Moshe davening 515 times to enter Eretz Yisrael

Question

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?

Answer 1

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).

Answer 2

In answer to your 2nd question, the following is taken from the Weekly Parsha titled "From the Orchards of Jerusalem" by Daneal Weiner:

When would have been the most appropriate time for Moshe to pray for entrance to Erets Yisrael? That would have been the last Rosh Hashanah (R"H) he experienced. Moshe knows that B"Y is going in to E'Y and he doesn't want to die before that happens. R"H is when the book of life is inscribed. Not all fates, however, are sealed on R"H. Some remain pending till Yom Kippur (Y"K). That is what the 10 days of Tshuva are all about. But Y"K is not the final final either.

The world is judged on Shmini Atseret which is the last day of Sukkos. (On Sukkos 70 sacrifices are brought on behalf of the 70 nations.) If G-d really wants to give a Yid a chance He waits till Shmini Atseres for signs of improvement. Shmini Atseres is always the 22nd day of Tishrei. Take a wild guess how many hours there are between Erev Rosh Hashana and just before the crack of dawn, Shmini Atseret??

If your answer was close to 515 then you were close! The answer is 515. Remember that a day starts the evening before so the crack of dawn would be half way thru the 22nd day. 21.5 x 24 = 516. Moshe Rabbeinu prayed every single hour from Rosh Hashanah till almost half way thru Shmini Atseres! Why stop short of half way? Good question! My guess would be that .5 rounds up to the whole.