I think that a specific number is impossible give for this one.
There exists humans with the gene that allows them to function normally on less sleep than most other humans.
Some other answers here point out "drowsy drivers". "Sleeping" whilst awake is indeed a thing.
You need to consider that there are still others whom have trained their bodies and souls to require minimal sustenance or to handle incredible amounts of pain.
Personal estimate for someone without training, the ability to sleep with their eyes open, or a special gene: 13 days. Record is officially 11.
