Quran-Islam.org - True Islam

Beyond Probability
God's Message in Mathematics

By: Abdullah Arik (edited version)
.

"Mathematics is the language in which
God wrote the universe."
Galileo (1564-1642 AD)

Introduction

The Quran was revealed in Arabic. The Book consists of 114 chapters which are called Suras. The shortest Sura in the Quran contains three verses, whereas the longest Sura has 286 verses.
The Quran is a unique book in that some of its Suras start with a letter, or a group of letters, instead of the usual text. These letters will be called initials, and the chapters that start with initials will be called the initialled Suras throughout this research.
There are 29 initialled Suras in the Quran. The first initialled Sura is Sura 2, and the last is Sura 68. Some of these Suras contain the same initials as used in other Suras, while some initials are not repetitions. There are a total of 14 different sets of initials and 14 different Arabic letters are used. Table 2 lists the 29 initialled Suras with the corresponding initials used. In this table, only the English equivalents of the Arabic letters are given.

Table 1.

The 114 Suras of the Quran with the

corresponding number of verses in each

Sura No.	Verses	Sura No.	Verses	Sura No.	Verses
1	7	39	75	77	50
2	286	40	85	78	40
3	200	41	54	79	46
4	176	42	53	80	42
5	120	43	89	81	29
6	165	44	59	82	19
7	206	45	37	83	36
8	75	46	35	84	25
9	127	47	38	85	22
10	109	48	29	86	17
11	123	49	18	87	19
12	111	50	45	88	26
13	43	51	60	89	30
14	52	52	49	90	20
15	99	53	62	91	15
16	128	54	55	92	21
17	111	55	78	93	11
18	110	56	96	94	8
19	98	57	29	95	8
20	135	58	22	96	19
21	112	59	24	97	5
22	78	60	13	98	8
23	118	61	14	99	8
24	64	62	11	100	11
25	77	63	11	101	11
26	227	64	18	102	8
27	93	65	12	103	3
28	88	66	12	104	9
29	69	67	30	105	5
30	60	68	52	106	4
31	34	69	52	107	7
32	30	70	44	108	3
33	73	71	28	109	6
34	54	72	28	110	3
35	45	73	20	111	5
36	83	74	56	112	4
37	182	75	40	113	5
38	88	76	31	114	6

Table 2.

The 29 initialled Suras, number of verses in each,

and the initials prefixing these Suras

Ch. No.	No. of Verses	Initials
2	286	A,L,M
3	200	A,L,M
7	206	A,L,M,S
10	109	A,L,M
11	123	A,L,R
12	111	A,L,R
13	43	A,L,M,R
14	52	A,L,R
15	99	A,L,R
19	98	K,H,Y,A,s
20	135	T,H
26	227	T,S,M
27	93	T,S
28	88	T,S,M
29	69	A,L,M
30	60	A,L,M
31	34	A,L,M
32	30	A,L,M
36	83	Y,S
38	88	S
40	85	H,M
41	54	H,M
42	53	H,M,A,S,Q
43	89	H,M
44	59	H,M
45	37	H,M
46	35	H,M
50	45	Q
68	52	N,N

Note: All initials occur in the first verse of these Suras with the exception of Sura 42. In this Sura, the first two initials occur in the first verse, then the last three initials occur in the second verse.

Ever since the revelation of the Quran, many scholars studying the Quran tried in vain to understand the significance of the initials and the initialed Suras. However, their significance remained a mystery until recently.

Discovery of the Mathematical System

An Egyptian-American biochemist and Muslim scholar, Dr. Rashad Khalifa, started translating the Quran into English in the early 1970's. He was determined to find an explanation for the mysterious initials. With this in mind, he initiated an extensive research on these initials after feeding the Quranic text with the initialed Suras into a computer. His objective was to search if there is a mathematical pattern which would explain the significance of the initials. He had no idea where or what to look for. After several years of research, Dr. Khalifa published his first findings in a book entitled "Miracle of the Quran: Significance of the Mysterious Alphabet" in 1973. Although his findings indicated a correlation between the frequency of the initials themselves, he did not relate these frequencies to any common denominator. By January 1974, he recognised 19 as a common denominator in the initials and throughout the Quran.

Continuing research after this discovery unveiled an intricate mathematical system which pervades the whole Quran and governs every possible element in it (Khalifa, R., 1981 and 1989).

Remarkable Design

The entire text of the Quran is mathematically composed with remarkable intricacy. The basis of this mathematical system is the number 19. Virtually every element of the Quran contains 19 as the common denominator.

Examples

The Quran being a book totally structured on the number 19, contains a vast number of patterns and features that are too many to mention them all. The following are only some of these examples:

The number of chapters in the Quran is 114 = 19 x 6
The total number of verses in the Quran is 6,346 = 19 x 334
The occurrence of the word God (Allah) in the Quran is 2,698 = 19 x 142
The sum of all the verse numbers where the word God occurs is 118,123 = 19 x 6,217
There are 30 different numbers mentioned in the Quran (e.g. 1 God, 2 brothers, 7 heavens ... etc.), If we add the 30 numbers we get a total of 162146 = 19 x 8534
The first statement in the Quran, "In the name of God, the Almighty, the Merciful" consists of 19 Arabic letters. It is known as the `Basmalah'
If we look at the four words of the Basmalah separately, we find that each word occurs in the whole Quran in a number that is a multiple of 19
The very first revelation that was given to the prophet was the first 19 words in sura 96
The total number of letters making up the 19 words is 76 = 19 x 4
The first revealed Sura (96) has 19 verses
Sura 96 consists of 304 Arabic letters = 19 x 16
The last Sura revealed (Sura 110) has 19 words, and its first verse has 19 letters
The main message in the Quran is that there is only One God. The word 'One' in Arabic is WAHED. The word WAHED appears in the Quran 19 times (when used to speak of God)
The Gematric Value (explained below) of the word WAHED is 19
The word 'Quran' occurs in 38 different Suras = 19 x 2
The word 'Quran' occurs in the Quran 58 times, however one of them, in 10:15, refers to "another quran". Thus, the frequency of the occurrence of God's Quran is 57 = 19 x 3
If we add the numbers assigned to all the Suras in the Quran, plus the numbers assigned to all of the verses in the Quran, plus the total number of verses in the Quran, we get a total of 346199 = 19 x 19 x 959
If we look at the Suras which start with Initials separately and add the Sura numbers, verse numbers and number of verses, the total is 190133 = 19 x 10007. It follows that the total for the un-initialled Suras, 156066, is also divisible by 19.

The above is only a very small selection of 19 related features out of a vast number of other features.

A totally independent feature of the mathematical structure of the book is the initialed letters which appear in the beginning of the initialed Suras, and their occurrence inside their chapters. All the initials occur in their corresponding Suras in multiples of 19, when looked at as individual sets. For example, there are two Suras that are initialed with the letter Q. The number of occurrence of the letter Q in each of these chapters is 57 or 19 x 3.
The details of the initialed letters, plus more details of the miracle of 19, can be found at: Miracle of the Quran

Gematric Value (G.V.)

Another aspect of the Quran's mathematical design is the use of the Gematric Value (G.V.) of the Arabic letters. The G.V. value of a letter is the numerical value assigned to it. When the Quran was revealed, fourteen centuries ago, numbers as we know them today did not exist. Instead, there was a universally accepted numerical system where the letters of the Arabic, Hebrew, Aramaic, and Greek alphabets were used as numerals. In actual fact, this system is still used today, for example the Roman letters are used in Law Reference books … e.g. V = 5, X = 10 …. Etc.

The Arabs at the time of the Quranic revelation also used letters for numbers. The number assigned to each letter is considered to be its G.V.. Thus the G.V. of the letter V (in Roman) is 5 .. etc.
Table 3 gives the G.V. of each letter in the Arabic alphabet, which is listed in its original order, the 'Abjadiyyah'. The choice of the English letters used for pronouncing each Arabic letter are based simply on the sounds of the Arabic letters.

Table 3.

The G.V. of the Arabic alphabet (Abjadiyyah)

10	9	8	7	6	5	4	3	2	1
(Y)	(Tta)	(Hha)	(Z)	(W)	(H)	(D)	(G)	(B)	(A)
100	90	80	70	60	50	40	30	20
(Q)	(S)	(F)	(Aa)	(S)	(N)	(M)	(L)	(K)
1000	900	800	700	600	500	400	300	200
(GH)	(DH)	(Dda)	(ZH)	(KH)	(TH)	(T)	(SH)	(R)

Why 19?

The mathematical coding of the Quran with the number 19 makes one wonder the divine reason for using the number 19 instead of some other number. Besides having unique mathematical properties, such as being a prime number, the number 19 is the G.V. of the word 'ONE' in all scriptural languages Aramaic, Hebrew, and Arabic. In Arabic, the word for 'ONE' is "WAHD" (pronounced Wahid). Based on Table 4, the G.V. of the letters W, A, H, and D are 6, 1, 8, and 4, respectively. These numbers add up to 19 (6 + 1 + 8 + 4 = 19).
Therefore, the number 19 can be looked at to signify the First Commandment in all scriptures that there is only ONE God.

In addition, the number 19 is made up of the two numerals 1 and 9, these are the first and last single numerals used in mathematics, thus the number 19 represents the First and Last, or the Alpha and Omega which is once again the attribute of God as confirmed in all Scriptures.

The Opening Statement

The first verse of the Quran is "In the name of God, the Almighty, the Merciful." In Arabic, it is pronounced as Bism Allah Al-Rahman Al-Raheem, and is known as the Basmalah.

The Basmalah is so special and unique that it constitutes the foundation upon which the Quran's 19-based mathematical composition is built. It is the opening statement of the Quran, and is composed of four words and exactly 19 Arabic letters. These letters are given below in Table 4 with the approximate English equivalents and their corresponding G.V..

Table 4.

The 19 Arabic letters of the Basmalah and

their corresponding G.V.

Letter No.	Arabic Letter	English	G.V.
1	Baa'	B	2
2	Siin	S	60
3	Miim	M	40
4	'Alif	A	1
5	Laam	L	30
6	Laam	L	30
7	Haa'	H	5
8	'Alif	A	1
9	Laam	L	30
10	Raa'	R	200
11	H!aa'	Hha	8
12	Miim	M	40
13	Nuun	N	50
14	'Alif	A	1
15	Laam	L	30
16	Raa'	R	200
17	H!aa'	Hha	8
18	Yaa'	Y	10
19	Miim	M	40

Mathematical Design of the Basmalah

The four words and the 19 letters of the Basmalah are put together according to a mathematical system which is humanly impossible to compose. This remarkable system is based on the number and the G.V. of the letters that constitute the four words of the Basmalah. Let us first summarise the information we need to know about the Basmalah in Table 5 before we review this incredible mathematical system.

Table 5.

The four words of the Basmalah, the English translation,

the number of Arabic letters in each word, and their G.V.

No.	Arabic	English	#Letters	G.V.	Total
1	Bism	In the name	3	2, 60, 40	102
2	Allah	God	4	1, 30, 30, 5	66
3	Al-Rahman	Most Gracious	6	1, 30, 200, 8, 40, 50	329
4	Al-Raheem	Most Merciful	6	1, 30, 200, 8, 10, 40	289

TOTAL

.......19

786

By using the data in Table 5, we obtain the following intricate mathematical design:

Fact 1

The first observation is that the Basmalah comprises 19 letters.

Fact 2

The letters of the Basmalah provide the first interesting calculation. The Basmalah is verse number 1 in the Quran. It consists of 19 Arabic letters. These 19 letters make up four words and the number of letters in the four words are 3,4,6 and 6 respectively.

When placed in sequence, the resulting number is 1 19 3466

1193466 = 19 x 19 x 19 x 174

The data of the number of letters and their frequency in the words of the Basmalah yields a number that is divisible by 19 not once, nor twice, but three times a multiple of 19.

Fact 3

The data derived solely from data of the words of the Basmalah also provide a significant calculation. There are 4 words, they contain 19 letters and the gematrical value of the 19 letters is 786

When placed in sequence, the resulting number is 4 19 786

4 19 786 = 19 x 22094

Fact 4

The sequence number of each word in the Basmalah followed by the number of letters in it forms an 8-digit number which is a multiple of 19:

1 3 2 4 3 6 4 6 = 19 x 19 x 36686

Fact 5

Replace the number of letters in each word in Fact 2 by the total G.V. of that word. Thus, the sequence number of each word is followed by its total G.V., to form a 15-digit number which is a multiple of 19:

1 102 2 66 3 329 4 289 = 19 x 5801401752331

Fact 6

Replace the total G.V. of each word in Fact 3 by the G.V. of every letter in that word. For instance, the total G.V. of the first word, 102, is replaced by 2 60 40. Similarly, the total G.V. of the second word, 66, is replaced by 1 30 30 5, and so on. The result is a 37-digit number which is a multiple of 19:

1 2 60 40 2 1 30 30 5 3 1 30 200 8 40 50 4 1 30 200 8 10 40

= 19 x 66336954226595422109686863843162160

Fact 7

As Fact 4, but this time we substitute the G.V. of every letter with the cumulative total G. V. of all preceding letters. So for the first letter we write its G.V. which is 2, next we write the total G.V. of letters 1 + 2 which is 62, then 1 + 2 + 3 = 102. The total is imported to word 2 and so on.

We end up with the following number:

1 2 62 102 2 103 133 163 168 3 169 199 399 407 447 497 4 498 528 728 736 746 786

= 19 x 66426432121753490359562736526003919735499922564670355094

Fact 8

Insert the sequence number of each letter in the word before its gematrical value in Fact 4. For example, the gematrical values of the letters in first word are 2 60 40. When we insert the sequence numbers of the letters, we get 1 2 2 60 3 40, where the sequence numbers are in italics, the gematrical values are in bold. Similarly, the gematrical values of the letters in the second word are 1 30 30 5. When we insert the sequence numbers of the letters, we get 1 1 2 30 3 30 4 5, and so on. When all the numbers are put together, the result is a 56-digit number which is a multiple of 19:

1 1 2 2 60 3 40 2 1 1 2 30 3 30 4 5 3 1 1 2 30 3 200 4 8 5 40 6 50 4 1 1 2 30 3 200 4 8 5 10 6 40

= 19 x 590843895848580686595327911581502139495327911581500560

Fact 9

Replace the total G.V. of each word in Fact 3 by the sum of the G.V. of the first and the last letter in that word. For instance, the total G.V. of the first word, 102, is replaced by 42. The number 42 is the sum of 2 and 40, which are the G.V. of the first and the last letter in the first word. Similarly, the total G.V. of the second word, 66, is replaced by 6, the sum of 1 and 5. Repeating this process for the four words of the Basmalah,we get an 11-digit number which is a multiple of 19:

1 42 2 6 3 51 4 41 = 19 x 748755339

(2+40) (1+5) (1+50) (1+40)

Fact 10

Consider the numbers used in Fact 2 and Fact 3. In Fact 2, the sequence number of each word is followed by the number of letters (3, 4, 6, and 6) in the word. In Fact 3, we replace the number of letters by the G.V. of the words (102, 66, 329, and 289). Now, for this case, the sequence number of each word will be followed by the sum of the number of letters and the gematrical value of the word. Therefore, the number we use for the first word will be 105 (3+102). It will be 70 (4+66) for the second word, 335 (6+329) for the third word, and 295 (6+289) for the fourth word.

Thus the sequence number of each word in the Basmalah is followed by the numbers 105, 70, 335, and 295 respectively to form a 15-digit number which is also a multiple of 19:

1 105 2 70 3 335 4 295 = 19 x 5817212281805

(3+102) (4+66) (6+329) (6+289)

FACT 11

Consider Fact 2, where the sequence number of each word in the Basmalah is followed by the number of letters in the word. In this case, the sequence number of each word will be followed by the total number of letters up to and including that word (cumulative total). For example, the number of letters in the Basmalah's four words are 3, 4, 6 and 6, respectively. Then the cumulative total number of letters will be 3 for the first word. It will be 7 (3+4) for the second word, 13 (3+4+6) for the third word, and finally 19 (3+4+6+6) for the last word. Therefore, we write down the sequence numbers of the words followed by the cumulative total number of letters corresponding to the word. The result is a 10-digit number which is also a multiple of 19:

1 3 2 7 3 13 4 19 = 19 x 69858601

(3) (3+4) (3+4+6) (3+4+6+6)

FACT 12

This fact is very similar to Fact 8. In this fact, instead of using the cumulative total number of letters for each word, we use the cumulative total of the G.V. of the letters corresponding to the word. For example, the G.V. of the letters in the Basmalah's four words are 102, 66, 329 and 289, respectively. Then the cumulative total of the G.V. of the letters will be 102 for the first word. It will be 168 (102+66) for the second word, 497 (102+66+329) for the third word, and finally 786 (102+66+329+289) for the last word.

Therefore, we write down the sequence numbers of the words followed by the cumulative total of the G.V. of the letters corresponding to the word. The resultant
16-digit number is a multiple of 19:

1 102 2 168 3 497 4 786 = 19 x 58011412367094

(102) (102+66) (102+66+329) (102+66+329+289)

FACT 13

Insert the sequence number of each word (1, 2, 3, and 4) at the end of the underlined numbers in Fact 10 while keeping all the numbers the same. The result is a 66-digit number that is a multiple of 19. The sequence numbers of the words are printed in italics:

2 1 60 2 40 3 1 1 4 30 5 30 6 5 7 2 1 8 30 9 200 10 8 11 40 12 50 13 3

1 14 30 15 200 16 8 17 10 18 40 19 4

= 19 x

11369685849634371880096364211095336907901742857974737727215886326

FACT 14

The G.V. of each letter is followed by its sequence number (1 through 19) in the Basmalah to form a 62-digit number that is a multiple of 19. The sequence numbers are printed enlarged:

2 1 60 2 40 3 1 4 30 5 30 6 5 7 1 8 30 9 200 10 8 11 40 12 50 13

1 14 30 15 200 16 8 17 10 18 40 19

= 19 x

1136968586476477143068905268848105921121654218526404300536001

In this fact, each one of the four words of the Basmalah is underlined to show the numbers representing these words. This information will be helpful to understand the next fact.

FACT 15

Consider the numbers in Fact 11, and replace the sequence numbers of the words (1, 2, 3, and 4) with their G.V. (102, 66, 329, and 289), while keeping all the other numbers the same. The result is a 73-digit number, also a multiple of 19:

2 1 60 2 40 3 102 1 4 30 5 30 6 5 7 66 1 8 30 9 200 10 8 11 40 12 50 13 329 1 14 30 15 200 16 8 17 10 18 40 19 289

= 19 x

113696858432331858240874647852637269158552701732180534315877984746527331

FACT 16

This time let us change the position of the G.V. of the words (102, 66, 329, and 289) in Fact 12, and put them preceding the words, instead of following them. The resultant number, still 73 digits, is also a multiple of 19:

102 2 1 60 2 40 3 66 1 4 30 5 30 6 5 7 329 1 8 30 9 200 10 8 11 40 12 50 13 289 1 14 30 15 200 16 8 17 10 18 40 19

= 19 x

53797907387691739635038574647852637269158552701521654218526404300536001

FACT 17

For each word of the Basmalah, write down the following:

a) Number of letters in the word

b) The total G.V. of the word

c) The G.V. of each letter in the word

For example, consider the first word of the Basmalah. It has three letters. The total G.V. of these letters is 102. The individual G.V. of each letter are 2, 60, and 40 respectively. Therefore, we write 3 102 2 60 40 for the first word, and so on. The entire number is 48 digits long, and is a multiple of 19. It is given below with the numbers for each word underlined.

3 102 2 60 40 4 66 1 30 30 5 6 329 1 30 200 8 40 50 6 289 1 30 200 8 10 40

= 19 x 16327686340322647664890158951792138363843162160

FACT 18

In Fact 14, the total G.V. of the words are printed in bold. Now, we draw your attention to these bold numbers as we place them as the last item in each underlined word. The resultant number, still 48 digits long, is also a multiple of 19:

3 2 60 40 102 4 1 30 30 5 66 6 1 30 200 8 40 50 329 6 1 30 200 8 10 40 289

= 19 x 17160005390159503505948425476333137527372686331

FACT 19

Let us represent each one of the four words of the Basmalah by the sequence number of the letters in it. For example, the first word is represented by 123, since it has the first three letters of the Basmalah. The second word is represented by 4567 since it contains the letters 4, 5, 6, and 7. Similarly, the third word is represented by 8910111213, and the fourth word by 141516171819, since they contain the letters 8-13 and 14-19 respectively. If we add these four numbers representing the words of the Basmalah, the result is a 12-digit number which is a multiple of 19:

123 + 4567 + 8910111213 + 141516171819= 150426287722 = 19 x 7917173038

FACT 20

Consider the numbers that represented each word of the Basmalah in

Fact 16. Instead of adding these numbers, we write each one down, followed by the sequence number of the word. For example, the first number, 123, which represents the first word, is followed by 1. The second number, 4567, which represents the second word, is followed by 2, and so on. The result is now a 33-digit number, also a multiple of 19:

1 2 3 1 4 5 6 7 2 8 9 10 11 12 13 3 14 15 16 17 18 19 4

= 19 x 6481351204790059017442903248326

Coincidence or Divine Design?

It is very incredible for the four words and the 19 letters of the Basmalah to result in so many numerical combinations based on the number 19. These combinations do not seem to be haphazard either. They are very consistent. For instance, let us look at the numbers in Facts 2 through 9. As you may have noticed, the numbers in these facts are in the same format:

1 ? 2 ? 3 ? 4 ? = n

The numbers 1, 2, 3, 4 represent the four words of the Basmalah. The question marks represent any integer number. The resultant number "n" is a multiple of 19. There are only two possible explanations for these numbers in Facts 2-9 being in this format. One explanation is that all this is coincidence. After all, miraculous things do occasionally occur that cannot be explained easily, if at all. The only other explanation is that the Basmalah has been deliberately structured in a certain way to result in this remarkable mathematical system. Let us try to figure out which explanation makes more sense based on the laws of probability.

First, what is the probability (chances) for the Basmalah's mathematical composition to occur by coincidence? Can we compute this probability? If we can, how? Based on our assumption of coincidental occurrence, we can treat each number in Facts 2-9 as a random number. The probability of several random numbers being not only in a certain format, but also forming a number "n" that is a multiple of 19, can be difficult to compute unless we make some assumptions to simplify the problem. For example, the highest probability (the best chance) of obtaining "n" will be when we assume that the four numbers represented by the question marks above are all single digit numbers (0-9). In that case, the resultant number nª will have 8 digits since we know that the other four numbers are also single digit (1, 2, 3, 4). Then we can easily compute the probability of 8 random numbers resulting in the desired format. Let us see how we can do this.

Imagine that we are playing a lottery. This lottery requires that we draw 8 numbers that are between 0 and 9. Anyone who satisfies the following conditions wins the jackpot:

1. The first number must be 1

2. The third number must be 2

3. The fifth number must be 3

4. The seventh number must be 4

5. All the numbers when put side by side must form a number that is a multiple of 19.

The resultant 8-digit lottery numbers can vary anywhere from 00,000,000 to 99,999,999. This means there are 100 million possible outcomes or combinations (minus 1). How many times will the above winning conditions be satisfied out of this many combinations? If we knew the answer, then we could determine the probability or the chances of winning the lottery. In order to answer this question, we wrote a computer program to go through every number from 0 to 99,999,999 and determine all the numbers that will satisfy the desired conditions. This program found only 527 such numbers which ranged from 10,203,247 (first possible combination) to 19,293,949 (last possible combination). Therefore, the chances of winning this lottery is 527 out of 100 million or 1 out of 189,753.

Based on this information, we can say that the probability of the occurrence of the mathematical phenomenon described in Fact 2, is 189,753 to 1. The probability of the mathematical phenomenon in Fact 2 and Fact 3 occurring by coincidence is the same as winning our lottery twice. To determine the probability of winning the lottery twice, we multiply 189,753 by 189,753:

189,753 * 189,753 = 36,006,201,009

In other words, the probability of the mathematical phenomenon in Fact 2 and Fact 3 occurring by coincidence is less than 1 in 36 billion. In comparison, in the California state lottery where six numbers are drawn out of 51, someone has to buy about 18 million $1 tickets to cover every 6-number combination for the grand prize. Therefore, the chances of winning the California lottery, 1 in 18 million, is much better than the chances of the mathematical phenomenon in Fact 2 and Fact 3 occurring by coincidence. Now, let us try the same process once more, and pick another set of eight numbers that will also meet the winning conditions. To determine the probability of winning the lottery three times, or the probability of the mathematical phenomenon in Fact 2, Fact 3 and Fact 4 occurring by coincidence, we multiply 189,753 by itself three times:

189,753 * 189,753 * 189,753 = 6,832,284,660,060,777

The above number is close to seven quadrillion! If you are wondering what a quadrillion is, you are not alone. We had to look in the dictionary to find out what follows the trillions. Thus, there is an almost 1 in seven quadrillion probability that Fact 2, Fact 3, and Fact 4 will occur by coincidence. As you can see, by considering just three of several mathematical facts, we realise that the probability of such numerical combinations occurring by coincidence is extremely minuscule. It is very clear that this probability will approach zero as we take more and more mathematical facts into consideration. Therefore, one would be illogical to even suggest that the mathematical composition of the Basmalah is nothing more than a mere coincidence.

If we rule out the possibility of coincidence, then we have to accept the other explanation that the Basmalah has been deliberately structured in a particular way to result in this remarkable mathematical system. Can we also rule out the possibility for such an intricate system being designed by any other than God?

The Missing Basmalah

The Basmalah occupies a special position in the Quran. It is the opening statement in every one of the 114 Suras in the Quran, except Sura 9. The absence of the Basmalah from Sura 9 had puzzled generations of people who had studied the Quran for the last 14 centuries. In fact, many theories were advanced to explain this phenomenon. As it turns out, this is also a part of the mathematical composition that has been intricately built into the Quran.

Since the Quran consists of 114 (19 x 6) Suras, the Basmalah missing from Sura 9 should result in a total of 113 Basmalahs in the Quran, a number that is not a multiple of 19.

However, if we start counting with Sura 9 being our first counted Sura, we find that Sura 27 will be the 19th counted Sura in the sequence. In Sura 27 we find an extra Basmalah. The first Basmalah is at the beginning of the Sura and the second Basmalah is found in verse 30. Thus, the total number of Basmalahs in the Quran is restored to 114 (19 x 6), with the additional Basmalah in Chapter 27. We also note that the sum of the Sura number (27) and the verse number (30) is 57 (19 x 3).

The connection between the missing and the extra Basmalah leads us to deliberate further on the mathematical design of the Quran. If we add the Sura numbers starting from Sura 9 (with the missing Basmalah) up to Sura 27 (with the extra Basmalah), the total is 342 (9 + 10 + 11 + ... + 27 = 342). This total is a multiple of 19, as it should be, since the sum of any 19 consecutive numbers is a multiple of 19. However, what is remarkable is that if we count the number of Arabic words from the first Basmalah in Sura 27 to the second one in verse 30 of the same Sura, we find that the total is also 342 (19 x 18).
The above patterns are the subject of the next 2 Facts.

Fact 21
There are 19 Suras from the missing Basmalah in Sura 9 to the extra one found in Sura 27 (both chapters inclusive).

Fact 22
The extra Basmalah is found in Sura 27, verse 30. These two numbers add up to 57, or 19 x 3.

Fact 23
The number of Arabic words from the first Basmalah in Sura 27 to the second one in verse 30 of the same Sura is 342, or 19 x 18. This is the same number obtained if we add all the chapter numbers from Chapter 9 (with the missing Basmalah) through Chapter 27.

A Unique Phenomenon

As stated earlier, every Sura in the Quran starts with a Basmalah, except Sura 9. However, none of these Basmalahs are assigned a verse number, except in Sura 1 where the Basmalah is in verse 1. Yet, the unnumbered Basmalahs are part of the Quran. The fact that they are unnumbered is also part of the mathematical composition of the Quran. To demonstrate this point, we assign a verse number of zero to each one of the unnumbered Basmalahs so that they can be included in our study.

Fact 24
Let us combine (put together) the Sura number with the verse number where the Basmalah occurs, for each of the 114 Basmalahs in the Quran, and add up all the combined numbers. The concept of combined numbers will be explained below with the examples.

The first Basmalah occurs in Sura 1, verse 1. The combined number for this Basmalah is 11 obtained by putting the two numbers (1 and 1) side by side. The second Basmalah occurs in Sura 2, verse 0. The combined number for this Basmalah is 20. If we add these two combined numbers, 11 and 20, we get 31. We continue this process for each chapter. We skip Sura 9 since it does not have a Basmalah. On the other hand, we include Sura 27 twice since there are two Basmalahs in this Sura; one in verse 0, the other is in verse 30. The combined numbers for this Sura are 270 and 2730, representing the two Basmalahs in this Sura.The last Basmalah occurs in Sura 114, verse 0. The combined number for this Basmalah is 1140. By adding up all of the 114 combined numbers, we get a total of 68,191 or 19 x 3,589. This process is demonstrated in Table 6.

Table 6.

Mathematical system of adding the combined numbers

of Sura and the verse number where the 114 Basmalahs occur

Chap. No.	Basmalah Verse No.	Combined No.
1	1	11
2	0	20
3	0	30
-	-	-
-	-	-
-	-	-
8	0	80
10	0	100
-	-	-
-	-	-
27	0	270
27	30	2730
-	-	-
-	-	-
112	0	1120
113	0	1130
114	0	1140

TOTAL

68191 = 19x3589

What is remarkable about the above phenomenon is that the 19-based mathematical relationship holds true also when we repeat the same process using only the odd or even numbered chapters. The resultant total for the odd numbered Suras is 35,131 (19 x 1,849). The total for the even numbered Suras is 33,060 (19 x 1,740).

The Four Words of the Basmalah

The frequency of occurrence of every (Arabic) word of the Basmalah in the entire Quran (excluding the unnumbered Basmalahs) is consistently a multiple of 19. These words are ISM, ALLAH, AL-RAHMAN, and AL-RAHEEM. Their English meanings are NAME, GOD, ALMIGHTY, and MERCIFUL, respectively. Note that we are using ISM (Name) as the first word of the Basmalah, instead of the word BISM (In the name). In other words, we are using the root word without the prefix B (In the) in this counting. Table 7 below summarises the mathematical facts based on the number of occurrences of the Basmalah's words.

Table 7.

The four words of the Basmalah and

their number of occurrences in the Quran

Word No.	Arabic	English	No. of Occurence
1	Ism	Name	19
2	Allah	God	2698 (19x142)
3	Al-Rahman	Most Gracious	57 (19x3)
4	Al-Raheem	Most Merciful	114 (19x6)

Now, let us itemise the facts summarised in Table 7 with the additional facts that make the mathematical system in the Quran even more incredible:

Fact 25
The first word in the Basmalah, ISM (Name), occurs in the Quran exactly 19 times. The verses where this word is mentioned are given in Table 8.

Fact 26
Using the information in Table 8, let us write down the Sura number followed by the verse number in which the word ISM (Name) occurs for each one of its 19 occurrences, without repeating the Sura number if there are more than one ISM in that Sura. The resultant number is 58 digits and is a multiple of 19. This is shown below with the Sura numbers printed in bold:

5 4 6 118 119 121 138 22 28 34 36 40 49 11 55 78 56 74 96 69 52 73 8 76 25 87 1 15 96 1 = 19 x 2874305890111 ...

Table 8.

The chapter and the verse numbers where

the word ISM (Name) occur in the Quran

No.	Chapter No.	Verse No.
1	5	4
2	6	118
3	6	119
4	6	121
5	6	138
6	22	28
7	22	34
8	22	36
9	22	40
10	49	11
11	55	78
12	56	74
13	56	96
14	69	52
15	73	8
16	76	25
17	87	1
18	87	15
19	96	1

Fact 27
The word ISM (Name) with the prefix B (In the) makes the word BISM (In the name). This word occurs in the Quran in this particular spelling only 3 times; in Sura 1, verse 1; Sura 11, verse 41 and Sura 27, verse 30. If we add the number of occurrence of this word (3), to the numbers of the chapters and the verses where the word is found, the total equals exactly to the number of chapters in the Quran:

3 + 1 + 1 + 11 + 41 + 27 + 30 = 114 (19 x 6)

Fact 28
The second word of the Basmalah, ALLAH (God), is mentioned in the Quran 2,698 (19 x 142) times.

Fact 29
The numbers of the verses where the word ALLAH (God) occurs add up to 118,123 (19 x 6,217). To determine this, we start from the beginning of the Quran, and check each verse for the occurrence of the word "God". If "God" is mentioned in that verse, whether once or more than once, we add the number of the verse to our total.

Fact 30
The third word of the Basmalah, AL-RAHMAN (Almighty), is mentioned in the Quran 57 (19 x 3) times.

Fact 31
The fourth and the last word of the Basmalah, AL-RAHEEM (Merciful), is mentioned in the Quran 114 (19 x 6) times.

Correlation with the Attributes of God

Professor Cesar Majul (1983) looked at the G.V. of the attributes of God, and discovered that there are only four attributes of God whose G.V. are a multiple of 19. This is summarised in Table 9 below.

Table 9.

The attributes (names) of God whose

G.V. are a multiple of 19

	Attribute of God	G.V.
1	Waahed (One)	19
2	Zul Fadl Al-Azim (Possessor of Infinite Grace)	2698 (19x142)
3	Majeed (Glorious)	57 (19x3)
4	Jaami (Summoner, Gatherer)	114 (19x6)

We can see from Table 7 and Table 9 above that the only attributes of God whose G.V. are multiples of 19 correspond exactly to the frequencies of occurrences of the Basmalah's four words. Let us summarise these mathematical facts:

Fact 32
The first word of the Basmalah, ISM (Name), occurs in the Quran 19 times, and the number 19 represents God's attribute WAAHED (One). The G.V. of the four Arabic letters in the word WAAHED are 6, 1, 8, and 4. These numbers add up to 19. Thus, 6 + 1 + 8 + 4 = 19 = WAAHED (One)

Fact 33
The second word of the Basmalah, ALLAH (God), occurs in the Quran 2,698 (19 x 142) times, and the number 2,698 represents God's attribute ZUL FADL AL- AZIM (Possessor of Infinite Grace). The G.V. of the 13 Arabic letters in this attribute of God are 700, 6 , 1, 30, 80, 800, 30, 1, 30, 70, 900, 10 and 40. These numbers add up to 2,698. Thus,

700 + 6 + 1 + 30 + 80 + 800 + 30 + 1 + 70 + 900 + 10 + 40= 2698 (19 x 142) = ZUL FADL AL- AZIM (Possessor of Infinite Grace)

Fact 34
The third word of the Basmalah, AL - RAHMAN (Almighty), occurs in the Quran 57 (19 x 3) times, and the number 57 represents God's attribute MAJEED (Glorious). The G.V. of the four Arabic letters in the word MAJEED are 40, 3, 10 and 4. These numbers add up to 57. Thus, 40 + 3 + 10 + 4 = 57 (19 x 3) = MAJEED (Glorious)

Fact 35
The fourth and the last word of the Basmalah, AL RAHEEM (Merciful), occurs in the Quran 114 (19 x 6) times, and the number 114 represents God's attribute JAAMI (Summoner, Gatherer). The G.V. of the four Arabic letters in the word JAAMI are 3, 1, 40 and 70. These numbers add up to 114. Thus,

3 + 1 + 40 + 70 = 114 (19 x 6) = JAAMI (Summoner, Gatherer)

Conclusion

The Quran's intricate numerical structure, based on the number 19, starts at its very first verse, the Basmalah, indicating to the reader of the Quran at the outset that he is reading the word of God. However, what is presented to you so far is a small fraction of this indescribably vast, elaborate mathematical system which extends all the way to the end of the Quran.

Acknowledgements

All praise and thanks are due to God who has allowed me to work on this project. I would like to acknowledge the work of Dr. Rashad Khalifa who discovered the existence of the 19-based mathematical system in the Quran.

Through his efforts and encouragement before he was killed on January 31, 1990, many individuals began research on the Quran's mathematical system. Based on this research, some individuals were blessed to discover different portions of this system by God's will. I would like to thank Professor Cesar Majul and brother Sharif of Egypt for their contribution to this particular volume.

For the editorial assistance, I am grateful to the following individuals: Gatut Adisoma, Donna Arik, Douglas Brown, Shakira Karipineni, Lydia Kelly, Lisa Spray, and many others in Masjid Tucson. May God bless them all.

References

Dan, J. and Talmage, F., eds, (1982), STUDIES IN JEWISH MYSTICISM, Association for Jewish Studies, Cambridge, Massachusetts.

Khalifa, R., (1973), MIRACLE OF THE QURAN: Significance of the Mysterious Alphabets, Islamic Productions, St. Louis, Missouri.

Khalifa, R., (1981), THE COMPUTER SPEAKS: God's Message to the World, Renaissance Productions, Tucson, Arizona.

Khalifa, R., (1982), QURAN: Visual Presentation of the Miracle, Islamic Productions, Tucson, Arizona.

Khalifa, R., (1989), QURAN: The Final Testament, Islamic Productions, Tucson, Arizona.

Majul, C. A., (1983), The Names of Allah in Relation to the Mathematical Structure of Quran, Pamphlet, Islamic Productions, Tucson, Arizona.

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