At the beginning of
the post it says that
the number 127 is the
7th Mersenne Prime, a
special class of primes.
The number 127 is
also part of a special
series of primes: 127 is
the 31st prime, with in
turn 31 also being a
prime, the 11th prime,
and 11 is also a prime,
the 5th prime, and 5 the
3rd prime, 3 the 2nd
prime, and 2 the 1st
prime.
It is interesting
that the 127th prime is
709, which is the next
prime after the number
704 that you discuss in
the post, and 709 = 704
+ 5.
Also interesting is
that 704 = 11 x 64,
which resonates with
more numbers in the
post, and also 704 is a
reflection of 407,
another number discussed
in the post, and
together 704 + 407 =
1111.
It turns out that the
number 1111 can be
represented as Elef plus
Alef, 1000 + 111, and
also 1111 is a
semi-prime, 1111 = 11 x
101, with 11 being the
5th prime and 101 being
the 26th prime. Also in
small gematria both 704
and 407 reduce to 7 + 4
= 11. (And it is
interesting that in
Yiddish the word עלף,
pronounce “Elef,” means
“eleven,” the number
11….)
That’s all for now,
Good Shabbos!
Shabbat
Shalom! Thank
you for those
comments. I with
I would have
caught that
prime series
myself which
gives us
Moshiach 358.
Amazing catch! I
am going to add
it to the very
next
section-most
grateful. BTW,
709 is the sum
of the letters
controlling the
7 planets
according to the
Sefer
Yetzirah.
Ezra, thanks for your reply to my comment, and for saying you will include an idea from it in your next post.
At first I didn’t see the connection of the number 127 to Moshiach, gematria 358, but upon reflection I found that the sum of series of the 6 primes 127 + 31 + 11 + 5 + 3 + 2 = 179, and the number 179 is also a special prime, part of a series of primes, since 179 is the 41st prime, with 41 being the 13th prime, and 13 being the 6th prime.
The gematria of Moshiach, 358, is a semi-prime, with 1 factor being 2, the 1st prime, and 1 factor being 179, the 41st prime (as just said), and doubling 179 (with the concept of doubling being related to the splitting of the Alef Beis into matching sections, 11 + 11 = 22, or 2 x 11 = 22) gives 179 + 179 = 358, and 2 x 179 = 358, and therefore 127, resonating with 179, the additive sum of its related primes, when doubled or paired is 358, a hint to Moshiach (and the idea of doubling also a key aspect of Moshiach’s mission, as explained in many places).
There is also another hint to Name of 42 that is evident from the number 358 for Moshiach, since the ordinal numbers of the component primes factors of 358, i.e., the ordinal numbers of the primes 2 and 179, are respectively 1 and 41 (since 2 is the 1st prime and 179 is the 41st prime), and this yields the sum 1 + 41 = 42, hinting to the Name of 42 which is an inner spiritual force inside Moshiach that he will reveal to the world.
There are probably many other ways as well to see further indications of Hashem’s explicit Divine providence in these numbers and their relationships, in the roots of mathematics, in science, and of course in the Torah, and to understand that it is all one, since it all stems from the One Hashem.
———-
While on the subject, the sums of the intermediate numbers in the prime series culminating in 127 that sum to 179 are also significant in their own right:
Combining the first 2 primes in the series, 2 + 3 = 5, corresponding to the 5 Books of the Torah.
Combining the first 3 primes, 2 + 3 + 5 = 10, corresponding to the 10 Commandments, the 10 Sayings, and the 10 Sefiros.
Combining the first 4 primes, 2 + 3 + 5 + 11 = 21, which is the gematria of the Divine Name Ekeyeh, and also the first three letters Yud Heh Vov, 10 + 5 + 6 = 21, of the Name Hashem.
Combining the first 5 primes, 2 + 3 + 5 + 11 + 31 = 52, corresponding to 52 = 2 x 26, i.e., the doubling of the full Name Hashem, and also corresponding to the Name of 52, one of the four ways of fully spelling out the 4 letters Yud Heh Vov and Heh of Hashem.
Somewhat similarly for the series of primes culminating in 179:
Combining the first 2 numbers in this series, 6 + 13 = 19, and 19 (like 179, 41, and 13, but not like 6) is itself also a prime, the 8th prime, and 6 + 13 also hints to 6-13, i.e., the 613 Mitzvos, and in small gematria 6 + 1 + 3 = 10, and reduces to 1, representing the 10 Commandments and that Hashem is Echod/One.
Combining the first 3 numbers in this series, 6 + 13 + 41 = 60, which 60 = 4 x 15, with 15 being the gematria of the Name Kah, Yud Keh, corresponding to a double doubling of this Divine Name, and 60 also corresponds to the 60 letters of the Birchas Kohanim, and to the 6 Orders of Mishnah, and to the 60 Tractates of Talmud, and to the 600,000 souls of Israel. If only the primes in the series are counted, then combining 13 + 41 = 54, the special number Ezra discussed in the blog post.
———-
In the post it was pointed out that the number 127 is a Mersenne prime, and to provide a bit more relevant background, Wiki explains (and see there for more) that “Mersenne primes, of the form (2 ^n) – 1, are the primes 3, 7, 31, 127, 8191, 131071, 524287, 2147483647, 2305843009213693951, 618970019642690137449562111, 162259276829213363391578010288127, 170141183460469231731687303715884105727 …, and as of 2018, there are 51 known Mersenne primes, and the 13th, 14th, and 51st have respectively 157, 183, and 24,862,048 digits. As of 2018, this class of prime numbers also contains the largest known prime: M-subscript 82589933, the 51st known Mersenne prime.”
Regarding the Wiki entry for the number 127, the first thing noted about it is that it is a Mersenne prime:
“As a Mersenne prime, 127 is related to the perfect number 8128. 127 is also an exponent for another Mersenne prime 2127 – 1, which was discovered by Édouard Lucas in 1876, and held the record for the largest known prime for 75 years – it is the largest prime ever discovered by hand calculations, as well as the largest known double Mersenne prime. Furthermore, 127 is equal to 2^7 – 1, and 7 is equal to 2^3 – 1, and 3 is the smallest Mersenne prime, this makes 7 the smallest double Mersenne prime and 127 the smallest triple Mersenne prime.”
Among various other special properties of 127, Wiki also mentions that 127 is a centered hexagonal number, which Ezra has discussed in his posts, and of special interest it states that 127 is the first “nice Friedman number” in base 10, since 127 = -1 + 2^7, as well as binary since 1111111 = (1 + 1)^111 – 1 * 1 (see Wiki for details; as far as I know I’m unrelated to mathematician namesake).
Unmentioned in Wiki’s entry on the number 127 is that it is also in the category of a “super prime.”
Super primes are one of 75 subcategories of primes that Wiki describes on its “List of prime numbers” page. Incidentally, the first of these alphabetically arranged subcategories of primes are “Bell primes,” and coincidentally we are also currently discussing Bell numbers here).
According to Wiki, “Super-prime numbers (also known as higher-order primes or prime-indexed primes) are the subsequence of prime numbers that occupy prime-numbered positions within the sequence of all prime numbers. The subsequence begins 3, 5, 11, 17, 31, 41, 59, 67, 83, 109, 127, 157, 179, 191, 211, 241, 277, 283, 331, 353, 367, 401, 431, 461, 509, 547, 563, 587, 599, 617, 709, 739, 773, 797, 859, 877, 919, 967, 991…”
———-
It comes out, that what I wrote about in my previous comment – “127 is part of a special series of primes: 127 is the 31st prime, with in turn 31 also being a prime, the 11th prime, and 11 is also a prime, the 5th prime, and 5 the 3rd prime, 3 the 2nd prime, and 2 the 1st prime” (and similarly in a my past comments with other examples of prime numbers is related series) – that these special primes are considered to be “super primes” (with the exception of 2, since its prime-numbered position is 1, and technically 1 is not included as a prime).
Even more, the super primes we have discussed are part of a series of super primes, and in this case, the series of super primes related to the super prime 127 is unique in that the series starts with 2, the 1st prime, making it what might be called an initial, primary, or origin-based series super prime. (I have not had time to investigate if these categories of super primes have been discussed as of yet in Wiki or elsewhere.)
The first 15 numbers in the origin based series of super primes that I have calculated with the help of online programs are: 2, 3, 5, 11, 31, 127, 709, 5381, 52711, 648391, 9737333, 174440041, 3657500101, 88362852307, 2428095424619, and so on.
In contrast, the super prime 179 – aside from being the sum of the 6 super primes in the series 2 through 127 – is also, together with (6) and 13, and 41, a part of a series of super primes, only the series it belongs to does not start from the 1st prime, or from any prime number, but rather from 6, which is only a semi-prime, the product of 2 x 3.
It is significant that in its entry on 127, Wiki includes the idea that the Torah mentions the number 127 prominently in connection with the 127 years of the life of Sarah, and the 127 countries ruled over by Achashveirosh and by Queen Esther, and these have been discussed before in this blog and in the comments as well.
———-
Another fascinating aspect of the number 127 is that 101 is the 26th prime, and 101 + 26 = 127, and this illustrates yet another connection to the Name Hashem, gematria 26.
This is an example of another special series of numbers that can be generated from primes, where the rule is to sum the primes themselves with the ordinal number of their position in the set of primes (I do not know if this series of prime-based numbers has been previously discussed or classified).
Calculating this rule for the first 11 primes generates the following numbers: (2 + 1 =) 3; (3 + 2 =) 5; (5 + 3 =) 8; (7 + 4 =) 11; (11 + 5 =) 16; (13 + 6 =) 19; (17 + 7 =) 24; (19 + 8 =) 27; (23 + 9 =) 32; (29 + 10 =) 39; and (31+ 11 =) 42.
It is fascinating to see that the first 3 numbers in this series are 3, 5, 8, and like the numbers at the beginning of the Phi number series that was discussed in past posts, this is another hint to the number 358, the gematria of Moshiach.
The following is a list of such numbers I generated through the 101st prime. In each equation the first number is the regular prime number, the second number added to it is its index or ordinal number in the set of primes, and the third number is the sum of the first two, the composite number of the prime number and its ordinal number in the set of primes. It is relatively easy to spot many significant numbers that are thus generated.
For clarity the prime ordinal numbers are highlighted, and likewise for comparison the primes among the composite numbers (using the * sign as highlighting for this version). The special primes generated this way are: 3, 5, 11, 19, 79, 101, 113, 127, 163, 173, 223, 271, 383, 419, 431, 503, 571, 599, 641…:
In total this list has 101 primes, with 26 primes in the prime ordinal index, and 19 primes in the composite sums.
The opening note about this was that 101 + 26 = 127. A closing note for now is that together with 19 for the number of thus generated primes, 127 + 19 = 146, a semi-prime with factors 2 x 73, with 2 being the 1st prime and 73 being the 21st prime, and adding 1 + 21 = 22, perhaps hinting to the 22 letters, which in Hebrew the letters also function as numbers.
[For further reference the next 26 primes (prime ordinal numbers 102-127) are: 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, and 709.]
My above (May 27) comment ended parenthetically, “For further reference the next 26 primes (prime ordinal numbers 102-127) are: 547, 557… 709.”
Correction: Prime number 547, with prime ordinal number 101, was already included in the last line of the summation table, 547 + 101* = 648. The extra reference should have begun with the 102nd prime, 557.
Since by Hashgacha Protis this focuses attention on the prime 557, here it is fitting to add that 557 + 102 = 659, and 659 is also a prime, the 120th prime. The prime ordinal number 120 has multifaceted significance and seems to resonate with the associated prime ordinal number 102.
Interestingly 659 + 120 = 779, and since 659 and its associated prime 557 have multiple 5’s, it seems we can join the idea of at least of these 5’s to 779 and get 5779, our current special Hebrew calendar year, a year of Moshiach, and as I pointed out in a previous comment, 5779 is also prime, the 758th prime.
[Just for fun, the sum of the primes 547 + 557 = 1104, the sum of their ordinal numbers 101 + 102 = 203 (the gematria of the first 3 letters of the Torah, Beis Reish Alef, and the 6th Bell Number, now being discussed in the blog), and the sum of 648 + 659 = 1307 (the 234th prime).]
While this post starts with discussion concerning the first verse of the Torah, with its 7 words and 28 letters, it is also important to realize and bear in mind, especially now as we prepare for the upcoming holiday of Shevuos celebrating the giving of the Torah, that in the Kabbalah Secrets discourse on “The 10 Commandments” and elsewhere it is explained that:
The verse that immediately precedes and introduces the 10 Utterances, Exodus 20:1, וידבר א-ל-ה-י-ם את כל הדברים האלה לאמר, “God spoke all these words, saying:” has 7 words and 28 letters, just like the Torah’s first verse.
Is seems very far fetched to think that this is just a “coincidence,” and most certainly there is exceptional Divine Providence and Planning involved, especially since the Divine Name Elokim occurs in each of these special verses, and as our sages teach in many places there there is a direct link between the “10 Sayings” that created the world and the “10 Commandments.” There are many aspects of this connection that have already been revealed, and they should be reviewed as much as possible, and probably there are much more interrelated ideas that are still to be revealed.
[Also as a reminder, as explained in a previous comment, this year will be the 3331rd anniversary of Matan Torah, and 3331 is a prime number, the 470th prime.]
Many thanks for this, Moshe. I’m sure there is a lot in this verse w/2 of the words and thus 7 of the letters the same as Bereshit 1:1
Ezra, it is your revelations in “The 10 Commandments” (linked on the sidebar) and in general that deserve the most thanks! There are so many amazing and stunning ideas you have shared, some of them astonishingly complex, that I’m still only beginning to scratch the surface of.
The correspondence between the Torah’s first verse, Breishis Bora Elokim Eis Ha’shomayim V’eis Ho’oretz, and the first verse of the 10 Commandments (Utterances), Vayedaber Elokim Eis Kol Hadevorim Ho’eileh Leimor, each with the exact same count of 7 words and 28 letters, is a relatively simple concept to grasp, and it is probably deserving of another post in and of itself, together with many other basic correspondences that are evident interconnecting the Torah’s account of Hashem’s Creation of the world and the Torah’s account of Hashem’s giving of the Commandments that could be explained.
———-
Here let me just add for now that the number 7 is a prime number, the 4th prime, and 7 x 4 = 28, and thus the average word size for each of these primary verses is exactly 4 letters long, perhaps hinting to the Tetragammaton, the special 4 letter Name of Hashem.
The sum of 7 + 28 = 35, which is the same as 7 x 5, and 5 too is a prime number, in fact it is a super prime, since it is the 3rd prime, and 3 is likewise prime, the 2nd prime, and 2 is likewise prime, the 1st prime, and thus 5 is not just a super prime, it is part of a series of super primes.
When 7 and 28 are doubled, by combining these 2 primary verses, then the respective sums of words and letters are 14 and 56, which sum to 14 + 56 = 70, and 70 is the same as 7 x 10, with 10 being 2 x 5.
It is possible to say that these numbers hint to the Two Tablets of the Covenant with the 10 Utterances divided into 5 Utterances on each Tablet. The First Tablet lists Utterances that stress the relationship between man and G-d, which in general expresses the theme of the Giving of the Torah on Mt. Sinai, i.e., between man and G-d, while the Second Tablet lists Utterances that stress the relationship between man and his fellow man, which in general expresses the theme of the Creation, i.e., and how man should interact with humanity and with his fellow creations .
———-
Last year the number 70 was emphasized, since it was the 70th year since the rebirth of the modern state of Israel. The number 70 as just explained hints to the completion of these two principle verses of the Torah, and surely the idea of this completion continues this year.
In addition, this year is the 71st year, and it is interesting to note that like the numbers 5779 (the 758th prime) and 3331 (the 470th prime) mentioned above, the number 71 is also a prime, the 20th prime.
Yesterday was Yom Yerushalayim, Jerusalem Day, and just to add something about that, the commemoration of the unification of the Holy City under Jewish control in 1967/5727, and when the Temple Mount returned to our hands:
It is interesting that the number 1967 has one digit that is a 7, and the digits 1 and 6 can be combined to make another 7. Also 1967, although not prime, is a semi-prime, the product of 7 x 281 = 1967, and that resonates with the idea of 7 words and 28 letters, since 281 is 28 x 10, plus 1 for the Kolel [It is also interesting that 281 is the 60th prime.].
Incidentally 1967 may be viewed as 19-67, and 19 is prime, the 8th prime, and 67 is prime, the 19th prime, and thus 67 is a super prime, since its prime ordinal number 19 is itself prime, the 8th prime, and the sum of these prime ordinal numbers 19 + 8 = 27, and with 1 for the Kolel equals 28.
The number 5727 has two digits that are 7, and the other two digits 5 and 2 also sum to 7, for a total of 3 x 7. [The number 5727 is non-prime, having prime factors of 3 x 23 x 83 = 5727, and these 3 primes sum to 3 + 23 + 83 = 109, which 109 is a prime, the 29th prime.]
It is possible to take the 2 x 7 in 1967 and the 3 x 7 in 5727, and sum them to 5 x 7 = 35, which is the same as the sum of 7 + 28 = 35, as explained above, and therefore these years when Jerusalem was unified also hint to both the first verse about Creation and the first verse about the Giving of the Torah.
This year we celebrate the 52nd anniversary of the return of Jerusalem to Jewish sovereignty. It is possible to say that the small gematria of 52 is 5 + 2 = 7, resonating with the idea of 70 years, and the 7 words in the two primary verses discussed. Also 52 = 4 x 13, hinting to the completeness of the unification (Echod, One, gematria 13) on 4 levels, corresponding to the 4 letters of Hashem’s Name, and also 52 = 2 x 26, i.e., a double hint to the Name Hashem gematria 26, and perhaps hinting to a fulfillment of Hashem’s plan both in the Creation and in the Giving of the Torah.
Kein Teyeh Lonu, Bimharo B’yomeinu!
Thank you. I’ll finish reading and give your comments the attention they deserve first chance I get. Meanwhile, I noticed, 5779 + 3331 = 9110
Every connection we make leads to several more…
Regarding 9110, it is 10 times 911, the gematria of the word ראשית, Reishis, “Beginning” (as in B’reishis, “In the Beginning” at the start of the Torah), and it is the 156th prime, and together with 71, the sum is 5779 + 3331 + 71 = 9181, which is also a prime, the 1138th prime. Again all these numbers lead to further connections…
———-
Regarding Yom Yerusholayim, it may be added that it is celebrated on the 28th of the Hebrew month of Iyar, and the date 28 corresponds to the 28 letters in each of the two first verses Breishis Bora and Vayedaber Elokim.
Also the 28th of Iyar is the 43rd day of the Omer, and the number 43 is prime, the 14th prime, with the prime ordinal number 14 corresponding to the 2 x 7 = 14 words in these two first verses when added together, and with 14 also being the gematria of דוד, Dovid, King of Israel, who conquered Jerusalem and set it as our eternal capital.
Also the sum of 28 + 43 = 71, bringing out a special resonance of Yom Yerusholayim unique to this year, the 71st year since the reestablishment of the state of Israel.
———-
Just one more brief related teaser. It is possible to connect the first verse of Shma with the first verse of Breishis and the first verse of Matan Torah, i.e., with 7 words and 28 letters:
The verse שמע ישראל יקוק אלקינו יקוק אחד, Shma Yisroel Hashem Elokeinu Hashem Echod, Hear O Israel Hashem our G-d Hashem is One, consists of 6 words and 25 letters, and to this we may combine 1 more word of 3 letters to sum to 7 words and 28 letters. This may be done in any one of several ways:
By adding the 3 letter word אמן, Amen, that may be said just before the Shma in answer to the blessing before the Shma said out loud by the Chazan, and also the initials of א-ל מלך נאמן, Kel Melech Ne’emon, “G-d, King, Who is trustworthy,” customarily recited by some just before the Shma.
By adding the 3 letter word אמת, Emes, “True,” which is a word said immediately after the 3 paragraphs of Shma.
Or by adding the 3 letter word and Divine Name ש-ד-י, Sha’da’i, which as I explained at length in previous comments is intimately connected with the Shma.
Note too that our sages connected the 10 Commandments to various hints in the Shma, and Bli Neder this will be explained further at another time.
At the beginning of the post it says that the number 127 is the 7th Mersenne Prime, a special class of primes.
The number 127 is also part of a special series of primes: 127 is the 31st prime, with in turn 31 also being a prime, the 11th prime, and 11 is also a prime, the 5th prime, and 5 the 3rd prime, 3 the 2nd prime, and 2 the 1st prime.
It is interesting that the 127th prime is 709, which is the next prime after the number 704 that you discuss in the post, and 709 = 704 + 5.
Also interesting is that 704 = 11 x 64, which resonates with more numbers in the post, and also 704 is a reflection of 407, another number discussed in the post, and together 704 + 407 = 1111.
It turns out that the number 1111 can be represented as Elef plus Alef, 1000 + 111, and also 1111 is a semi-prime, 1111 = 11 x 101, with 11 being the 5th prime and 101 being the 26th prime. Also in small gematria both 704 and 407 reduce to 7 + 4 = 11. (And it is interesting that in Yiddish the word עלף, pronounce “Elef,” means “eleven,” the number 11….)
That’s all for now, Good Shabbos!
Shabbat Shalom! Thank you for those comments. I with I would have caught that prime series myself which gives us Moshiach 358. Amazing catch! I am going to add it to the very next section-most grateful. BTW, 709 is the sum of the letters controlling the 7 planets according to the Sefer Yetzirah.
Ezra, thanks for your reply to my comment, and for saying you will include an idea from it in your next post.
At first I didn’t see the connection of the number 127 to Moshiach, gematria 358, but upon reflection I found that the sum of series of the 6 primes 127 + 31 + 11 + 5 + 3 + 2 = 179, and the number 179 is also a special prime, part of a series of primes, since 179 is the 41st prime, with 41 being the 13th prime, and 13 being the 6th prime.
The gematria of Moshiach, 358, is a semi-prime, with 1 factor being 2, the 1st prime, and 1 factor being 179, the 41st prime (as just said), and doubling 179 (with the concept of doubling being related to the splitting of the Alef Beis into matching sections, 11 + 11 = 22, or 2 x 11 = 22) gives 179 + 179 = 358, and 2 x 179 = 358, and therefore 127, resonating with 179, the additive sum of its related primes, when doubled or paired is 358, a hint to Moshiach (and the idea of doubling also a key aspect of Moshiach’s mission, as explained in many places).
There is also another hint to Name of 42 that is evident from the number 358 for Moshiach, since the ordinal numbers of the component primes factors of 358, i.e., the ordinal numbers of the primes 2 and 179, are respectively 1 and 41 (since 2 is the 1st prime and 179 is the 41st prime), and this yields the sum 1 + 41 = 42, hinting to the Name of 42 which is an inner spiritual force inside Moshiach that he will reveal to the world.
There are probably many other ways as well to see further indications of Hashem’s explicit Divine providence in these numbers and their relationships, in the roots of mathematics, in science, and of course in the Torah, and to understand that it is all one, since it all stems from the One Hashem.
———-
While on the subject, the sums of the intermediate numbers in the prime series culminating in 127 that sum to 179 are also significant in their own right:
Combining the first 2 primes in the series, 2 + 3 = 5, corresponding to the 5 Books of the Torah.
Combining the first 3 primes, 2 + 3 + 5 = 10, corresponding to the 10 Commandments, the 10 Sayings, and the 10 Sefiros.
Combining the first 4 primes, 2 + 3 + 5 + 11 = 21, which is the gematria of the Divine Name Ekeyeh, and also the first three letters Yud Heh Vov, 10 + 5 + 6 = 21, of the Name Hashem.
Combining the first 5 primes, 2 + 3 + 5 + 11 + 31 = 52, corresponding to 52 = 2 x 26, i.e., the doubling of the full Name Hashem, and also corresponding to the Name of 52, one of the four ways of fully spelling out the 4 letters Yud Heh Vov and Heh of Hashem.
Somewhat similarly for the series of primes culminating in 179:
Combining the first 2 numbers in this series, 6 + 13 = 19, and 19 (like 179, 41, and 13, but not like 6) is itself also a prime, the 8th prime, and 6 + 13 also hints to 6-13, i.e., the 613 Mitzvos, and in small gematria 6 + 1 + 3 = 10, and reduces to 1, representing the 10 Commandments and that Hashem is Echod/One.
Combining the first 3 numbers in this series, 6 + 13 + 41 = 60, which 60 = 4 x 15, with 15 being the gematria of the Name Kah, Yud Keh, corresponding to a double doubling of this Divine Name, and 60 also corresponds to the 60 letters of the Birchas Kohanim, and to the 6 Orders of Mishnah, and to the 60 Tractates of Talmud, and to the 600,000 souls of Israel. If only the primes in the series are counted, then combining 13 + 41 = 54, the special number Ezra discussed in the blog post.
———-
In the post it was pointed out that the number 127 is a Mersenne prime, and to provide a bit more relevant background, Wiki explains (and see there for more) that “Mersenne primes, of the form (2 ^n) – 1, are the primes 3, 7, 31, 127, 8191, 131071, 524287, 2147483647, 2305843009213693951, 618970019642690137449562111, 162259276829213363391578010288127, 170141183460469231731687303715884105727 …, and as of 2018, there are 51 known Mersenne primes, and the 13th, 14th, and 51st have respectively 157, 183, and 24,862,048 digits. As of 2018, this class of prime numbers also contains the largest known prime: M-subscript 82589933, the 51st known Mersenne prime.”
Regarding the Wiki entry for the number 127, the first thing noted about it is that it is a Mersenne prime:
“As a Mersenne prime, 127 is related to the perfect number 8128. 127 is also an exponent for another Mersenne prime 2127 – 1, which was discovered by Édouard Lucas in 1876, and held the record for the largest known prime for 75 years – it is the largest prime ever discovered by hand calculations, as well as the largest known double Mersenne prime. Furthermore, 127 is equal to 2^7 – 1, and 7 is equal to 2^3 – 1, and 3 is the smallest Mersenne prime, this makes 7 the smallest double Mersenne prime and 127 the smallest triple Mersenne prime.”
Among various other special properties of 127, Wiki also mentions that 127 is a centered hexagonal number, which Ezra has discussed in his posts, and of special interest it states that 127 is the first “nice Friedman number” in base 10, since 127 = -1 + 2^7, as well as binary since 1111111 = (1 + 1)^111 – 1 * 1 (see Wiki for details; as far as I know I’m unrelated to mathematician namesake).
Unmentioned in Wiki’s entry on the number 127 is that it is also in the category of a “super prime.”
Super primes are one of 75 subcategories of primes that Wiki describes on its “List of prime numbers” page. Incidentally, the first of these alphabetically arranged subcategories of primes are “Bell primes,” and coincidentally we are also currently discussing Bell numbers here).
According to Wiki, “Super-prime numbers (also known as higher-order primes or prime-indexed primes) are the subsequence of prime numbers that occupy prime-numbered positions within the sequence of all prime numbers. The subsequence begins 3, 5, 11, 17, 31, 41, 59, 67, 83, 109, 127, 157, 179, 191, 211, 241, 277, 283, 331, 353, 367, 401, 431, 461, 509, 547, 563, 587, 599, 617, 709, 739, 773, 797, 859, 877, 919, 967, 991…”
———-
It comes out, that what I wrote about in my previous comment – “127 is part of a special series of primes: 127 is the 31st prime, with in turn 31 also being a prime, the 11th prime, and 11 is also a prime, the 5th prime, and 5 the 3rd prime, 3 the 2nd prime, and 2 the 1st prime” (and similarly in a my past comments with other examples of prime numbers is related series) – that these special primes are considered to be “super primes” (with the exception of 2, since its prime-numbered position is 1, and technically 1 is not included as a prime).
Even more, the super primes we have discussed are part of a series of super primes, and in this case, the series of super primes related to the super prime 127 is unique in that the series starts with 2, the 1st prime, making it what might be called an initial, primary, or origin-based series super prime. (I have not had time to investigate if these categories of super primes have been discussed as of yet in Wiki or elsewhere.)
The first 15 numbers in the origin based series of super primes that I have calculated with the help of online programs are: 2, 3, 5, 11, 31, 127, 709, 5381, 52711, 648391, 9737333, 174440041, 3657500101, 88362852307, 2428095424619, and so on.
In contrast, the super prime 179 – aside from being the sum of the 6 super primes in the series 2 through 127 – is also, together with (6) and 13, and 41, a part of a series of super primes, only the series it belongs to does not start from the 1st prime, or from any prime number, but rather from 6, which is only a semi-prime, the product of 2 x 3.
It is significant that in its entry on 127, Wiki includes the idea that the Torah mentions the number 127 prominently in connection with the 127 years of the life of Sarah, and the 127 countries ruled over by Achashveirosh and by Queen Esther, and these have been discussed before in this blog and in the comments as well.
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Another fascinating aspect of the number 127 is that 101 is the 26th prime, and 101 + 26 = 127, and this illustrates yet another connection to the Name Hashem, gematria 26.
This is an example of another special series of numbers that can be generated from primes, where the rule is to sum the primes themselves with the ordinal number of their position in the set of primes (I do not know if this series of prime-based numbers has been previously discussed or classified).
Calculating this rule for the first 11 primes generates the following numbers: (2 + 1 =) 3; (3 + 2 =) 5; (5 + 3 =) 8; (7 + 4 =) 11; (11 + 5 =) 16; (13 + 6 =) 19; (17 + 7 =) 24; (19 + 8 =) 27; (23 + 9 =) 32; (29 + 10 =) 39; and (31+ 11 =) 42.
It is fascinating to see that the first 3 numbers in this series are 3, 5, 8, and like the numbers at the beginning of the Phi number series that was discussed in past posts, this is another hint to the number 358, the gematria of Moshiach.
The following is a list of such numbers I generated through the 101st prime. In each equation the first number is the regular prime number, the second number added to it is its index or ordinal number in the set of primes, and the third number is the sum of the first two, the composite number of the prime number and its ordinal number in the set of primes. It is relatively easy to spot many significant numbers that are thus generated.
For clarity the prime ordinal numbers are highlighted, and likewise for comparison the primes among the composite numbers (using the * sign as highlighting for this version). The special primes generated this way are: 3, 5, 11, 19, 79, 101, 113, 127, 163, 173, 223, 271, 383, 419, 431, 503, 571, 599, 641…:
2 + 1 = 3*
3 + 2* = 5*
5 + 3* = 8
7 + 4 = 11*
11 + 5* = 16
13 + 6 = 19*
17 + 7* = 24
19 + 8 = 27
23 + 9 = 32
29 + 10 = 39
31+ 11* = 42
37 + 12 = 49
41 + 13* = 54
43 + 14 = 57
47 + 15 = 62
53 + 16 = 69
59 + 17* = 76
61 + 18 = 79*
67 + 19* = 86
71 + 20 = 91
73 + 21 = 94
79 + 22 = 101*
83 + 23* = 106
89 + 24 = 113*
97 + 25 = 122
101 + 26 = 127*
103 + 27 = 130
107 + 28 = 135
109 + 29* = 138
113 + 30 = 143
127 + 31* = 158
131 + 32 = 163*
137 + 33 = 170
139 + 34 = 173*
149 + 35 = 184
151 + 36 = 187
157 + 37* = 194
163 + 38 = 201
167 + 39 = 206
173 + 40 = 213
179 + 41* = 220
181 + 42 = 223*
191 + 43* = 234
193 + 44 = 237
197 + 45 = 242
199 + 46 = 245
211 + 47* = 258
223 + 48 = 271*
227 + 49 = 276
229 + 50 = 279
233 + 51 = 284
239 + 52 = 291
241 + 53* = 294
251 + 54 = 305
257 + 55 = 312
263 + 56 = 319
269 + 57 = 326
271 + 58 = 329
277 + 59* = 336
281 + 60 = 341
283 + 61* = 344
293 + 62 = 355
307 + 63 = 370
311 + 64 = 375
313 + 65 = 378
317 + 66 = 383*
331 + 67* = 398
337 + 68 = 405
347 + 69 = 413
349 + 70 = 419*
353 + 71* = 424
359 + 72 = 431*
367 + 73* = 440
373 + 74 = 447
379 + 75 = 454
383 + 76 = 459
389 + 77 = 466
397 + 78 = 475
401 + 79* = 480
409 + 80 = 489
419 + 81 = 500
421 + 82 = 503*
431 + 83* = 514
433 + 84 = 517
439 + 85 = 524
443 + 86 = 529
449 + 87 = 536
457 + 88 = 545
461 + 89* = 550
463 + 90 = 553
467 + 91 = 558
479 + 92 = 571*
487 + 93 = 580
491 + 94 = 585
499 + 95 = 594
503 + 96 = 599*
509 + 97* = 606
521 + 98 = 620
523 + 99 = 624
541 + 100 = 641*
547 + 101* = 648
In total this list has 101 primes, with 26 primes in the prime ordinal index, and 19 primes in the composite sums.
The opening note about this was that 101 + 26 = 127. A closing note for now is that together with 19 for the number of thus generated primes, 127 + 19 = 146, a semi-prime with factors 2 x 73, with 2 being the 1st prime and 73 being the 21st prime, and adding 1 + 21 = 22, perhaps hinting to the 22 letters, which in Hebrew the letters also function as numbers.
[For further reference the next 26 primes (prime ordinal numbers 102-127) are: 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, and 709.]
My above (May 27) comment ended parenthetically, “For further reference the next 26 primes (prime ordinal numbers 102-127) are: 547, 557… 709.”
Correction: Prime number 547, with prime ordinal number 101, was already included in the last line of the summation table, 547 + 101* = 648. The extra reference should have begun with the 102nd prime, 557.
Since by Hashgacha Protis this focuses attention on the prime 557, here it is fitting to add that 557 + 102 = 659, and 659 is also a prime, the 120th prime. The prime ordinal number 120 has multifaceted significance and seems to resonate with the associated prime ordinal number 102.
Interestingly 659 + 120 = 779, and since 659 and its associated prime 557 have multiple 5’s, it seems we can join the idea of at least of these 5’s to 779 and get 5779, our current special Hebrew calendar year, a year of Moshiach, and as I pointed out in a previous comment, 5779 is also prime, the 758th prime.
[Just for fun, the sum of the primes 547 + 557 = 1104, the sum of their ordinal numbers 101 + 102 = 203 (the gematria of the first 3 letters of the Torah, Beis Reish Alef, and the 6th Bell Number, now being discussed in the blog), and the sum of 648 + 659 = 1307 (the 234th prime).]
While this post starts with discussion concerning the first verse of the Torah, with its 7 words and 28 letters, it is also important to realize and bear in mind, especially now as we prepare for the upcoming holiday of Shevuos celebrating the giving of the Torah, that in the Kabbalah Secrets discourse on “The 10 Commandments” and elsewhere it is explained that:
The verse that immediately precedes and introduces the 10 Utterances, Exodus 20:1, וידבר א-ל-ה-י-ם את כל הדברים האלה לאמר, “God spoke all these words, saying:” has 7 words and 28 letters, just like the Torah’s first verse.
Is seems very far fetched to think that this is just a “coincidence,” and most certainly there is exceptional Divine Providence and Planning involved, especially since the Divine Name Elokim occurs in each of these special verses, and as our sages teach in many places there there is a direct link between the “10 Sayings” that created the world and the “10 Commandments.” There are many aspects of this connection that have already been revealed, and they should be reviewed as much as possible, and probably there are much more interrelated ideas that are still to be revealed.
[Also as a reminder, as explained in a previous comment, this year will be the 3331rd anniversary of Matan Torah, and 3331 is a prime number, the 470th prime.]
Many thanks for this, Moshe. I’m sure there is a lot in this verse w/2 of the words and thus 7 of the letters the same as Bereshit 1:1
Ezra, it is your revelations in “The 10 Commandments” (linked on the sidebar) and in general that deserve the most thanks! There are so many amazing and stunning ideas you have shared, some of them astonishingly complex, that I’m still only beginning to scratch the surface of.
The correspondence between the Torah’s first verse, Breishis Bora Elokim Eis Ha’shomayim V’eis Ho’oretz, and the first verse of the 10 Commandments (Utterances), Vayedaber Elokim Eis Kol Hadevorim Ho’eileh Leimor, each with the exact same count of 7 words and 28 letters, is a relatively simple concept to grasp, and it is probably deserving of another post in and of itself, together with many other basic correspondences that are evident interconnecting the Torah’s account of Hashem’s Creation of the world and the Torah’s account of Hashem’s giving of the Commandments that could be explained.
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Here let me just add for now that the number 7 is a prime number, the 4th prime, and 7 x 4 = 28, and thus the average word size for each of these primary verses is exactly 4 letters long, perhaps hinting to the Tetragammaton, the special 4 letter Name of Hashem.
The sum of 7 + 28 = 35, which is the same as 7 x 5, and 5 too is a prime number, in fact it is a super prime, since it is the 3rd prime, and 3 is likewise prime, the 2nd prime, and 2 is likewise prime, the 1st prime, and thus 5 is not just a super prime, it is part of a series of super primes.
When 7 and 28 are doubled, by combining these 2 primary verses, then the respective sums of words and letters are 14 and 56, which sum to 14 + 56 = 70, and 70 is the same as 7 x 10, with 10 being 2 x 5.
It is possible to say that these numbers hint to the Two Tablets of the Covenant with the 10 Utterances divided into 5 Utterances on each Tablet. The First Tablet lists Utterances that stress the relationship between man and G-d, which in general expresses the theme of the Giving of the Torah on Mt. Sinai, i.e., between man and G-d, while the Second Tablet lists Utterances that stress the relationship between man and his fellow man, which in general expresses the theme of the Creation, i.e., and how man should interact with humanity and with his fellow creations .
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Last year the number 70 was emphasized, since it was the 70th year since the rebirth of the modern state of Israel. The number 70 as just explained hints to the completion of these two principle verses of the Torah, and surely the idea of this completion continues this year.
In addition, this year is the 71st year, and it is interesting to note that like the numbers 5779 (the 758th prime) and 3331 (the 470th prime) mentioned above, the number 71 is also a prime, the 20th prime.
Yesterday was Yom Yerushalayim, Jerusalem Day, and just to add something about that, the commemoration of the unification of the Holy City under Jewish control in 1967/5727, and when the Temple Mount returned to our hands:
It is interesting that the number 1967 has one digit that is a 7, and the digits 1 and 6 can be combined to make another 7. Also 1967, although not prime, is a semi-prime, the product of 7 x 281 = 1967, and that resonates with the idea of 7 words and 28 letters, since 281 is 28 x 10, plus 1 for the Kolel [It is also interesting that 281 is the 60th prime.].
Incidentally 1967 may be viewed as 19-67, and 19 is prime, the 8th prime, and 67 is prime, the 19th prime, and thus 67 is a super prime, since its prime ordinal number 19 is itself prime, the 8th prime, and the sum of these prime ordinal numbers 19 + 8 = 27, and with 1 for the Kolel equals 28.
The number 5727 has two digits that are 7, and the other two digits 5 and 2 also sum to 7, for a total of 3 x 7. [The number 5727 is non-prime, having prime factors of 3 x 23 x 83 = 5727, and these 3 primes sum to 3 + 23 + 83 = 109, which 109 is a prime, the 29th prime.]
It is possible to take the 2 x 7 in 1967 and the 3 x 7 in 5727, and sum them to 5 x 7 = 35, which is the same as the sum of 7 + 28 = 35, as explained above, and therefore these years when Jerusalem was unified also hint to both the first verse about Creation and the first verse about the Giving of the Torah.
This year we celebrate the 52nd anniversary of the return of Jerusalem to Jewish sovereignty. It is possible to say that the small gematria of 52 is 5 + 2 = 7, resonating with the idea of 70 years, and the 7 words in the two primary verses discussed. Also 52 = 4 x 13, hinting to the completeness of the unification (Echod, One, gematria 13) on 4 levels, corresponding to the 4 letters of Hashem’s Name, and also 52 = 2 x 26, i.e., a double hint to the Name Hashem gematria 26, and perhaps hinting to a fulfillment of Hashem’s plan both in the Creation and in the Giving of the Torah.
Kein Teyeh Lonu, Bimharo B’yomeinu!
Thank you. I’ll finish reading and give your comments the attention they deserve first chance I get. Meanwhile, I noticed, 5779 + 3331 = 9110
Every connection we make leads to several more…
Regarding 9110, it is 10 times 911, the gematria of the word ראשית, Reishis, “Beginning” (as in B’reishis, “In the Beginning” at the start of the Torah), and it is the 156th prime, and together with 71, the sum is 5779 + 3331 + 71 = 9181, which is also a prime, the 1138th prime. Again all these numbers lead to further connections…
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Regarding Yom Yerusholayim, it may be added that it is celebrated on the 28th of the Hebrew month of Iyar, and the date 28 corresponds to the 28 letters in each of the two first verses Breishis Bora and Vayedaber Elokim.
Also the 28th of Iyar is the 43rd day of the Omer, and the number 43 is prime, the 14th prime, with the prime ordinal number 14 corresponding to the 2 x 7 = 14 words in these two first verses when added together, and with 14 also being the gematria of דוד, Dovid, King of Israel, who conquered Jerusalem and set it as our eternal capital.
Also the sum of 28 + 43 = 71, bringing out a special resonance of Yom Yerusholayim unique to this year, the 71st year since the reestablishment of the state of Israel.
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Just one more brief related teaser. It is possible to connect the first verse of Shma with the first verse of Breishis and the first verse of Matan Torah, i.e., with 7 words and 28 letters:
The verse שמע ישראל יקוק אלקינו יקוק אחד, Shma Yisroel Hashem Elokeinu Hashem Echod, Hear O Israel Hashem our G-d Hashem is One, consists of 6 words and 25 letters, and to this we may combine 1 more word of 3 letters to sum to 7 words and 28 letters. This may be done in any one of several ways:
By adding the 3 letter word אמן, Amen, that may be said just before the Shma in answer to the blessing before the Shma said out loud by the Chazan, and also the initials of א-ל מלך נאמן, Kel Melech Ne’emon, “G-d, King, Who is trustworthy,” customarily recited by some just before the Shma.
By adding the 3 letter word אמת, Emes, “True,” which is a word said immediately after the 3 paragraphs of Shma.
Or by adding the 3 letter word and Divine Name ש-ד-י, Sha’da’i, which as I explained at length in previous comments is intimately connected with the Shma.
Note too that our sages connected the 10 Commandments to various hints in the Shma, and Bli Neder this will be explained further at another time.