Your screen should go off by itself after a certain amount of time if you're not in any app (aka, on the home screen)
Otherwise, your screen off delay is set to something high. You can change it in settings > my device > display > screen timeout
its currently set to 15 seconds and the screen does not turn off, if I reboot the phone the screen will automatically shutoff like its supposed to however after a short period of time (maybe an hour?) the screen will no longer automatically turn off. This is why I suspect some program I have loaded is preventing the screen from sleeping.
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