It is worth noting that cultures around the ancient world, from Rome to China, acribed great lengths of years to important figures, legendary, mythological, or historical. The most extreme cases can be found in Jainism, where the Tirthankaras are given ages of tends or even hundreds of thousands of years. In China Fu Xi, the first of the Three Sovereigns who Chinese mythology says laid the foundation for Chinese civilization is said to have lived several hundred years. In Greece and Rome Tiresias the seer lived over 600 years.
You have made an error here. Tiresias is not claimed to have lived over 600 years. This is a mistake I have seen floating around the internet, because people never check primary sources.
It comes from the Macrobii, a work assumed to be by Lucian, meaning the Long-Lived:
"Likewise Tereisias the seer outlasted six generations, tragedy says: and one may well believe that a man consecrated to the gods, following a simpler diet, lives very long."
Notice he says six generations, not 600 years. Now where that comes from, is from the Saeculum. This is a length of about a 100 years, a specific division of time of the Romans, for the maximum presumed length of a man's life. The idea being, that a person born in the previous Saeculum, would be dead before the next, so every man can only experience one Saecular Games in their lifetime - a religious festival held about every hundred years or so.
So someone at some point read 'six generations' and assumed the maximum a Roman would consider a generation would be a hundred, hence 600 years. It is an erudite, but frankly foolish, mistake.
For the generations don't start after the previous finished, but run concurrently. A son is the next generation after his father. The Romans had a boy set aside the Toga Praetexta at 14, and enter into manhood by donning the Toga Virilis. This would be the next generation in Roman eyes.
For ease of calculation, let's say 20 years for a generation about, so the final generation that is 'outlasted' by Tiresias would start at about 100 years, and enter manhood when Tiresias is 120. If we take a saeculum as the maximum possible length of a generation, then at most, Tiresias is said to be 200 years.
Lucian is likely refering to the Greek plays though, where Tiresias is often used as a sort-of stock seer for Thebes. These are the tragedies he is refering to, often ending with the eradication of the blood-lines, the end of the generations therefore. So Tiresias is said to have outlasted 'six generations': these are the Theban kings Cadmus, then Pentheus, then Laius, then Oedipus, then his sons Eteocles and Polynices, and finally Eteocles' son Laodamas, who dies by the hand of the Epigoni. So if you take the full cycle of plays of Theban history, we are looking at about 120-130 years for Tiresias, outlasting the six generations of the dynasty of Cadmus at Thebes.
The Macrobii does mention people of Seres (likely China) and Chaldeans (Babylonians), living 300 years or more - but these are refering to the claims of longevity made by them. Nestor is also said to 'survive three generations', which of course, does not mean 300 years. No Greek or Roman source claims ridiculously long ages for heroes or such. They have long, but humanly possible, lifespans; or become gods, at which point 'lifespan' becomes moot.
