Some Fun with assumed distributions - ignore me

${\displaystyle f(x)=\sum _{n=0}^{x-1}2^{n}}$

let B = Number of Indexed Backlinks

${\displaystyle f(x)\approx {\sqrt {Backlinks}}}$

${\displaystyle {\sqrt {Backlinks}}\approx \sum _{n=0}^{PR-1}2^{n}}$

My PR Factor Function M ${\displaystyle M(x,B)={\frac {\sqrt[{4}]{B}}{x}}}$

Exact PR Point function g ${\displaystyle g(x)={\sqrt {\frac {f(x)}{x}}}}$

Logarythmic distence to next g(x+1)

${\displaystyle D(x)=g(x+1)-g(x)}$

long hand ${\displaystyle D(x)=g(x+1)-g(x)={\sqrt {\frac {f(x+1)}{x+1}}}-{\sqrt {\frac {f(x)}{x}}}}$

Estimated Percentage of the distence to the next level

${\displaystyle {\frac {D(Pagerank)}{M(Pagerank,Backlinks)}}*100}$

Full Math

${\displaystyle {\frac {{\sqrt {\frac {f(Pagerank+1)}{Pagerank+1}}}-{\sqrt {\frac {f(Pagerank)}{Pagerank}}}}{\frac {\sqrt[{4}]{Backlinks}}{Pagerank}}}*100}$

\sum_{0}^ {PR} 2^n

${\displaystyle {\frac {{\sqrt {\frac {\sum _{n=0}^{PR}2^{n}}{Pagerank+1}}}-{\sqrt {\frac {\sum _{n=0}^{PR-1}2^{n}}{Pagerank}}}}{\frac {\sqrt[{4}]{Backlinks}}{Pagerank}}}*100}$

${\displaystyle g(x)={\sqrt {\frac {f(x)}{PR}}}}$

${\displaystyle {\sqrt {\frac {f(PR)}{PR}}}-{\frac {\sqrt[{4}]{Backlinks}}{PR}}}$

(1 - (4th root of B) / PR)

square root(15 + 16) / 5 = 1.11355287
(4th root of 237) / 4    = 0.980905332
square root(15) / 4     = 0.968245837
(4th root of 237) / 5    = 0.784724265


\left = a_0 + a_1 (x-c) + a_2 (x-c)^2 + a_3 (x-c)^3 + \cdots