I did not say that none were first-hand accounts, just to set the record straight. But, more to the point, if it is Mark's gospel, then it isn't Peter's account. It is Mark reporting of Peter's account. So that makes it, at the least, a second-hand account.
.Ten different appearances of our risen Lord are recorded in the New Testament. They may be arranged as follows:
To Mary Magdalene at the sepulchre alone. This is recorded at length only by John (20:11-18), and alluded to by Mark (16:9-11).
To certain women, "the other Mary," Salome, Joanna, and others, as they returned from the sepulchre. Matthew (28:1-10) alone gives an account of this. (Comp. Mark 16:1-8, and Luke 24:1-11.)
To Simon Peter alone on the day of the resurrection. (See Luke 24:34; 1 Cor. 15:5.)
To the two disciples on the way to Emmaus on the day of the resurrection, recorded fully only by Luke (24:13-35. Comp. Mark 16:12, 13).
To the ten disciples (Thomas being absent) and others "with them," at Jerusalem on the evening of the resurrection day. One of the evangelists gives an account of this appearance, John (20:19-24).
To the disciples again (Thomas being present) at Jerusalem (Mark 16:14-18; Luke 24:33-40; John 20:26-28. See also 1 Cor. 15:5).
To the disciples when fishing at the Sea of Galilee. Of this appearance also John (21:1-23) alone gives an account. To the eleven, and above 500 brethren at once, at an appointed place in Galilee (1 Cor. 15:6; comp. Matt. 28:16-20).
To James, but under what circumstances we are not informed (1 Cor. 15:7).
To the apostles immediately before the ascension. They accompanied him from Jerusalem to Mount Olivet, and there they saw him ascend "till a cloud received him out of their sight" (Mark 16:19; Luke 24:50-52; Acts 1:4-10).