What is the longest fast recorded in the Bible?

In the Gospel accounts which record this, it is after His baptism by John the Baptist. The synoptic gospels say that Jesus went into the wilderness for forty days, an allusion to the prophet Elijah.

Mark 1:13 tells of Jesus in the wilderness forty days, ministered to by angels, just as Elijah was ministered by an angel and in the wilderness forty days (1 Kings 19:5-7).

The 'Q' document follows the allusion to Elijah in a subtly different way, taking the angel out of the gospel story and instead having Jesus fast for forty days (in the company of Satan), just as Elijah did after the angel ministered to him. This version in found in the Gospels of Matthew and Luke.