No single Bible total
There isn't a verse that totals every prophet from Genesis to Revelation. Scripture presents prophets as people God called to speak his message, but some are central figures in long stories while others appear only briefly. Moses stands out in Israel's story, and Deuteronomy says that no prophet like him had arisen in Israel at that point (Deuteronomy 34:10).
The Bible also describes groups rather than naming everyone. While Ahab and Jezebel opposed the Lord's servants, Obadiah hid one hundred prophets in two caves and provided for them (1 Kings 18:4). So a count of named people will always miss some.
And there arose not a prophet since in Israel like unto Moses, whom the Lord knew face to face,
Why people say sixteen
When someone says there are sixteen prophets, they usually mean the people traditionally associated with the Old Testament's prophetic books. This group is commonly divided into four major prophets and twelve minor prophets. “Major” and “minor” refer to the books' length, not to how much God valued those who spoke for him.
That number can be useful when finding your way around the Old Testament, but it is not a complete biblical census. It leaves out prophets such as Moses, Samuel, Elijah, Elisha, Nathan and Gad, along with unnamed prophetic communities. Jesus himself referred to Daniel as a prophet (Matthew 24:15).
When ye therefore shall see the abomination of desolation, spoken of by Daniel the prophet, stand in the holy place, (whoso readeth, let him understand:)
Prophetesses matter too
Scripture explicitly names women as prophetesses. Miriam is called a prophetess after Israel crossed the Red Sea (Exodus 15:20). Deborah was both a prophetess and a judge in Israel (Judges 4:4), and she delivered the Lord's command to Barak before the battle against Sisera (Judges 4:6-7).
Huldah was a prophetess whom Josiah's officials consulted when the Book of the Law was found (2 Kings 22:14). She then gave them the Lord's message about Jerusalem and Judah (2 Kings 22:15-17). In the New Testament, Anna is called a prophetess (Luke 2:36), and she spoke of Jesus to people waiting for redemption in Jerusalem (Luke 2:38). Philip's four daughters also prophesied (Acts 21:9).
A prophet was not always trustworthy
The word prophet does not automatically mean a person truly spoke for God. Moses warned Israel about people whose signs or predictions might seem convincing but whose message drew people away from the Lord (Deuteronomy 13:1-3). Later, John urged believers to test spiritual claims rather than accept every voice (1 John 4:1).
So the best answer is simple: the Bible contains many prophets, but it gives no final total. Sixteen is a helpful label for a particular set of Old Testament writing prophets, not a number for everyone God used. Try reading one prophetic story, perhaps Deborah's or Elijah's, alongside a shorter book such as Jonah. The prophets keep calling people to listen to God.
Beloved, believe not every spirit, but try the spirits whether they are of God: because many false prophets are gone out into the world.