Who knows eighty-four?
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84 years passed from Rivkah's premonition/prophecy that her two sons would die on the same day (Gen. 27:45) until it actually came true, when Eisav was killed while trying to prevent Yaakov's burial in the Cave of Machpelah (Sotah 13a).
[Her statement was made in the aftermath of Yaakov's receiving the blessings from Yitzchak, which occurred when he was 63 years old (Rashi to Gen. 28:9); he lived to be 147 (ibid. 47:28).]
The "tikkun" for the sin of wasting seed is to fast 84 fasts.
It is said that one who partakes of the meal at a Pidyon HaBen is considered as if he fasted 84 fasts (presumably because the first two letters of פדיון = eighty-four). The Arizal reportedly said that one who is present in the house where a Pidyon HaBen takes place is considered as having fasted for 84 days.
Legend has it that a talmid of Rav Schach zt"l once missed shiur because he was attending a Pidyon HaBen of a relative. Rav Schach called him to task, and the fellow excused himself by saying that it is so important that it's like fasting 84 fasts. Rav Schach replied that he could accomplish the same by learning Gemara because after all, "daf" (דף) also has the numerical value of 84! (See here, at end.)