"The 25 year episcopate of Peter at Rome is evidently due to the statement of Justin Martyr regarding the labors of Simon Magus at Rome".
Why don't you finish the sentence:
The twenty-five years' episcopate of Peter at Rome is evidently due to the statement of Justin Martyr regarding the labors of Simon Magus at Rome (see above), combined with the tradition of Peter's residence in the same city, especially as it would seem that the Roman Church had actually been formed early in the reign of Claudius through the indirect influence of the Petrine Christianity of Palestine.
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"The twenty-five years' episcopate of Peter at Rome is evidently due to the statement of Justin Martyr regarding the labors of Simon Magus at Rome (see above), combined with the tradition of Peter's residence in the same city, especially as it would seem that the Roman Church had actually been formed early in the reign of Claudius through the indirect influence of the Petrine Christianity of Palestine."
Note that the encyclopedia refers to Peter's residence as "tradition" not fact, but "as it would seem", and the phrase "the indirect influence" meaning what? If Peter had been involved in its formation it would have been "direct influence", but the encyclopedia says "indirect" meaning that Peter was not there personally, but what was Petrine Christianity in Palestine made its way to Rome indirectly.
Why don't you finish the sentence:
Why don't you finish the page: "All this giving rise to ... the legend of his twenty-five year residence in Rome"
And this:
"it was not until the middle of the third century that Peter was definitely claimed as bishop of Rome".
So here we have the answer to our question of when Peter became bishop of Rome: Peter became bishop of Rome in the middle of the third century by virtue of the pen of Cyprian and embellished upon a short time later by Eusebius.