Monday, May 7, 2012

The Qur'an and Theorem of Nineteen

A theorem in mathematics of the number 19, said:
 Assume you have a pair of two-digit numbers, x and y, where x consists of digits a and b, y consists of digits c and d, such that a, b, c and d are nonzero. If x + y = ab + cd = 100, then a + b + c + d = 19
In the previous posts have described about the Nineteen - The Authenticity Detector of the Qur'an , as mentioned in Surah Al-Muddatstsir verse 30:
[74:30] Over it are nineteen
and further described in the next verse what is Allah's intention to make the "19" over it :

[74:31] ... and We have fixed their numbers :
- only as a trial for Unbelievers,
- in order that the People of the Book may arrive at certainty
- and the Believers may increase in Faith,
- and that no doubts may be left for the People of the Book and the Believers,
- and that those in whose hearts is a disease and the Unbelievers may say,
"What symbol doth Allah intend by this?"
Thus doth Allah leave to stray whom He pleaseth, and guide whom He pleaseth: and none can know the forces of thy Lord, except He and this is no other than a warning to mankind.
Back to the theorem mentioned above, the proof can be described as follows:

ab + cd = 100, where ab is a number with two digits and the cd is a number with two digits, then (a x 10) + b + (c x 10) + d = 100. (a x10) + (c x 10) is a multiple of 10 (because each is multiplied by 10) and a, b, c, d can not be zero, then b + d must also be a multiple of 10 because 100 is a multiple of 10. Because b and d is the number one digit between 1 and 9, and b + d is a multiple of ten, then b + d = 10. This leads to (a x 10) + (c x 10) = (a + c) x 10 must be equal to 90 or a + c = 9. Because b + d = 10 and a + c = 9, so that a + b + c + d = 19, Q.E.D.
Pairs of number that meet the above theorem are:

(11,89) (12,88) (13,87) (14,86) (15,85) (16,84) (17,83) (18,82) (19,81) (21,79) (22,78) (23,77) (24,76) (25,75) (26,74) (27,73) (28,72) (29,71) (31,69) (32,68) (33,67) (34,66) (35,65) (36,64) (37,63) (38,62) (39,61) (41,59) (42,58) (43,57) (44,56) (45,55) (46,54) (47,53) (48,52) (49,51) (51,49) (52,48) (53,47) (54,46) (55,45) (56,44) (57,43) (58,42) (59,41) (61,39) (62,38) (63,37) (64,36) (65,35) (66,34) (67,33) (68,32) (69,31) (71,29) (72,28) (73,27) (74,26) (75,25) (76,24) (77,23) (78,22) (79,21) (81,19) (82,18) (83,17) (84,16) (85,15) (86,14) (87,13) (88,12) (89,11)

There are a total of 72 pairs of number that meet the above theorem. Moving on from these 72 pairs of number, let's open surah 72 in the Qu'ran. The total verses of this surah is 28 , where (72,28) is one of 72 pairs of number that meet the theorem, in which 72 + 28 is 100. Now if we add each of its constituent digits: 7 + 2 + 2 + 8, we will obtain the results of 19, according to the above theorem.

Al-Qur'an surah 72 verse 28 reads:

[72:28] "That He may know that they have (truly) brought and delivered the Messages of their Lord: and He surrounds (all the mysteries) that are with them, and takes account of every single thing."
Yes, Allah takes count of every single thing when revealed His words, He did it by counting things one by one, no even single little thing is missed.

From the sum of 72 + 28 that obtained the number 100, let's see surah 100 in surah of the Qu'ran, in which composed of 11 verses. The composition of 100 and 11 which consists of two digits 0 and 1 reminds us of the binary number, that if 100 (surah number) and 11 (total verses of the surah) are combined into a binary 10011, will form 19 in decimal which if used in its decimal.


Initials and Twin Primes

Now let's take a look all surah in the Qur'an one by one. In the Qu'ran there are several surah with the initials / fawatih, such as alif laam miiim, alif lam mim sha'ad, sha'ad, nun, alif lam ra. Surah Al-Baqarah (surah 2) is the first initials-have surah (alif lam mim), and Al-Qalam (surah 68) is the last initials-have surah (nun). An interesting fact that the number of occurrences of the letter alif + lam + mim in surah Al-Baqarah is 9899 which is a multiple of 19  (19 x 521). fact that 19 is prime, brings us to the twin prime pairs ( twin prime ). Twin primes are pairs of primes that differed by two, such as (3, 5) or (5, 7) or (11, 13).

List of twin prime pairs can be seen  on http://primes.utm.edu/lists/small/100ktwins.txt?bcsi_scan_E07337FFBB32A8B2=0&bcsi_scan_filename=100ktwins.txt

The 521th pairs of twin prime is (33767, 33769), where the middle number of that pair is 33768. This 33768 has a unique phenomenon associated with the number 19 in the Qur'an, where its digits is a combination of 337 and 68.

337 is the 68th prime number, and 68 are the last initial-have surah  in the Qur'an.


wallahu a'lam
Allah the Most Righteous with His words  
(from various sources) 

To view and search the verses of the Qur'an can be through http://www.quranplus.com