The Basmala is composed of 19 letters. 19 is a prime number, and will be the main mathematical prime key, to unlock the construction and harmony in this mathematical sequence.
The first introduction of the prime number 19, is in the primary building block of the sequence, which is the count of letters (elements) in this sequence.
19 letters (elements) grouped into 4 words (groups). From the very starting building block, this prime number, is introduced in the most logical, organized, powerful, beautiful way.
The prime number 19 is introduced in a sequence of prime numbers leading to the main prime number, to establish a sophisticated prime-based mathematical structure, leaded by the prime number 19.
Basmalah is (3,4,6,6) letters respectively, which means (3, 7, 13, 19) in cumulative format.
(3, 7, 13, 19) all of them are prime numbers, and not only that, they are the first 4 even-positioned primes in numbers.
3 —–> 2nd prime number
7 —–> 4th prime number
13 —-> 6th prime number
19 —-> 8th prime number
Also note that the index of these primes is always double the word position
1st word —-> 2nd prime
2nd word —-> 4th prime
3rd word —-> 6th prime
4th word —-> 8th prime
Another key for prime numbers in (3,4,6,6) in grouping this letters count sequence, into two groups, one containing the unique counts (3,4,6) and the other containing the repeating count (6).
We will notice that the sum of the unique counts group (3+4+6) = 13, and the repeating count group’s sum = 6. It’s a well known fact that 13 is the 6th prime number.
To introduce a prime number leaded by a series of first or harmonious group of prime numbers, we have six options
1st Option:- To introduce the first 4 prime numbers (2,3,5,7) if used as original reference, and cumulative reference will be (2,5,10,17) leading to the prime number 17
2nd Option:- To introduce the first 4 prime numbers (2,3,5,7) leading to the prime number 7 if used as cumulative reference, and original reference will be (2,1,2,2)
3rd Option:- To introduce the first 4 odd-indexed prime numbers (2,5,11,17) leading to the prime number 17 if used as cumulative reference. And cannot be used as original reference, because (2+5+11+17 = 35) and 35 is not a prime number.
4th Option:- To introduce the first 4 even-indexed prime numbers (3,7,13,19) leading to the prime number 19 if used as cumulative reference. And cannot be used as original reference, because (3+7+13+19 = 42) and 42 is not a prime number.
And we have another two options, to use a sequence of primes, that is not the first of any thing, but with indeces that is a multiple of the word position.
5th Option:- To introduce primes (5,13,23,37) the 3rd, 6th, 9th, 12th primes in cumulative form. And cannot be used as original reference, because no way a word will contain 23 or 37 letters, and also (5+13+23+37 = 78) and 78 is not a prime number
6th Option:- To introduce primes (7,19,37,53) the 4th, 8th, 12th, 16th prime in cumulative form. And cannot be used as original reference, because no way a word will contain 19, 37, or 53 letters & also (7+19+37+53 = 116) and 116 is not a prime number
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So let’s test the 6 available options, to see which option fits the best to introduce a prime number, leaded by a series of harmonious prime numbers, from three main aspects
1st Aspect:- To be more logical to be practically used to form words in languages
2nd Aspect:- To be mathematically fitting basic formulas using ID & value, to confirm at least the two basic counts, in original and cumulative formats, through the formulas (1x 2x 3x 4x) or (x1 x2 x3 x4), where (1,2,3,4) are the word positions (IDs), and x is the changing value, that represents the count of letters in each word, once in it’s original format, and the other in cumulative format.
So for each option, we will do 4 checks (2 formats x 2 directions of the formula)
** We will test the formula in both directions (1x 2x 3x 4x) and (x1 x2 x3 x4) but preferably, one direction should lead the construction in confirming both basic information.
3rd Aspect:- To have additional mathematical signs and relationships, that gives it a better position, as a sign of mathematical design.
OK let’s have our tests
1st Option:-
(2,3,5,7) the original form
(2,5,10,17) the cumulative form
– 1st Aspect:- (2,3,5,7) as original form, seems logical to introduce usual words in most languages.
– 2nd Asepct:-
OK now our lead prime would be 17, let’s check if we can confirm the basic information, through our basic formulas, in both directions, to confirm both info (orginal & cumulative) through a 17-based multiplication system.
1 2
2 3
3 5
4 7
= NOT MULTIPLE OF 17
1 2
2 5
3 10
4 17
= NOT MULTIPLE OF 17
2 1
3 2
5 3
7 4
= NOT MULTIPLE OF 17
2 1
5 2
10 3
17 4
= NOT MULTIPLE OF 17
** As We can see the basic information, cannot be confirmed via a 17-multiple system.
3rd Aspect:-
No repeating digits, to balance between the sum of a group of unique counts, and group of repeating digits, for one to be a prime number, and the other to be it’s prime index.
2nd Option:-
(2,1,2,2) the original form
(2,3,5,7) the cumulative form
– 1st Aspect:- (2,1,2,2) seems very challenging to compose most words in most human languages.
– 2nd Asepct:-
OK now our lead prime would be 7, let’s check if we can confirm the basic information, through our formulas.
1 2
2 1
3 2
4 2
= NOT MULTIPLE OF 7
1 2
2 3
3 5
4 7
= NOT MULTIPLE OF 7
2 1
1 2
2 3
2 4
= NOT MULTIPLE OF 7
2 1
3 2
5 3
7 4
= 7 x 3046482
** As We can see the cumulative format only can be confirmed through a 7-multiple system in the (x1 x2 x3 x4) formula, but the original form, cannot be confirmed.
3rd Aspect:-
The unique counts in (2,1,2,2) are 2 & 1 with sum = 3, but the sum of repeating counts group (2+2 = 4), and 3 is not the 4th prime. However if we said the repeating digit is (2), it can refer to the sum (3) as the (2nd) prime which is true.
3rd Option:-
(2,3,6,6) the original form
(2,5,11,17) the cumulative form
– 1st Aspect:- (2,3,6,6) seems logical to compose usual words in languages
– 2nd Asepct:-
OK now our lead prime would be 17, let’s check if we can confirm the basic information, through our formulas.
1 2
2 3
3 6
4 6
= NOT MULTIPLE OF 17
1 2
2 5
3 11
4 17
= NOT MULTIPLE OF 17
2 1
3 2
6 3
6 4
= 17 x 12544921
2 1
5 2
11 3
17 4
= NOT MULTIPLE OF 17
** As We can see the original format only can be confirmed through a 17-multiple system in the (x1 x2 x3 x4) formula, but the cumulative format, cannot be confirmed.
3rd Aspect:-
The unique counts in (2,3,6,6) are (2,3,6) with sum = 11, but the sum of repeating counts group = 6, and 11 is the 5th prime, but the repeating digit, is 6 and not 5, so it doesn`t refer to 11 as the 5th prime, which doesn’t produce harmonious prime indexing relationship.
4th Option:-
(3,4,6,6) the original form
(3,7,13,19) the cumulative form
– 1st Aspect:- (3,4,6,6) seems a logical choice to form usual words in most languages
– 2nd Asepct:-
OK now our lead prime would be 19, let’s check if we can confirm the basic information, through our formulas.
1 3
2 4
3 6
4 6
= 19 x 19 x 697034
1 3
2 7
3 13
4 19
= 19 x 69858601
3 1
4 2
6 3
6 4
= NOT MULTIPLE OF 19
3 1
7 2
13 3
19 4
= NOT MULTIPLE OF 19
** As We can see both original and cumulative formats, can be confirmed with formulas in same direction, through a 19-based multiplication system, and also one of them is a double multiple of 19.
3rd Aspect:-
The unique counts in (3,4,6,6) are (3,4,6) with sum = 13, and the repeating digit is (6), and 13 is the 6th prime number, which indicates a harmonious prime indexing relationship.
Also (34+66 = 100) a sign for perfection
3+7+13+19 = 42 (42 is the 28th composite) which is in harmony with using from (2)nd to (8)th primes, and Also with the language with 28 letters, that will build the sequence in language words format.
3+7+1+3+1+9 = 24 (24 is the 14th composite) which is in harmony with using from (1) to (4) words, and also 14 is half of 28, and also the initialed letters are 14
42+24 = 66 = the sum value of letters of the word ALLH (1+30+30+5 = 66)
24 & 42 are reflective numbers.
5th Option:-
(5,8,10,14) the original form
(5,13,23,37) the cumulative form
– 1st Aspect:- (5,8,10,14) seems an accepted choice to form usual words in languages, although not most words in most languages are upto 14 letters.
– 2nd Asepct:-
OK now our lead prime would be 37, let’s check if we can confirm the basic information, through our formulas.
1 5
2 8
3 10
4 14
= NOT MULTIPLE OF 37
1 5
2 13
3 23
4 37
= NOT MULTIPLE OF 37
5 1
8 2
10 3
14 4
= NOT MULTIPLE OF 37
5 1
13 2
23 3
37 4
= NOT MULTIPLE OF 37
** As We can see, we can`t confirm the original or cumulative formats, in both directions, through a 37-multiple system.
3rd Aspect:-
No repeating digits, to balance between the sum of a group of unique counts, and group of repeating digits, for one to be a prime number, and the other to be it’s prime index.
6th Option:-
(7,12,18,16) the original form
(7,19,37,53) the cumulative form
– 1st Aspect:- (5,8,10,14) seems very odd to find (12,18,16) lettered words respectively in most languages.
– 2nd Asepct:-
OK now our lead prime would be 53, let’s check if we can confirm the basic information, through our formulas.
1 7
2 12
3 18
4 16
= NOT MULTIPLE OF 53
1 7
2 19
3 37
4 53
= NOT MULTIPLE OF 53
7 1
12 2
18 3
16 4
= NOT MULTIPLE OF 53
7 1
19 2
37 3
53 4
= NOT MULTIPLE OF 53
** As We can we can`t confirm the original or cumulative formats, in both directions, through a 53-multiple system.
3rd Aspect:-
No repeating digits, to balance between the sum of a group of unique counts, and group of repeating digits, for one to be a prime number, and the other to be it’s prime index.
SO it’s obvious our best two options are either using (3,7,13,19) as cumulative reference or (2,5,11,17) as cumulative reference
(2,5,11,17) passed only to confirm it’s original format, but failed to confirm it’s cumulative format.
Also the original format (2,3,6,6) leading to a non harmonious prime indexing, because (2+3+6 = 11) which doesn’t correspond as index with the repeating digit (6), because 11 is the 5th prime number not the 6th.
From other hand (3,7,13,19) passed both original and cumulative formats, in same direction (1x 2x 3x 4x), and one of the formats was a double multiple of 19.
Also the original format (3,4,6,6) leads to a harmonious prime indexing, because (3+4+6 = 13), and 13 is the 6th prime index, which corresponds with the repeating digit (6).
Another signs to strengthen the position of (3,7,13,19) as a choice:-
1- Using (3) as prime no. (2) & using (7) as prime no. (4) & using (13) as prime no. (6) & using (19) as prime no. (8)
3,2 + 7,4 + 13,6 + 19,8 = 440 (words and letters are presented in 44 digits)
2-
3 + 7 + 13 + 19 = 42 (42 is the 28th composite number) refering to using even primes with indeces from (2) to (8), and using a language with 28 letters.
3 + 7 + 1+3 +1+9 = 24 (24 is the 14th composite number) refering to using words with IDs from (1) to (4)
Also 14 is half 28, and 14 is the count of Quranic intialed letters.
24 & 42 are reflectives
24 + 42 = 66, which is the sum of letters values of the word ALLH (1+30+30+5 = 66)
3-
(3,6) are the first and last letters letters count
(6,6) are the last two letter count attached to two GOD attributes
36 is the sum of the unique letters of ALLH
66 is the sum of all the letters of ALLH
** Note that 66 is 47th composite and the nearest prime is the 19th prime (47+19 = 66)
** Also ALLH is between 4th and 7th letter, and the last word ALRHYM sum of digits of letters = 19 & the other three words = 47
4- 34 + 66 = 100 …. sign for perfection
5- (3,8,18,24) is the original letters count x word position
1 3
2 8
3 18
4 24
= 19 x 69911496
6-
123 + 4567 + 8910111213 + 141516171819 = 150426287722
= 19 x 7917173038
7-
12345678910111213141516171819
1234
= 19 x 6497725742163796390271669378486
8-
123 1
4567 2
8910111213 3
141516171819 4
= 19 x 6481351204790059017442903248326
** CONCLUSION:-
This manifistation proves, that using the prime number (19) leaded by a series of primes as (3,7,13,19) is the best mathematical option, to introduce the primary building block, the count of elements in each group, and the whole sequence, in a way, that introduce prime numbers, in a harmonious way, from the very beginning, that fits basic mathematical formulas, that confirm it’s basic information in all possible logical ways, which is a powerful start, to show the intention of building a prime-based system, from the very beginning.