How many prophets did God send to mankind? This is a debated issue, but what we know is what God has told us in the Quran.
God says he sent a prophet to every nation. He says:
“For We assuredly sent amongst every People a Messenger, (with the command): ‘Serve God, and eschew Evil;’ of the people were some whom God guided, and some on whom Error became inevitably (established). So travel through the earth, and see what was the end of those who denied (the Truth)” (Quran 16:36)
This is because one of the principles by which God operates is that He will never take a people to task unless He has made clear to them what His expectations are.
The Quran mentions the names of 25 prophets and indicates there were others. It says:
“Of some messengers We have already told you the story; of others We have not; - and to Moses God spoke direct.” (Quran 4:164)

The Names of the 25 Prophets Mentioned are as follows:
Adam
Idris (Enoch)
Nuh (Noah)
Hud (Heber)
Salih (Methusaleh)
Lut (Lot)
Ibrahim (Abraham)
Ismail (Ishmael)
Ishaq (Isaac)
Yaqub (Jacob)
Yusuf (Joseph)
Shu’aib (Jethro)
Ayyub (Job)
Dhulkifl (Ezekiel)
Musa (Moses)
Harun (Aaron)
Dawud (David)
Sulayman (Solomon)
Ilias (Elias)
Alyasa (Elisha)
Yunus (Jonah)
Zakariya (Zachariah)
Yahya (John the Baptist)
Isa (Jesus)
Muhammad

Peace Be Upon Them All.