No gospel at all bothers to tell us about this important appearance to Peter, which Paul puts at the head of his list (I Corinthians 15:3ff.) with the one to himself last.
Luke tells us Peter finds no body in the tomb on the first day of the week, but by the end of this same day Peter is matter of factly said to have had his own encounter with the risen Jesus distinct from an appearance to the eleven, which quickly follows in its turn, as does Jesus' ascension into heaven. There is no appearance to Mary at the tomb, and instead of an appearance in and ascension from Galilee as in Matthew Luke has all this in the vicinity of Jerusalem.
The compression of events by Luke is noteworthy for its similarity to the summary quality of the other accounts. It's almost as if there is a felt need of discomfort by all to get the story over with as quickly as possible. Perhaps because it's so uncertain?
Then arose Peter, and ran unto the sepulchre; and stooping down, he beheld the linen clothes laid by themselves, and departed, wondering in himself at that which was come to pass. ... And certain of them which were with us [the Emmaus travelers] went to the sepulchre, and found it even so as the women had said: but him they saw not. ... And they [the Emmaus travelers] rose up the same hour, and returned to Jerusalem, and found the eleven gathered together, and them that were with them, [who said], The Lord is risen indeed, and hath appeared to Simon.
-- Luke 24:12, 24, 33-34
