The following is based on Rabbi Aryeh Kaplan's understanding of the history as presented in his introduction to: The Torah Anthology - Book of Esther (translation of Yalkut Me'am Loez by Rabbi Aryeh Kaplan). It is based in part on Megila 11b-12a.
Versions of Yirmiyahu's prophecy: (said in 3331 - 460 BCE)
וְהָיְתָה כָּל הָאָרֶץ הַזֹּאת לְחָרְבָּה לְשַׁמָּה וְעָבְדוּ הַגּוֹיִם הָאֵלֶּה אֶת מֶלֶךְ בָּבֶל שִׁבְעִים שָׁנָה.
וְהָיָה כִמְלֹאות שִׁבְעִים שָׁנָה אֶפְקֹד עַל מֶלֶךְ בָּבֶל וְעַל הַגּוֹי הַהוּא נְאֻם יְהֹוָה אֶת עֲוֹנָם וְעַל אֶרֶץ כַּשְׂדִּים וְשַׂמְתִּי אֹתוֹ לְשִׁמְמוֹת עוֹלָם
- And all this land shall become waste [and] desolation, and these nations shall serve the king of Babylon for seventy years. And it shall be at the completion of seventy years, I will visit upon the king of Babylon and upon that nation, says the Lord, their iniquity, and upon the land of the Chaldeans, and I will make it for everlasting desolations. (Yermiyahu 25:11-12)
כִּי כֹה אָמַר יְהֹוָה כִּי לְפִי מְלֹאת לְבָבֶל שִׁבְעִים שָׁנָה אֶפְקֹד אֶתְכֶם וַהֲקִמֹתִי עֲלֵיכֶם אֶת דְּבָרִי הַטּוֹב לְהָשִׁיב אֶתְכֶם אֶל הַמָּקוֹם הַזֶּה
- For so said the Lord: For at the completion of seventy years of Babylon I will remember you, and I will fulfill My good word toward you, to restore you to this place. (Yirmiyahu 29:10)
בִּשְׁנַת אַחַת לְמָלְכוֹ אֲנִי דָּנִיֵּאל בִּינֹתִי בַּסְּפָרִים מִסְפַּר הַשָּׁנִים אֲשֶׁר הָיָה דְבַר יְהֹוָה אֶל יִרְמִיָה הַנָּבִיא לְמַלֹּאות לְחָרְבוֹת יְרוּשָׁלִַם שִׁבְעִים שָׁנָה
In the first year of his reign, I, Daniel, contemplated the calculations, the number of the years that the word of the Lord had come to Jeremiah the prophet, since the destruction of Jerusalem seventy years. (Daniel 9:2)
Possible starting points for the seventy years
- 3319 (442 BCE) - Rise of Babylonian Kingdom (King Nevuchadnetzar)
- 3320 (441 BCE) - Nevuchadnetzar overpowers Jewish King Yehoyakim
- 3321 (440 BCE) - Yermiyahu first predicts the destruction of the Temple (Yirmiyahu 25)
- 3327 (434 BCE) - Nevuchadnetzar exiles Yehoyachin along with the cream of the Jewish people (Malachim Beis 24:14-15)
- 3338 (423 BCE) - Destruction of the First Beis Hamikdosh, Exile of Tzidkiyahu
- 3389 (372 BCE) - Belshatzar understood "seventy years of Babylon" to mean 70 years from the rise of the kingdom. He calculated 70 years from when Nevuchadnetzar became king, made a banquet using the vessels of the Beis Hamikdosh and was killed that night (Daniel 5)
- 3390 (369 BCE) - Daniel calculated seventy years from when Nevuchadnetzar overpowered Yehoyakim. When he saw that the time was nearly up and no redemption was in sight he thought the Jewish peoples sins had caused the delay and began to pray and fast. The angel Gavriel appeared to him and explained his miscalculation (Daniel chapter 9).
- 3391 (370 BCE) - Koresh calculated 70 years from Yirmiyahu's prophecy, and orders the rebuilding of the Beis Hamikdosh. However this was not a full-fledged redemption but rather only Hashem "remembering" His people (Megila 12a), since it was 70 years from the exile of Bavel (as recorded in Yirmiyahu), not 70 years from the destruction of Yerushalayim (as recorded in Daniel). Few Jews answered this call and the building was halted shortly after when Achashverosh became king.
- 3395 (366 BCE) - Achashverosh understood "seventy years of Babylon" to mean 70 years from the exile of the kingdom. He calculated 70 years from the exile of Yehoyachin; one of the reasons for the feast 3 years into his rule (Esther 1:3) [considered 70 years because parts of the years where multiple kings reigned were counted extra]
- 3408 (353 BCE) - The final calculation - 70 years after the actual destruction of the Beis Hamikdosh, Daryavesh II allowed them to rebuild it (Ezra 4:24, see Rashi)
With the above timeline in mind, the GR"A, in a note on Seder Olam Rabbah, explains that there were three 70 year periods.
Period 1: Rise of Nevuchadnetzar until the fall of the Babylonian Empire with Belshatzar's death.
Period 2: From the Overpowering of King Yehoyachin until the "remembering of the Jewish People, when Koresh gave permission to start rebuilding the Beit Hamikdash.
Period 3: From the Destruction of the Holy Temple until the Rebuilding of Jerusalem.