In the study of history as an academic discipline, a primary source (also called original source or evidence) is an artifact, a document, diary, manuscript, autobiography, a recording, or any other source of information that was created at the time under study.
That's from wikipedia. I think that of all the sources we have discussed Ignatius was the earliest at around 110 AD. The others range from 180 to 400 AD.
Now when Peter was in Rome is somewheres around 42 to 67 AD. Guess what? With the possible exception of Ignatius (and even this is doubtful) NONE OF THESE WRITERS WERE ALIVE WHEN IT HAPPENED!!!! They didn't write what they wrote when it happened. You can't produce a primary source if you weren't even born yet.
I am a civil war buff. I have read countless civil war books and watched many documentaries. I can write some great and truthful essays on the civil war, but I can't be a primary source. None of the church fathers we are discussing are primary sources.
The only primary source in this discussion is the Bible... And you folks blast me for sticking to it and not wavering on it.