Dear Hasmukh K. Tank,
1. When I say Large number I mean 10^121, that may be reason that I cited Scott Funkhouser.In " An explanation for the 'Large Number Coincidence' 10^40 in astrophysics". In formula (18) you ingeniously re-write Newton Gravitational formula. So, I have same for Universal Gravitational constant as you in 1997 year, but with quite diferent approach. And, it is both quite good without mentioning Hubble.
2. The dimensionless expression of a cycle, in my essay give results similar to yours. The difference is that you are using pion parameters but I am using fundamental particle defined as you can see in my articles.
3. About: „How should we think of infinity?" I cited RuÄ'er BoÅ¡ković [1, paragraph 391]. "Now, although I do not hold with infinite divisibility, yet I do admit infinite componibility". More you can see in paragraphs 391 to 396. Therefore I say: mass and radius of the universe are not physically real mass and radius of the universe; but the mass, radius and any other fenomenon is finite but the number of their combination is infinite.
4. The base 2 of logarithms is usefull tool (see FQXi contests, 2013 year). For calculating values of gravitational constant you can use formula from [2] (You alsow know that h=c*mp*lambdap), so, the proton parameters are used for both, Planck-constant and gravitational constant.
5. Mentioned attempt gave results with accuracy of 12 significant digits for numerous phisical constants;
You do not mentioned anything about pion and Hubble parameters in your articles. Maybe you would think about that later.
Best Regards,
Branko Zivlak
[1] Boscovich J. R.: (a) "Theoria philosophia naturalis redacta ad unicam legem virium in naturaexistentium", first (Wien, 1758) and second (Venetiis, 1763) edition in Latin language; (b) "A Theory of Natural Philosophy", in English, The M.I.T. Press, Massachusetts Institute of Technology, Cambridge, Massachusetts and London, England, first edition 1922, second edition 1966
[2] Branko Zivlak, Universal Gravitational Constant Via Proton, http://viXra.org/abs/1310.0018