i thought the false prophet was the anti-christ

No, not the same. The false prophet does insitute the mark(666)

And I beheld another beast coming up out of the earth; and he had two horns like a lamb, and he spake as a dragon.
And he exerciseth all the power of the first beast before him, and causeth the earth and them which dwell therein * to worship the first beast, whose * deadly wound was healed.
And he doeth great wonders, so that he maketh fire come down from heaven on the earth in the sight of men,

Rev.13