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In the gospel of Matthew, it makes it sound in the NASB like the temptations came first after 40 days of fasting.
2 And after He had fasted for forty days and forty nights, He then became hungry. 3 And the tempter came and said to Him, “If You are the Son of God, command that these stones become bread.” Matthew 4:2-3
Did Satan first come to Messiah on day 40?
There is a parallel account in (NIV) Luke 4:
1 Jesus, full of the Holy Spirit, left the Jordan and was led by the Spirit into the wilderness, 2where for forty days he was tempted by the devil. He ate nothing during those days, and at the end of them he was hungry.
3The devil said to him, “If you are the Son of God, tell this stone to become bread.”
Satan had been tempting Jesus all along for 40 days. Only the final three temptations were recorded in detail.