The Bible says six hundred, threescore and six. Some later translations came up with 666. 616 is totally bogus, but neither work. The actual number is also in the O/T for the number of the talents of gold that came to Solomon (the son of David, BTW) in a year. It's an indication of great wealth. But the underlying number must be expressed in Hebrew numerals which are their letter equivalent: Taw-400 + Resh-200 + Samek-60 + Waw-6. Those letters spell trsw, the the Hebrew word for Tarsus.
There are only 22 letters in the Hebrew alphabet, and these are their corresponding Arabic numerals:
Numeric Values of the Hebrew Alef-bet
'alef =1, bet =2, gimel =3, dalet =4, he =5, waw =6, zayin =7, het =8, tet= 9,
yod =10, kaf =20, lamed =30, mem =40, nun =50, samek =60, `ayin =70, pe =80, sadey=90,
qof =100, resh =200, shin =300, taw =400
Obviously very clumsy, as were Roman numerals and such, which is why the world settled on the Arabic (actually Indian, introduced to the West by an Arab) numeral system. So actually, gematria goes back to ancient Hebrew, it being nothing but adding up the equivalent values of the letters in any name
616 isn't totally bogus. The oldest and best manuscripts we have put the number at 616. It's not six hundred, threescore and six. And the literal reading of the Greek text is 666 or 616. Six hundred sixty six, or six hundred and sixteen. That is literally what the Greek is saying.
To break it down. The number is represented by three words: ἑξακόσιοι ἑξήκοντα ἕξ (as taken from the Novum Testamentum Graece, the Nestle-Aland 27th edition). ἕξ is the Greek for six. And here, we can see that it is the base of the other two words. ἑξακόσιοι is literally, 600, and ἑξήκοντα is literally 60. So the number is six hundred and sixty six. Its no different from six hundred, threescore and six besides I'm using common english right now, and not taking the text from an early translation.
So the Greek language had access to those numbers. And what we are seeing is the Greek use of those numbers. Now the 616 version was known by Irenaeus, but decided against it for whatever reason. However, he also mentions that there were other versions of it as well, stating that they were scribal mistakes. For instance, we also see the number 665. But, we have a fragment from Papyrus 115, which is the oldest text we have of Revelation 13, uses the number 616. We also see its use in the great codices that we have. This has all led scholars to accept that the original number was 616.
As for Tarsus working, I guess if you squint enough. But then what not say Paul of Tarsus? Or Saul of Tarsus? Why not give some indication, in rest of the work, that it is Paul who being talked about? Here you have to take a leap to see it as Paul, as, by your version, we only have the word Tarsus.
We have another option though. We can look at Nero Caesar in Greek. In the Hebrew alphabet, that comes out to נרון קסר, or transliterated, to NRON QSR. Those numbers are 200, 60, 100; 50, 60, 200, 50. That equals 666. We know that Nero was addressed like this because we have scrolls from that time that refer to him in that manner.
What really solidifies this though is that it also works with 616. So taking the Latin version, we drop the second Nun in the title, and it comes out to נרו קסר in Hebrew. Transliterated, it is NRO QSR. Those numbers are 200, 60, 100; 6, 200, 50. That equals 616. Again, we know Nero was addressed in this manner because we have evidence from that time period.
Putting this in context. We are told that the Beast has a mark (the mark of the Beast). Paul never had a mark. Tarsus didn't have a mark. Nero did. So the term used in Greek is χάραγμα. It was also used in regards for imprints on documents or coins, specifically, it is really attested to in regards to an imperial seal that was used in the Roman Empire during that time (1st and 2nd century). Again, another point for Nero. There was even rumors, or legends, that after Nero died, he would return. Or that he wasn't even dead. Nero really fits the mold here.
The mark really takes an effect here as you couldn't buy or sell items in the Roman Empire really without using mark which was on basically every coin in the Empire. For Christians, this was a problem as it required the participation in Roman idolatry. And this really wasn't any small deal. In fact, when the Jews had revolted against Rome, one of the initial things they did was coin their own money.
So what we are really looking at, when taking into the whole context of Revelations, isn't something about Tarsus, or Paul. We are looking at a critique of the Roman Empire. Of the new Babylon. And it's Nero, the Beast, who sits there. Christians or Jews couldn't openly say these things, so they wrote them in code.
As for the gematria topic, I think you missed my point. Jewish gematria wasn't really written down in Jewish texts until somewhere around 200 C.E. But we know that gematria in general goes back before that. So obviously there were predecessors. The same holds true with numerals. You stated that 666 or 616 couldn't have been used because they are Arabic numerals, and that system wasn't event until around 500 C.E. But the fact is, we know that other numeral systems, predecessors, were being used at the time of Jesus and much before that. That's why we can have the number 666 or 616, six hundred and sixty six or six hundred and sixteen, written in the book of Revelations.