Eusebius: the Same.

Again, in the same books Clement has set down a tradition which he had received from the elders before him, in regard to the order of the Gospels, to the following effect. He says that the Gospels containing the genealogies were written first, and that the Gospel according to Mark was composed in the following circumstances:--

Peter having preached the word publicly at Rome, and by the Spirit proclaimed the Gospel, those who were present, who were numerous, entreated Mark, inasmuch as he had attended him from an early period, and remembered what had been said, to write down what had been spoken. On his composing the Gospel, he handed it to those who had made the request to him; which coming to Peter's knowledge, he neither hindered nor encouraged. But John, the last of all, seeing that what was corporeal was set forth in the Gospels, on the entreaty of his intimate friends, and inspired by the Spirit, composed a spiritual Gospel.