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I have recently heard that since the gematria of Va'etchanan is 515, Moshe davened 515 times to enter Eretz Yisrael before Hashem told him he couldn't daven anymore. The reason is that if he would have davened 1 more time, Hashem would have had to let Moshe enter Eretz Yisrael on the 516th time.

Some people say that the reason why Hashem would have had to let Moshe in on the 516th time is that there are 516 hours between the beginning of Rosh Hashanah until the end of Hoshanah Rabbah, so Moshe davened every hour to be let into Eretz Yisrael.

I thought that this made sense, however after doing some math, I realized that Hoshanah Rabbah is the 21st day of Tishrei, and there are only 504 hours in 21 days. So where do they get the extra 12 hours from?

I am asking 2 questions:

  1. I am not sure of the source for this statement so I wanted to know if anyone knows the source since that might help me solve my problem?
  2. Where do the Rabbanan get the extra 12 hours from?
  • I've heard it was because 516 is 6 times the Gematria of Elokim (86). Not sure why 6, though. Apparently the source is Megaleh Amukos, and R' Yonasan Eibshutz in Divrei Yehonasan calculates where 515 tefillos came from. – DonielF Jul 30 '17 at 2:32
  • When you say that you're unsure of the source for this statement, do you mean the source that he davened 515 times, or the source that 516 corresponds to the hours in Tishrei? – DonielF Jul 30 '17 at 2:33
  • @DonielF I am unsure of the source for both – Ploni Almoni Jul 30 '17 at 2:35
  • @DonielF For the article you gave, how can they say that Rosh HaShannah is on Shabbat if there are two days of Rosh HaShannah? – Ploni Almoni Jul 30 '17 at 2:44
  • Nowadays there are two days, since there was no way for the messengers to get anywhere - even inside Israel - to announce the new month. Therefore, we keep two days out of doubt. See further, Beitzah 4b. Back then, when the entirety of the Jewish people lived in one place, that wasn't a concern, and therefore they could have just one day of Rosh HaShanah. That's my assumption of the thinking behind the article, anyway. – DonielF Jul 30 '17 at 3:18
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This is found in the Midrash Aggada (ed. Buber) to Deuteronomy (3:23):

ואתחנן. תקט"ו תפלות עשה על זה הדבר כמנין ואתחנן אעפ"כ לא קבל הקדוש ברוך הוא תפלתו

Vaethanan: He prayed 515 prayers on this, like the numerical value of 'vaethanan' (ואתחנן), but nevertheless God did not accept his prayer.

It is also found in Deuteronomy Rabba (ed. Vilna: 11:10), Yalkut Shim'oni to Parashat Vayelekh (940), and Da'at Z'kenim to Vaethanan (3:23).

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