Let's begin. According to the Vilna Gaon (whose Yahrzeit is 19 Tishrei, the day after today's Yahrzeit of Rabbeinu), the books of the Chumash (Note: Chumash is the Gematria of Na Nach Nachma Nachman -354) corresponds to the slated 6,000 years of this world's existance. He notes that the story of Ma'asei Bereishis corresponds to the first 1,000 years, and the remainder of Sefer Bereishis corresponds to the next 1,000 years, Sefer Shemos corresponds to the 3rd millenium, etc. So according to this, Sefer Devorim corresponds to our present and final millenium.
Now, based on the Vilna Gaon's words, each Parsha of Sefer Devorim corresponds to 100 years. For this purpose, the Parshiyos of Nitzovim-Vayeilech, the only Parshiyos of this Sefer that are sometimes combined on Shabbos, count as one Parsha, making a total of 10 Parshiyos for this Sefer. Indeed, this Parsha/Parshiyos corresponds to this century 5701-5800. To note, there are 70 Pesukim in Nitzavim-Vayeilech (40 in Nitzovim & 30 in Vayeilech); and hence, each year corresponds to 0.7th of the Parsha.
With this said, what Posuk corresponds to our year 5772? The 0.7th for this is the 49.8th thru the 50.4th Posuk. In other words, they are the 50th & 51th of the 70th Pesukim. Now, the first of the Pesukim is (Devorim 31:10) - "Moshe commanded them (the Jews) saying: At the end of seven years, at the appointed time of the year of Shemitta on the holiday of Succos".
To briefly explain, this is the Mitzva of Hakhel of the Jews gathering in the Beis HaMikdash every seven years immediately following the year of Shemitta on Succos to hear parts of Sefer Devorim being read by the king. Now, in terms of Moshiach coming, the Talmud Bavli notes that Moshiach will come on Motzoei Shevi'is, the year immediately following the Shemitta year while the Talmud Yerushalmi notes that it will be the Shemitta year itself. Both Talmuds mention their respective statements in connection with the reason as to why the Beracha of Re'eh Na B'Anyeinu about redeeming the Jewish people is the seventh of the Berachos of Shemonei Esrei.
This is all very nice, but this year 5772 fits neither of these categories, and is in fact the middle year of the Shemitta cycle, so how can we prove from here of the possibility of Moshiach coming this year? You see, the letters of this Hebrew year are Hei-Tav-Shin-Ayin-Beis. Now, noting the midst of this Posuk where it says Miketz Sheva Shanim "at the end of seven years", first - the word used for "at the end" is Miketz, instead of Sof or Acharis, as it is related to the word Ketz which is associated with the Geula, and second - the last three letters of this Hebrew year spells Sheva. I saw it explained that while this year may not be a Shemitta year, it is (or may be considered) a Shemitta year in the spiritual worlds (Note: The way that we observe Shemitta nowadays, it is not an unbroken chain of Shemitta observance due to the past destruction of Bayis Rishon. Moreover, unlike in the past, we do not observe Yovel these days, which would otherwise change the year of the Shemitta being observed every 50 years). So, in case anybody thought that they would have a chance to sneak a few Aveiros before Moshiach comes, well, it may not be such a good idea now because if Moshiach comes this year, it will be too late to do Teshuva when he arrives...
Again, this is all very nice, but what does this have to do with Na Nach?
1)This verse concludes with Shnas HaShemitta B'Chag HaSuccos "Year of the Shemitta on the holiday of Succos". The year Shemitta is the Gematria of Na Nach Nachma Nachman - 354, and the word HaSuccos, in this instance (which is not always spelled with the exact same letters) consisting of the letters Hei-Samech-Kaf-Vav-Sav, is the Gematria of Na Nach Nachma Nachman MeUman - 491.
2)Rabbeinu's name begins and ends with a Noon=50, this Posuk is the 50th Posuk of Nitzovim-Vayeilech.
3)Rabbeinu's Yahrzeit is the fourth & middle day of the seven days of Succos, just as Year 5772 is the fourth and middle year of this seven-year Shemitta cycle - and consists of 354 days, just as Na Nach Nach Nachman is the Gematria of 354.
4)This Posuk mentions Moshe Rabbeinu's name, and Rabbeinu's Yahrzeit is also the day of the celebrated Succah guest - Moshe Rabbeinu of the Ushpizin. This may not sound so significant since in the Chumash, Moshe's name is mentioned 646 times, more times than anyone else in the Chumash, but doing the math, his name is mentioned once out of every 11 Pesukim, that is, less than 10% of the Pesukim. Moreover, in connection to the number seven, Moshe is the seventh generation in parental line from Avrohom Ovinu, the first Jew who was also the first to do Hafatza.
5)The 51st Posuk "When all the Jews come to see the face of Hashem your G-d in the place that He will choose, you shall read this Torah in front of all the Jews in their ears" begins with the word Bevo (when they come) - Beis,Veis,Vav,Aleph - which is the Gematria of 11, and as we know, the Petek consists of 51 words and 11 lines. Moreover, Saba's first name Yisroel is mentioned twice in this Posuk.
6)This Mitzva of Hakhel is the 612nd Mitzva of the Torah - the 2nd to the last Mitzva of the Torah, just as the word Bris - the Gematria of 612 - and as referring to Bris Mila, is the 2nd to the first Mitzva of the Torah. This is a most fitting connection to Rabbeinu as he is among the top of the rabbis to promote Shemiras HaBris, and instituted the Tikkun HaKelali as a rectification for Pegam HaBris.
7)Based on the view of those who hold that the reading of the Torah for Hakheil consisted of from the beginning of Sefer Devorim through the first paragraph of the Shema, the second paragraph of the Shema, and then from Aser Teaser (in Parshas Re'eh) through the Tochacha in Parshas Ki Tavo, there are exactly 148 Mitzvos (according to the Rambam and the Sefer Mitzvos Hashem, among other sources), and Rabbeinu's name is the Gematria of 148.
Yes indeed, 5772 -THE YEAR OF NA NACH ON THE HOLIDAY OF NA NACH!!!
P.S. I once read somewhere of parallels between the Petek and a section of Parshas Nitzovim (Devorim 30:11-14), which includes the fact that each consists of 51 words (also noting that Nitzovim is the 51st Parsha). Now, based on the above computations of the Pesukim corresponding to the years, the year 5744 in which Saba received the Haskama from Rabbi Moshe Feinstein ZT"L for the Petek in order to spread Hafatza and Rabbeinu's teachings, corresponds to the 30.2nd thru the 30.8th Posuk of Parshas Nitzovim, in other words, the 31st Posuk - the first of the Pesukim that correspond to the Petek HaGeula!