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Date : 11-Jan-2015
Place : University of Yangzhou, Yangzhou, Jiangsu, China
Authors : Dr Haifeng Xu, Zuyi Zhang
Emails : hfxu@yzu.edu.cn, zhangzuyi1993@hotmail.com
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Based on Ali Adams' email below with the following findings:
Quran = Key + Message
114 chapters = 1 + 113 unit and additive prime
6236 verses = 7 + 6229 additive primes
where
Key = 7 verses = 29 words = 139 letters
and
7, 29, 139, 729139 and 139297 are additive prime numbers,
Dr Haifeng Xu has found after discussion with his student Zuyi Zhang that the numbers 7, 29, 139 are the first Triplet {a, b, c} where:
Let a, b, c are odd primes (e.g. 7, 29, 139).
Let s1, s2, s3 be the digit sums of a, b, c respectively (e.g. 7=7, 2+9=11, 1+3+9=13).
Let a_b_c as the number joined by a, b and c (e.g. 7, 29, 139 become 729139).
Let c_b_b as the number joined by c, b and a (e.g. 7, 29, 139 become 139297).
Then the triple {a, b, c} satisfies the following conditions:
(1) s1 < s2 < s3 are consecutive primes,
(2) s1 + s2 + s3 is prime,
(3) a_b_c and c_b_a are both prime.
First few triples calculated by Haifeng Xu:
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7 29 139
7 29 373
7 29 1327
7 29 2083
7 29 3217
7 29 4603
7 47 157
7 47 1831
7 47 4153
7 47 6151
7 83 283
7 83 337
7 83 373
7 83 1039
7 83 1381
7 83 3109
7 83 7321
7 137 733
7 227 823
7 263 409
7 353 373
23 61 353
.. .. ...
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In above triplets, there are some that are even more interesting where their digit revesal is also prime. Here are the first few such triplets:
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7 47 157 747157
7 47 1831 7471831
7 47 4153 7474153
7 83 337 783337
7 83 1039 7831039
7 83 3109 7833109
7 83 7321 7837321
7 137 733 7137733
7 353 373 7353373
.. .. ... .......
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The authors "are extremely grateful to Ali Adams for proposing such an interesting problem."
Email: hfxu@yzu.edu.cn
haifengxu.xhf@gmail.com
Web: http://www.atzjg.net/
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To hfxu@yzu.edu.cn zhangzuyi1993@hotmail.com zhoujr1982@hotmail.com
CC Jeff Gilchrist Ben Buhrow pi@primenumbers.org primenumbers@yahoogroups.com
Dear Xu Haifeng, Zhang Zuyi and Zhou Jiuru,
I enjoyed your outstanding paper http://arxiv.org/pdf/1406.0429v4.pdf
Periodicity related to a sieve method of producing primes which I found on The Structure of Prime Numbers and Twin Prime Gaps - CodeProject
I would like to share with you a new definition of prime number which clearly show why 1 is not a prime number.
If we assume that "number divisibility" always breaks a whole number into smaller whole numbers,
then
1 is indivisible.
1 is the father of all numbers or the proton in chemistry
Primes are divisible by themselves only (not by 1 because 1 never breaks them into smaller numbers).
Primes are the mothers of their multiples or the atoms in chemistry.
Composites are divisible by themselves and one or more numbers below them.
Composites are the children of their prime mothers or the molecules in chemistry.
Finally, there is a Book that has two parts: a Key and a Message:
Key = 1 chapter = 7 lines = 29 words = 139 letters
first 7 lines = 29 words
and
first 7 words = 29 letters.
Message = 113 chapters = 6229 lines
last 7 lines = 29 words
and
last 7 words = 29 letters.
All these numbers are primes AND their digit sums are primes too.
(e.g. 29 is prime and 2+9 = 11 is also prime)
Such primes with prime digit sums are called Additive Prime Numbers
NOTE The 7th additive prime number is 29
The total chapters in the book (1+113 = 114) have the following number of lines:
{ 7, 286, 200, 176, 120, 165, 206, 75, 129, 109, 123, 111, 43, 52, 99, 128, 111, 110, 98, 135, 112, 78, 118, 64, 77, 227, 93, 88, 69, 60, 34, 30, 73, 54, 45, 83, 182, 88, 75, 85, 54, 53, 89, 59, 37, 35, 38, 29, 18, 45, 60, 49, 62, 55, 78, 96, 29, 22, 24, 13, 14, 11, 11, 18, 12, 12, 30, 52, 52, 44, 28, 28, 20, 56, 40, 31, 50, 40, 46, 42, 29, 19, 36, 25, 22, 17, 19, 26, 30, 20, 15, 21, 11, 8, 8, 19, 5, 8, 8, 11, 11, 8, 3, 9, 5, 4, 7, 3, 6, 3, 5, 4, 5, 6 }
These numbers are truly amazing as they have many hidden features including the Golden ratio.
Here are some patterns:
If we arrange these numbers in a column vertically and give them position 1 to 114 and sum the position with each number (e.g. 1+7=8, 2+286=288, 3+200=203, ..., 114+6=120)
Then:
Pattern 1: the count of odd sums = the count of even sums = 57
Pattern 2a: the sum of odd sums = the sum of the positions = 6555
Pattern 2b: the sum of even sums = the sum of the numbers = 6236
Pattern 3: the sum of all sums is prime = 12791
Pattern 4: the sum of the duplicate sums / the sum of the unique sums = 7906 / 4885
= 1.6184237461617195496417604912999...
which is accurate to within 0.0003897574118247014371736569343... of the golden ratio φ.
If instead of summing, we multiply each position with its numbers (e.g. 1*7=7, 2*286=576, 3*200=600, ..., 114*6=684)
Then:
Pattern 5: the sum of all multiplications is prime = 209029
Pattern 6: the 57th chapter has 29 lines.
Note 57 = 114 / 2 and
29 is the midpoint between 1 to 57 and therefore
the multiplication 57 * 29 = Sum(1+2+3+....+57) = 1653
AND
the 16th prime is 53
Pattern 7a: if we sort the table by the multiplication column is ascending order, chapter 57 stays in position 57 (1653 is the 57th sorted multiplication value).
Pattern 7a: if we sort the table by the multiplication column is descending order, chapter 57 should move to position 58 but it stays in position 57 because chapter 87 has 19 lines and its multiplication is also 1653.
By the way, chapter 57 is called The Iron and Iron has the most stable nucleus of all chemical elements. Elements below it become Iron eventually by nuclear fusion and elements above it also become Iron eventually by nuclear fission. This is why the core of stars is made of Iron.
I used to think of maths as a tool to help science model systems, but now I believe maths is the foundation of all sciences. That means the propagation of light (energy quanta) from the Big Bang singularity point must follow some mathematical pattern(s) to produce our specialized Physical reality from the generic dark energy. Think of light as a helix and comes out from the singularity point either clockwise or counter-clockwise following similar distribution as the prime numbers.
This why God swears (gives oath)
89:3 "By The Standalone and By The Codependent"
My Questions:
1) Can someone please tell me how to calculate the probability of each of the above patterns and then multiply them to get a total probability?
2) Can someone please tell me what is the significance to the "error" 0.0003897574118247014371736569343... away from the golden ratio φ.
Here are all the Excel calculation: http://heliwave.com/AmazingQuran.xls
Ali Adams
Quran and Prime Numbers
God >
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