Perhaps what I wrote was less than clear.
Peter was seen by many who came along centuries after the first Apostles as having "primacy".
Being "prime" as in being first, is a position which logically can only be taken up by that one who is themself "first".
One prime as in one numero uno, or else we are always resetting back to "one" all over again -- which makes counting impossible.
Would a person sit and count marbles, One marble, then again for the next say "one" marble, setting that aside to again say or count "one" marble, for the third one in succession?
What's would be the use?
By that example only one can be "first". Being that notions or concepts towards "Petrine primacy" begin with and/or based upon him being in some ways "first", then successors to this "first" cannot themselves have "primacy" in the same manner -- for they cannot be first, if indeed Peter was.
They can only come after Peter, leaving the notion that "primacy" is inheritable to be more a figment of imagination and wishful thinking from the get-go, than anything else.
Sounds like someone is losing his marbles, one day at a time.