Legendre's Constant

One of the equations I presented earlier seemed to imply that Legendre's Constant, of which only a few digits are known, was related to both the Twin Prime Constant and the Feigenbaum Alpha Constant. Assuming this is an accurate equation (which is a bit speculative at this point), my estimation of the Legendre Constant to several more decimal places would be as follows:

Legendre ~= acosh(ln(Feigenbaum Alpha - e^(Twin Prime)) / ln(sinh((Twin Prime)))

{Feigenbaum Alpha = 2.50290787509589282228390287321821578; Twin Prime = 0.66016181584686957392781211001455577}

Which is the same as:

B ~= cosh^-1(log_sinh(C2)(α - e^C₂))

        ~= 1.083660002419934580439575716176792

Again: this is highly tentative. There could be other elements of this equation which are missing. But it's at the very least a starting point past the five decimal digits of Legendre's Constant which were previously known.