Evidence: The Gathering

[TheRocketSurgeon]

Notice the date of Tacitus' birth; he would have been about 39 years old at the time that the last living apostle John wrote his gospel in AD 95. The immediate successors of the apostles - people like Clement of Rome, Polycarp of Smyrna, Ignatius of Antioch - were all still alive at the time that Tacitus was in Rome and gathering the data that later formed his two works of history. Clement of Rome, for example, was a disciple of Peter and Paul, and he was in Rome (and pope) until his death in AD 99. So, that's not "three whole generations" from Jesus to Tacitus. Peter taught Clement, and Tacitus was in Rome at the same time that Clement was head of the Church in that city.

Jesus --> Peter --> Clement

Randy, Randy... Do you know how many people, at that time, claimed to have been disciples of the original disciples?
Do you know how many texts were in circulation claiming to have been written by one of those original apostles?
Do you know why they didn't all survive the biblical editing?

For all we know, Clement merely claimed to have gathered info from Peter to boost his credibility with his audience.
Of course, even then, it is relevant in the fact that there were people who were followers of the christ figure all the way in Rome, so that this Clement could have someone to whom pass that message.
The existence of followers of the christian cult in Rome is quite odd at such an early stage of the cult... either there was a sort of mass migration from the middle-east to Europe , or those few christians that did go to Rome on business or leisure had a great rhetoric that convinced the pagans.
Still, it's not much evidence for the existence of the Jesus fellow... just evidence for the existence of followers of the message allegedly brought forth by him.

Now, you may claim that John was still around, but you'll quickly find that the account in the bible attributed to John is widely agreed by the experts to not have been written by the apostle John.... just another phony... which makes one wonder at the accuracy of its contents.

I think it's pretty clear from the writings of Tacitus that the people he was interviewing for his report were Christians about to be martyred in Rome. That doesn't necessarily mean they lived in Rome. It does mean that their testimonies given at trial (which Tacitus mentions) are likely to include the full mythology of their young religion-- from the Crucifixion to the trial by Pilate. 

Several of the historians who look at those writings fail to account for the simple expedient of interviewing the condemned and/or reading from transcripts of the trials (which Senator Tacitus, especially, as a member of a council that kept track of heretical cults, would have had access to in both cases), and instead presume without evidence that Tacitus was operating from official Roman records about Pilate, since it was Tacitus' usual method to use documentation when available. But he gives no evidence in that chapter that such is the basis for his writings about the Christians; the only documents he references in that passage are the accounts given by "both" sides as to why Nero was burning the city, since some said Nero did it to distract from other problems and tried to blame the Christians in Rome for it... even Tacitus writes as though that idea is silly, however.

But at no point does Tacitus give a clear indication of an historical Jesus, only of secondhand accounts which are as likely to come from the Christians themselves as from any sort of records (which, given Tacitus' tendency to mention his records, when in use, seems to be less likely).