Apocorubik's Cube (10,000 blocks across): How long to solve if a quarter turn takes 2.8 seconds?

Question

Suppose you have a Rubik's cube, $10,000$ blocks across (so, $600,000,000$ total tiles), scrambled. Assuming an ideal solving algorithm, approximately how long will the cube take to be solved, given one quarter turn can be made every 2.8 seconds?

Answer 1

According to https://arxiv.org/abs/1106.5736 the asymptotic bound for God's Number on higher order cubes is:

$$\Theta(n^2/\log n)$$

But this is only asymptotic, so you can't just plug in $n$ and expect to get the exact right answer. But we use it as a very loose approximation. Since God's Number for $n=3$ is 26 (using quarter-turn metric), we can do:

$$ \frac{10000^2}{\log 10000} * \frac{\log 3}{3^2} * 26 = 34458757 $$

So to round off your question take that number, multiply it by 2.8s, and you get about 3.1 years.