Jesus did not say only three denials. At the Last Supper and before a long dissertation, He foretold of three denials before a cock-crow (Jn. 13:38).
Then, while in the street on the way to the Garden of Gethsemane (Jn. 18:1, Mk. 14:26), Jesus foretold that the disciples would be offended. To which Peter again insisted that he would not. Then Jesus predicted three denials from Peter that would take place before a second cock-crow would take place (Mk. 13:30).
The Bible, since it is typically reliable, is correct.
Sigh ...
**Jesus did not say only three denials.**
He said three denials. In response to the Lord’s prophecy of denial, proud Peter was declaring a pledge of allegiance; an attempted contradiction of the Lord’s all knowing mind. The denials were quite the opposite of pledges of allegiance.