I've read a brain shot from a .600 Nitro, that misses the actual brain by a few minutes will knock the elephant out for up to 20 minutes.

The .577 Nitro, 10 minutes, or so.

Those are Stopping Rifles, imho.

You can kill an elephant with a 300gr. solid from a .375 H&H, however, it is not a stopping rifle ctg., it is a killing rifle, useful for hunting, not stopping.