Jesus names Abiathar as high priest when he wasn't

At one point fairly early on in his ministry, the synoptics record that Jesus was questioned about an apparent breach of the sabbath. This is in Mark 

And he said to them, 'Have you never read what David did when he and his companions were hungry and in need of food? He entered the house of God, when Abiathar was high priest, and ate the bread of the Presence, which it is not lawful for any but the priests to eat, and he gave some to his companions.' (Mark 2:25-26)

                               ----------------- Jesus makes mistake------------------------

Then David came to Nob to Ahimelech the priest. And Ahimelech came to meet David trembling and said to him, "Why are you alone, and no one with you?" (1 Samuel 21:1)

It certainly seems that either Jesus or Mark has made a mistake and named the wrong priest. How can he make such a mistake?? Why lie about the name if he wasn't sure That's breaking the law of the OT, unless he read another book which isn't part of the tanak..