Who are the first generation of tannaim?

Question

Of all the known tannaim, how many of them were considered first generation tannaim? This link gives a list of a few first generation tannaim, but I'm sure there should be more in the list, such as Admon ben Gaddai and Hanan ben Avishalom.

But first, how do we define the period of the first generation? Would it be after the deaths of Hillel and Shammai until 80 C.E., or would the period of the first generation be defined differently?

Once we've defined the above, what are the list of names of those who lived during the first generation of Tannaim?

Answer 1

In the Sefer HaDoros HaKotzair it breaks the Tannaim down into their generations. Starting on p.54 here it enumerates the first generation as follows (interestingly it places the zugos before the period of tannaim):

1. Rabban Shimon the son of Hillel HaZakein
2. Rabban Gamliel HaZakein
3. Rabban Yochanan ben Zakai
4. Rabban Shimon ben Gamliel

This was followed by the destruction of the Second Beis Hamikdash (year 3828) during which time also saw the Aseres Harugei Malchus:

4. Rabban Shimon ben Gamliel I (as above)
5. Rabbi Chaninah ben Chachinai
6. Rabbi Yishmael ben Elisha Kohen Gadol
7. Rabbi Akiva ben Yosef
8. Rabbi Yehuda ben Bava
9. Rabbi Chaninah ben Teradyon
10. Rabbi Chutzpis the Turgeman
11. Rabbi Yoshayvev the sofer
12. Rabbi Elazar ben Shamuah (HaKohen) 13 Rabbi Yehuda ben Damah (and some say ben Teimah)

In my edition, the page numbers are slightly different but pages look like this: