Mohammad was born 635 AD. He was illiterate. He never wrote anything. The koran was, contrary to the lies of Muslim clerics, not written down for hundreds of years later, after Ishaq completed the one and only record of Mohammads life and sayings. You might say it was Ishaq who wrote the Koran. Before that, it was passed along from memory, and we know just how well that works.
I just started reading through Robert Spencer's Politically Incorrect Guide to Islam and the Crusades. He states Muhammad lived from 570 to 632 AD. Lots more to read.