I've read that the minimum number of moves for solving a 3x3x3 cube in its most scrambled state ("God's number") is just 20 moves, and this was verified through

I've read that the minimum number of moves for solving a 3x3x3 cube in its most scrambled state ("God's number") is just 20 moves, and this was verified through brute force search. I'm uncertain as to whether there is an algorithm for solving an arbitrarily scrambled cube in just 20 moves, or if it's just known that it is possible to be solved in 20 moves, but probably the latter. Anyway, I can't seem to find a corresponding God's number for the 4x4x4 cube but it seems perhaps the lower bound is in the 30-40 move range. I not a cuber (?) by any means so I don't know if there's any sort of formula to even approximate the lower bound for solving successively higher level cubes, but if there is, I'd be very curious to know what the approximate God's number is for this 34x34x34 beast. Anyway if we were to go with just a very naive guess that each higher level takes 1.5x the moves of the previous level so 3x3x3=20, 4x4x4=30, 5x5x5=45 and so on, that would yield 34x34x34= 5,752,532 moves (or 5,817,104 if you round up 1 at every fractional result), which at a second per move, would take over 2 months to solve. I suspect that in practice, any algorithmic means to solve such a cube would take somewhat longer, so much so that a thoroughly scrambled cube might never be unscrambled.