2) + x^5) / PNP^3) - PNP/x)
605054707
13490.6
44850.4
44850.7
44850.1
0.300795
44850.5 - 44850.09614
0.40386
44850.7 - 44850.09614
0.60386
PNP = 605054707
NSolve[((PNP^4/x + 2* (PNP^2 * x^2) + x^5) /
PNP^3) - .6 == ((PNP^2/x) + x^2)/PNP - 0.4, x]