Papias- He lived around the turn of the second century, probably born around 60 and died somewhere around 139. He is purported to have written extensively, authoring a five volume work entitled Expositions of the Sayings of the Lord. Unfortunately, his works only survive as fragments in later writer's works.

Eusebius (260-340) states in his Chronicle,

Irenaeus and others record that John, the theologian and apostle, survived until the time of Trajan [98-117]. After this Papias of Hierapolis and Polycarp, bishop of Smyrna, both of who had heard him, became well known.

This may appear to be a powerful testimony that the apostle John did indeed live into the second century, until we read from Eusebius' Church History a conflicting and more comprehensive account.

Five books of Papias are in circulation, which are entitled "Expositions of the sayings of the Lord." Irenaeus also mentions these as the only works written by him, saying something like this: "Papias, a man of the early period, who was a hearer of John and a companion of Polycarp, bears witness to these things in writing in the fourth of his books. For there are five books composed by him." So says Irenaeus. Yet Papias himself, in the preface to his discourses, indicates that he was by no means a hearer or eyewitness of the holy apostles, but shows by the language he uses that he received the matters of the faith from those who had known them:

I will not hesitate to set down for you, along with my interpretations, everything I carefully learned then from the elders and carefully remembered, guaranteeing their truth. For unlike most people I did not enjoy those who have a great deal to say, but those who teach the truth. Nor did I enjoy those who recall someone else's commandments, but those who remember the commandments given by the Lord to the faith and proceeding from the truth itself. And if by chance someone who had been a follower of the elders should come my way, I inquired about the words of the elders- what Andrew or Peter said, or Philip, or Thomas or James, or John or Matthew or any other of the Lord's disciples, and whatever Aristion and the elder John, the Lord's disciples, were saying. For I did not think that information from books would profit me as much as information from a living and abiding voice. [3.39.1-4]

So indeed, Papias own testimony is that he did not receive his information from the original disciples, but rather from those who had heard them. Thus, Irenaeus' statement about John the apostle living into the second century must be suspected as being in error. Papias lived and wrote quite some time before Irenaeus, and his word must bear more weight, it would seem. Thus, we find that the best evidence for an apostle living beyond A.D. 70 is really no evidence at all.