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well, let me make it more clear for you. The catholic church cannot claim an unbroken chain back to Peter because of realities like the 'Rule of Harlots' 904-963: The following popes were either brought to Rome to run the popery as pope or raised up from the illegitimacy of harlots such as Theodora and her daughter prostitutes who placed popes on the papal throne. They directly placed the following 'unbroken succession':

Sergius iii (904 - 911)
John x (914 - 928)
Leo vi (928-929)
Stephen vii (929 - 931)
John xi (931 - 936)
Leo vii (936 - 939)
Stephen viii (939 - 942)
Martin iii (942 - 946)
Agepotus ii (946 - 955)
John xii (958 - 963)

And that list is just the Rule of Harlots period. Followed by two popes lit6erally buying the throne to sit it. Shall we go to Innocent iii to see where your specious transubstantiton comes from? Or the decree of infallibility? Or the forbidding of reading the Bible in the vernacular? Or the denouncing of the Magna Carta? Or the instituting of the Inquisition?

Yet catholics are taught that their religion is lead by an unbroken line of 'Vicars of Christ' (pope Innocent went further, naming himself the Vicar of God with all power over life and death on Earth). Just the unvarnished truth of your line of succession should cause a catholic who fears God to flee from that false religion!