Comment by albert_roca

Valid question. The significance is that the 4^32 scaling factor emerged earlier in the model as a geometric constraint, and 4^64 appears in this equation, apparently because G is inversely proportional to the square of m_P. Hitting G within 8 ppm using a pre-existing constraint to link quantum constants with the proton mass is statistically extremely unlikely. I admit the precision was a surprise to me too, but the fact that it consistently reproduces Schwarzschild dynamics suggests it's not just a lucky number.