Who was the first muslim prophet?

It is widely accepted that the first Muslim Prophet was Muhammad, full name Abū al-Qāsim Muḥammad ibn ʿAbd Allāh ibn ʿAbd al-Muṭṭalib ibn Hāshim.

It is the tradition of many cultures (Arabs for example) that they are respectedly called by the name "father of ......".  In this case:
Abu -  meaning father
Qasim  - The name of Prophet Muhammad's first son
Muhammad - his real name
ibn - son of
Abd Allah - The name of Prophet Muhammad's father
so, you get
Abū al-Qāsim Muḥammad ibn ʿAbd Allāh = Father of Qasim, Muhammad, the son of Abd Allah...
Abd Allah is the son of Abd al-Muttalib, who is the son of Hashim.

However, Muslims may not agree that Muhammad was the first prophet as they believe that Muhammad restored the unaltered  original monotheistic faith of Adam, Noah, Abraham, Moses, Jesus and other prophets. Apparently there is some contradiction on the Quaran, but as I am not Muslim and don't wish to upset those who are, it is hard to make a decision on this.