*In the name of God, Most Gracious, Most Merciful*

##### Mathematical Miracle of God in Quran’s H.M. initialed Suras based on # 19: Impossible to imitate.

- Some Background, Summary of the Miracle, and Challenge
- The Requirements for Variables
- Conditions for Conforming with the 19-based Quranic Structure
- What is involved in solving this 19-linked challenge?
- How will this change with improving computing speeds?
- Appendix: Verifying the Arabic Text of Chapters 40-46

**(I) Some Background, Summary of the Miracle, and Challenge:**

The Quran is characterized by a unique phenomenon never found in any human authored book. Every element of the Quran is mathematically composed beyond human capability. Even with the fastest supercomputer available today, it would take over a **trillion years** (many times longer than the current estimated age of the universe) to even partially replicate the numbers in one set of initialed chapters (Suras) in the Quran.

At the time of the revelation of the Quran, there were no computers. The H.M. component of the mathematical miracle is one piece of a much larger proof. Further, this does not include the computing cost of putting the letters together as part of meaningful sentences and verses across 7 chapters of the Quran.

**The trillion-year time estimate is based on looking only at a subset of the actual numbers involved as explained in this document.** Even with increasing computing speeds, the challenge remains impossible in the foreseeable future. Please see section V(v) of this document for more details.

*Mathematical Challenge *

[2:23] If you have any doubt regarding what we revealed to our servant,* then produce one sura like these, and call upon your own witnesses against **GOD**, if you are truthful. **2:23-24 The Quran’s miraculous mathematical code provides numerous proofs as it spells out the name “Rashad Khalifa” as God’s servant mentioned here. Some literary giants, including Al-Mutanabby and Taha Hussein, have answered the literary challenge, but they had no awareness of the Quran’s mathematical composition. It is the Quran’s mathematical code, revealed through God’s Messenger of the Covenant, Rashad Khalifa, that is the real challenge ― for it can never be imitated. See Appendices 1, 2, 24, & 26 for the detailed proofs.*

[11:1] A.L.R. This is a scripture whose verses have been perfected, then elucidated.* It comes from a Most Wise, Most Cognizant.* *11:1 Our generation is fortunate to witness two awesome phenomena in the Quran: (1) an extraordinary mathematical code (Appendix 1), and (2) a literary miracle of incredible dimensions. If humans attempt to write a mathematically structured work, the numerical manipulations will adversely affect the literary quality. The Quran sets the standard for literary excellence.*

The verse translations are from Quran: The Final Testament, Authorized English Version by Rashad Khalifa, Ph.D.. This is available for free down load at: http://www.masjidtucson.org/downloads/qe/index.html or http://www.submission.info/downloads/qe/index.html . Or for online viewing at: http://www.masjidtucson.org/quran/

To summarize, a grid based super-computer operating at petaflop speeds (quadrillion operations per second), would take trillions of years (many times longer than the universe’s age: http://en.wikipedia.org/wiki/Age_of_the_universe) to replicate the mathematical structure of one set of Quranic chapters, prefixed by the initials H and M. This does not factor in the need for literary excellence, nor the words and chapters that contain meaningful passages with religious enlightenment, to go along with the mathematical structure.

Chapters 40 – 46 of the Quran are prefixed with the initials H and M (in Arabic *Hã* and *Mîm*). Other initials prefix various chapters (suras) of the Quran (please see Appendix 1 of the Quran at http://www.masjidtucson.org/quran/appendices/appendix1verify.html for details). The role of the Quranic initials is summarized in Quran 10:1 (and other verses as well).

*[10:1] A. L. R.* These (letters) are the proofs of this book of wisdom. *10:1 These letters constitute a major portion of the Quran’s awesome mathematical code and proof of divine authorship. See Appendix 1 for details.*

In sura 11 verse 13 of the Quran, we see a mathematical challenge that proves that the Quran’s authorship is far beyond human capability. Please note also that at the time of revelation of the Quran (AD 610), and establishment of all its parameters, there were no computers. Yet this challenge is open to all generations.

*The Quran: Impossible to Imitate*

[11:13] If they say, “He fabricated (the Quran),” tell them, “Then produce ten suras like these, fabricated, and invite whomever you can, other than **GOD**, if you are truthful.”* **11:13 The Quran’s mathematical miracle is inimitable (See Appendix 1).*

Let us consider just the contiguous block of chapters from 40-46 (seven chapters) having initials H and M as the first verse. In aggregate, the total frequency of these initials in the seven chapters is 2147 or 19×113. The counts of these initials in the seven chapters along with the challenge of coming up with the specific values of H and M that appear in each of the chapters is summarized in Table 1. The part of this Table in italics is a sample of the challenge from the Arabic Quran.

**Table 1: The H.M. Counts**

Challenge |
An illustration of the inimitability inthe Arabic Quran |
|||||||

Col | Col 1 | Col 2 | Col 3 | Col 4 | Col 5 | Col 6 | Col 7 | Col 8 |

Row | Sura |
Letter Count ”H” |
LetterCount “M” |
Digits addition of H+M |
Total count of H+M |
|||

R-A | A1 | A2 | Digit Sum (A1, A2) | 40 | 64 | 380 | 21 | 444 |

R-B | B1 | B2 | Digit Sum (B1, B2) | 41 | 48 | 276 | 27 | 324 |

R-C | C1 | C2 | Digit Sum (C1, C2) | 42 | 53 | 300 | 11 | 353 |

R-D | D1 | D2 | Digit Sum (D1, D2) | 43 | 44 | 324 | 17 | 368 |

R-E | E1 | E2 | Digit Sum (E1, E2) | 44 | 16 | 150 | 13 | 166 |

R-F | F1 | F2 | Digit Sum (F1, F2) | 45 | 31 | 200 | 6 | 231 |

R-G | G1 | G2 | Digit Sum (G1,G2) | 46 | 36 | 225 | 18 | 261 |

292 |
1855 |
113 |
2147(19x113) |

In this table, the columns are numbered C-1 through C-8, and the rows R-A through R-G.

The specific challenge is to come up with values for the table elements A1, A2, B1, B2, … G1, G2 (shaded yellow) so that the combination of existing numerical patterns is preserved. The existing counts of the initials in 40-46 are seen in columns 5-6, rows A-G (shaded green). Column C-7 is obtained by adding the digits of the H and M occurrence for that corresponding sura. So for sura 40, we see 64 Hs and 380 Ms, and (6 + 4) + (3 + 8 + 0) = 21. The corresponding challenge column is C-3.

##### (II) The Requirements for variables A1-G2:

1. *The sum of values in column C-3 (which is derived by adding the digits of the corresponding solution in C-1 and C-2) for rows A,B,C =21+27+11=59. 21, 27 and 11 are the specific solutions found in the Quran, however the challenge simply requires the numbers to add to 59.*

2. *The sum of values in column C-3 for rows* **D,E,F,G** = **54** (17+13+6+18).

3. *The sum of the values in C-3 for rows*** B,C,D** = **55** (27+11+17).

4. *The sum of the values in C-3 for rows* **A,E,F,G** = **58** ( 21+13+6+18).

##### (III) Conditions for Conforming with the 19-based Quranic structure:

1. The sum of the numbers in C8 for rows** A,B,C** are a multiple of 19.* In the Arabic Quran, the sum comes to 1121=19x 59 – compare with (1) above.*

2. The sum of the numbers in C8 for rows **D,E,F,G** are also a multiple of 19. *In the Arabic Quran, the sum comes to 1026=19x 54 – compare with (2) above.*

3. The sum of the numbers in C8 for rows** B,C,D** are a multiple of 19.* In the Arabic Quran, the sum comes to 1045=19x 55 – compare with (3) above.*

4. The sum of the numbers in C8 for rows **A,E,F,G** are also a multiple of 19. *In the Arabic Quran, the sum comes to 1102=19x 58 – compare with (4) above.*

##### (IV) What is involved in solving this 19-linked challenge?

As any computer scientist will tell you, the following steps are involved in developing an algorithm to solve the challenge.

Since no single-digit combinations would satisfy the criteria listed in the “Requirements” or “Conditions” section, let us assume that the solution values involve 2 digit numbers and work on that basis (i.e., assuming values under 100). When it does not work out and no matching result found, we could switch to a 3-digit solution (limiting number: 1000).

Since the total count of the 7 H’s & 7 M’s (7+7=14) across the chapters is 2147, we can place an estimate that on average each cell value is (2147/14) = approximately 150.

*What is the cost of such a search?
*Suppose there we just 2 cells labeled A and B (instead of 14 cells). Since we don’t know exactly what number is in each cell, we’ll write our program to try all numbers from 1 – 150 in each cell. So it would start with the number 1 in A, and the number 1 in cell B. Since that won’t work, we’ll keep the 1 in A, and increment to a 2 in cell B. If that doesn’t work, then we’ll try a 3 in cell B. Until we’ve tried 150 numbers in cell B. Next we’ll change cell A to the number 2, and try 150 combinations in cell B. In total our program tries 150 combinations in A, and for each of those 150 numbers, we’ll try 150 different numbers in B. In total we’ll be trying 150 x 150 = 150

^{2}combinations. Similarly, if there were 3 cells, we’d be trying 150 x 150 x 150 = 150

^{3}combinations.

When we have 14 cells, we will write 14 nested loops in our program. This gives us a total of 150^{14} numerical combinations (i.e., 150^14) = (2.9 x 10^{30})

[where ^ denotes to the power of, i.e., 150^14 means 150^{14}].

Next we must add some factor for the cost of each combination. Each time we come up with a new combination in the 14 cells, we perform the 84 digit additions (*see requirements* 1-4 above) and 28 number additions (*see conditions* 1-4 above). This gives us (84+28) = 112. Assume that the cost of these operations is fixed at one unit of computation time, in programming terms: one floating point operation. On average let us say we only perform 25% of the operations because if any of the checks fail we will probably not try the next.

So, let us say in each iteration, or trial, the cost of the algorithm is: 0.25 * 112 = 28.

For the total run of the program, the cost is: 28 * 150^{14} = 8.17 * 10^{31} operations [where * denotes multiplication].

*How long will it take?
*We have the number of operations from the previous paragraphs. Now we need to divide by number of operations a computer performs per second. And then by the seconds in a year.

Assume a computer can perform 1 trillion operations /second. To find out how long that computer would take to solve our problem, we divide the number of operations (8.17 x 10^{31}) by 1 trillion

(10^{12}). So we get:

= (8.17 * 10^{31})/ ( 10^{12})

= 8.17 * 10^{19}

The above number is in seconds. To find how many years those number of seconds take, we further divide the result above by the number of seconds per year. The number of seconds in a year is:

(60 seconds * 60 min * 24 hour * 365.25 days) = 3.16 x 10^{7}

= 8.17 * 10^{19} / 3.16 * 10^{7
}= 2.59 * 10^{12} years

We know however, that solutions going only up to 150 will not work. We also know that with grid computing, we now have speeds of petaflops instead of teraflops. So, a more accurate estimation of the cost would be as follows. Let us assume our 14 nested loop counters go from 1-500 instead of 1-150.

This means, our operation cost estimate is:

28 x 500^{14} = 1.71 * 10^{39
}

Strictly speaking, the last iteration we will not go up to 500 for cell A1, instead only to 64. So that the time reduces slightly to:

28 * ( 64 * 500^{13}) = 2.19 * 10^{38}

Let us assume we have a super computer operating at 10 petaflops, i.e., 10 quadrillion operations per second (more on this in the next section). In other words, the computer performs 10^{16} operations per second.

This means, the time taken is:

(2.19 x 10^{38 }) / (10^{16}) = 2.19 x 10^{22} seconds

As before, let us divide by number of seconds in a year:

(2.19 x 10^{22}) / (3.16 x 10^{7}) = 6.93 x 10^{14} years

**(V) How will this change with improving computing speeds?**

(i) Let us assume that we are using the Fastest Grid-Computing (Distributed Systems) described by Wikipedia below:

* “Folding@home is the most powerful distributed computing cluster in the world, according to Guinness, and one of the world’s largest distributed computing projects. The goal of the project is “to understand protein folding, misfolding, and related diseases.”*

http://en.wikipedia.org/wiki/F@H

Processing speed is about 5 petaFLOPS (5 x 10^{15} = 5,000,000,000,000,000 floating point operations per second) i.e., 5,000 trillion operations per second.

(ii) Computation speeds continue to increase, and have increased by a factor of a million during the past 20 years.

The well-known Moore’s law tells us that computing power doubles every two years. Wikipedia estimates that this is likely to slow down from 2013 and double every three years (http://en.wikipedia.org/wiki/Moore%27s_law ). Let us assume it will continue to double every two years (instead of 3). So if we extrapolate for the next 100 years, i.e., we get a doubling of power 50 times. What this means is we are likely to see a rise of 2^{50} increase in the processing power in a hundred years. Or 1.13 x 10^{15} increase in processing power. So it will not be for another 100 years before we can solve the problem in under a year. If Wikipedia’s estimate for slowing increase in computing power is correct, we are looking at a longer time frame. But why are we presenting all this information? Let us take a moment to reflect on the next point.

(iii) The Quran was sent down over 1400 years ago. There were no computers at that point. This points out the impossibility of any human being having creating the mathematical code. The simplest and only logical explanation of this mathematical code is that the author of the Quran is Almighty God. Mind you, the table is just the count of two letters. It does not take into account the other aspects of the Quran’s miraculous mathematical code, nor the requirement of shaping these letters are parts of words, phrases and passages that make coherent sense and contain spiritual wisdom.

**(iv) The computation discussed above is a physical fact based on programming loops and computation cycles. One need not know Arabic to physically check the H & M initials Table alongside this challenge.**

(v) Further, even the above subset does not consider the Quran’s literary excellence, consistent statements, advocating of righteousness, focus on submission to God Alone, narrations of historical facts and the like. Of course, this is over and above the fact that Chapter 42 has another Mathematical miracle in its second verse, the letters: ‘A.S.Q. which are part of another series of proofs. The various letters, words and verses in chapters 40 – 46 also participate in numerous other Mathematical Miracles of 19 as can be verified in Appendices 1, 2, 24, 26 at http://www.masjidtucson.org/quran/appendices/; and at http://www.masjidtucson.org/quran/appendices/appendix1verify.html, http://www.masjidtucson.org/quran/appendices/appendix2verify.html, http://www.masjidtucson.org/quran/appendices/appendix24verify.html

Praise be to God, Lord of the Universe.

##### (VI) Appendix: Verifying the Arabic Text of Chapters 40-46

One may have the Arabic text verified: The H-M initialed Suras with color-highlighted H & M can be verified from http://www.19miracle.org/math-miracle-of-quran/ – Sura 40, Sura 41, Sura 42, Sura 43, Sura 44, Sura 45, Sura 46.

**(The Arabic text of the above is from an external source: tanzil.net)**

It can also be verified by downloading from:

http://www.19miracle.org/hm/HM-color-coded.zip or verified individually:

Suras: 40.html, 41.html, 42.html, 43.html, 44.html, 45.html, 46.html

(The Arabic text of the above is displayed correctly in Internet Explorer; also in Firefox & other browsers – but in smaller fonts – so one may enlarge these using Control and +).

The Arabic can also be verified from pages 122 to 147 from “Quran: Visual Presentation of the Miracle” – Rashad Khalifa, Ph.D., 1982″ – i.e., Fact 31 http://www.masjidtucson.org/publications/books/vp/ http://www.masjidtucson.org/publications/books/vp/fact31.pdf.

This is the Section / Fact 31 titled:

Seven chapters are initialed with the 2 letters “HH” and “M”, namely, Chapters 40 through 46. The total frequency of occurrence of these two letters in the seven chapters is 2,147, and this number is a multiple of 19.