How to modify possible values screen timeout on rooted devices?
In order to keep screen awake forever:


Download No Screen Off app and install it.
(Ignore this PLEASE) If you know android programming, you can use this snippet in your app: 


getWindow().addFlags(WindowManager.LayoutParams.FLAG_KEEP_SCREEN_ON);


Some phones have "Keep screen turned on" option in Screen timeout
settings.
(Requires Root) You can use PerApp for making change in Screen timeout
settings and add your own value.(customize)
There is a stay awake option in "Developer Options" to Stay awake
while USB debugging and charging.