There was a virtual consensus from the 2nd century onward that the evangelist Mark was the interpreter of Peter. This tradition was recorded probably ca 110 CE (or ca 130) by the bishop Papias of Hierapolis, who in turn received it earlier from some enigmatic figure known as the presbyter John (quoted in Eusebius, Ecclesiastical History 3.39.15).* Here is Bart Ehrman‘s translation in the LOEB series:
And this is what the elder used to say, ‘when Mark was the interpreter [or translator] of Peter, he wrote down accurately everything that he recalled of the Lord’s words and deeds – but not in order. For he neither heard the Lord nor accompanied him, but later, as I indicated, he accompanied Peter, who used to adapt his teachings for the needs at hand, not arranging, as it were, an orderly composition of the Lord’s sayings. And so Mark did nothing wrong by writing some of the matters as he remembered them. For he was intent on just one purpose: to leave out nothing that he had heard or to include any falsehood among them.
To see the Greek and translation choices of different scholars for this fragment of Papias, see J.B. Lightfoot & J.R. Harmer (cf. Rev Daniel R. Jennings reproduces their list of fragments), T.C. Schmidt, Richard Bauckham, Stephen Carlson, Alexander Roberts & James Donaldson. On the one hand, Papias attributes the tradition to the Elder John so he did not just read it out of 1 Peter 5:13 (though Eusebius mentions that Papias knew 1 Peter and 1 John), but, on the other hand, Mark’s accuracy in faithfully recording the preaching of the Apostle Peter seems to be a way to neutralize the critique of Mark as lacking “order” (τάξις). While the rest of the patristic tradition largely follows Papias on the Mark-Peter connection, there are some interesting developments to consider when comparing the various references to Mark in Justin Martyr (Dialogue with Trypho the Jew 106.3), Irenaeus of Lyons (Against Heresies 3.1.2; cf. Eusebius, E.H. 5.8.2-4), Clement of Alexandria (quoted in Eusebius, E.H. 2.15.1-2; 6.14.5-7; Adumbr. in I Pet. 5.13, the Letter to Theodore [Secret Mark]), Origen (commentary on Matthew, quoted in Eusebius, E.H. 6.25.5), Tertullian (Against Marcion 4.5.3), Epiphanius (Panarion 51.6.10-14a), Jerome (On Illustrious Men 8; Prologue of the Four Gospels), the so-called Anti-Marcionite Prologue, the Monarchian Prologue, Augustine (On the Consensus of the Evangelists 1.6), John Chrysostoam (Homily [1:7] on Matthew). I have listed sites below to look up each individual reference, but I want to leave some questions that call attention to the important differences. For instance, 1) did the evangelist write after Peter’s death (if exodos is a euphemism for death in Irenaeus) or while Peter was still living, 2) if the latter, what was Peter’s attitude towards Mark’s Gospel, 3) is the location of Mark’s writing left unspecified, in Rome, vaguely in the regions of Italy or in Alexandria, Egypt, 4) at whose request or for what purpose did Mark write the Gospel, 5) what is the historical order of the 4 Gospels?
For external evidences, see Stephen Carlson’s Synoptic Problem (on the old site or new site), Ben Smith’s Text Excavations (external evidence to The Four Gospels, the Latin Prologues), Peter Kirby’s Early Christian Writings, the Christian Classics Ethereal Library Early Church Fathers, Kevin Edgecomb’s Patristic Stuff (esp. Dialogue with Trypho), Roger Pearse’s the Tertullian Project, Mahlon Smith’s Synoptic Gospel’s Primer (see Index “Traditional Opinions”)
*My thanks to Nazaroo for preserving my rough notes on Papias from the last blog, though my bibliography on Papias has since grown much larger and some of my opinions have changed from a year ago.