I remember seeing an early authoritative source (Rishonim, maybe a Tosfos?) that noted which numbers are always (technically not always) used by the Rabbis to indicate exaggeration in stories (60, 300, etc.), but I don't remember where I saw it. So I pose the question:
What is the earliest source you can find that identifies certain numbers as being used by Chazal as hyperbole (not just in a situation or two, but systematically), and which numbers are they?
Maharsha in Bechoros Daf 57b quotes a Tosfos not sure where the Tosfos is.
וטבעה ס' כרכים כו' גוזמא קאמר כמ"ש התוספות בכמה דוכתי דמנין ס' בכל מקום לאו דוקא
As noted in this answer by Moshe Steinberg, Rashbam on Pesachim 119a writes that three hundred is always used as an inexact number throughout the Talmud.
13 is also an exaggeration throughout the Talmud according to Rashi in Shabbos 119a, quoting Rabbeinu Halevi
תליסר גמלי - גוזמא בעלמא הוא. כך פירש רבינו הלוי וכן בכל מקום
Although in a corresponding Rashi in Chullin 95b, some have the text תריסר, which is twelve
This idea can also be found in Tosfos Berachos 20a תליסר:
ותליסר לאו דוקא, אלא לשון הרגיל בגמ' כמו 'תליסר (חולין דף מד:) זוזי פשיטי'.
13 is used commonly by the gemara but is lav davka.
See Mevo Hatalmud by R. Tzvi Hirsch Chajes (perek #30) who brings several sources stating that many numbers are hyperbolic.
The earliest source is probably Chullin 90b. While not systematic, I think it is relevant:
אמר ר' יצחק בר נחמני אמר שמואל בשלשה מקומות דברו חכמים לשון הואי אלו הן תפוח גפן ופרוכת תפוח הא דאמרן גפן דתנן גפן של זהב היתה עומדת על פתחו של היכל ומודלה על גבי כלונסות וכל מי שהיה מתנדב גרגיר או אשכול מביא ותולה בה אמר רבי אלעזר ברבי צדוק מעשה היה ונמנו עליה שלש מאות כהנים לפנותה פרוכת דתנן רבן שמעון בן גמליאל אומר משום רבי שמעון הסגן פרוכת עוביה טפח ועל שבעים ושנים נירים נארגת ועל כל נימה ונימה עשרים וארבעה חוטין ארכה ארבעים באמה ורחבה עשרים באמה ומשמונים ושתי רבוא נעשת ושתים עושים בשנה ושלש מאות כהנים מטבילין אותה:
Rabbi Yitzḥak bar Naḥmani says that Shmuel says: In three places the Sages spoke in exaggerated language, and they are with regard to the circular mound of ashes on the altar; the vine; and the Curtain separating the Sanctuary and Holy of Holies. The case of the circular mound of ashes is that which we said.
The case of the vine is as we learned in a mishna (Middot 36a): A golden ornament in the form of a vine was standing at the entrance to the Sanctuary, and it was hung upon poles. And whoever would donate an ornamental golden leaf, grape, or cluster of grapes to the Temple would bring it to the Temple and hang it upon the vine. Rabbi Elazar, son of Rabbi Tzadok, said: There was once an incident, and three hundred priests were enlisted to move the vine because of its immense weight. According to Shmuel, this description is also an exaggeration.
The case of the Curtain is as we learned in a mishna (Shekalim 8:2): Rabban Shimon ben Gamliel says in the name of Rabbi Shimon, the deputy High Priest: The Curtain is the thickness of a handbreadth [tefaḥ]. It is woven from seventy-two strands [nirim] of yarn, and each and every strand [nima] of those seventy-two is made from twenty-four threads consisting of six threads each of sky-blue wool, purple wool, scarlet wool, and fine linen. Its length is forty cubits, the height of the Sanctuary, and its width is twenty cubits, the width of the entrance. And it is made from eighty-two ten-thousands, i.e., 820,000 dinars. And the overseers of the Temple make two new Curtains every year. And the Curtain was so heavy that when it was immersed, three hundred priests would immerse it.
