As mentioned in my comment I could get nothing as such that could be treated as against the  Papal Succession in Bible.  

 Having said this, the presence of many verses and references in the New Testament indicates that Peter was first in authority among the apostles. Whenever they were named, Peter headed the list (Matt 10:1-4, Mark 3:16-19, Luke 6:14-16, Acts 1:13).  Sometimes the apostles were referred to as "Peter and those who were with him (Luke 9:32). Peter was one who generally spoke for the apostles (Matt 18:21, Mark 8:29, Luke 12:41 John 6:68-69) and he figured in many of the most dramatic scenes (Matt 14:28-32, 17:24-27, Mark 10:23-28). On the Pentecost it was Peter who first preached the crowds (Acts 2:14-40). He worked the first healing in the Church Age (Acts 3:1-7). It is Peter's faith that will strengthen his brethren (Luke 22:31-32). He led the first council in Jerusalem (Acts 15) and announced the first dogmatic decision (Acts 15: 7-11). It was Peter that the revelation came that Gentiles were to be baptised and accepted as Christians (Acts 10:46-48).