Debunking the odd-even mathematical miracle in the Qur’an


By Martin Taverille


Other articles on this site
Dhu’l Qarnayn and the muddy spring in Qur’an 18:86 – New Evidence
Dhu’l Qarnayn and the muddy spring – Shorter version
Greek and Jewish ideas about reproduction in the Qur’an and Hadith


Introduction to the “miracle”

The Qur’an contains 114 surahs, or chapters, and each surah is further divided up into ayats, or verses, so that all together, there are 6236 ayats in the Qur’an. There is a widely spread claim circulating on the web[1] that there is a “mathematical miracle” in the Qur’an concerning the sums of the surah numbers, and the sums of the ayats, or verses. It is sometimes called a binary, odd-even, or checksum miracle. It supposedly consists of two apparently remarkable coincidences.

For each surah, I will call the sum of its surah number and the number of ayats it contains as the surah’s “s+a number”. The surahs whose s+a number is odd go into the odd s+a group and the surahs whose s+a number is even go into the even s+a group.

The sum of the s+a numbers in the odd group is 6555, the sum of the surah numbers in the Qur’an. The sum of the s+a numbers in the even group is 6236, the sum of the ayat numbers in the Qur’an.

In this article, I will show that these properties of the numbering of the Qur’an are in fact something much more simple and far less unlikely than it at first seems, and why it is perfectly plausible that it happened by chance, without any deliberate intention, whether divine or human.

1 coincidence, not 2

Before beginning, it’s well worth pointing out that the number of ayats into which the Qur’an is divided was not part of Muhammad’s “revelation” (I’m talking here about the numbering, not the text itself or its ordering). Rather there were different systems of dividing up the surahs into ayats (6000, 6204 etc.), and the 6236 divisions devised by the Kufah school simply became most popular.[2]

The first thing to notice is that added together, the sum of the even s+a numbers plus the sum of the odd s+a numbers must equal the sum of all the surah numbers plus all the ayats in the Quran (since every surah belongs to one of the two groups). Thus if one group = the sum of the surahs, it just follows trivially that the other group must = the sum of the ayats. One half of the “miracle” automatically implies the other. We can further deconstruct things from another angle. We can simply state the “miracle” as follows:

1. Total surah numbers + ayats in odd s+a group = total surah numbers

6555 = 6555

2. Total surah numbers + ayats in even s+a group = total ayats

6236 = 6236

Each surah belongs either to the odd s+a group or the even s+a group. If we subtract all the surahs numbers belonging to the odd s+a group from both sides of the first equation, we can see that it becomes:

Total ayats in the odd s+a group = total surah numbers in the even s+a group

If we then subtract all the ayats belonging to surahs in the even s+a group from both sides of the second equation we can see that it becomes:

Total surah numbers in the even s+a group = total ayats in the odd s+a group

Swap the sides of this equation round and you’ll see that it is identical to the other equation. To illustrate visually:

Thus both apparent coincidences just simplify to a single one because both in fact count the same quantity as part of each side of its equation. They are not two independent coincidences. They both follow trivially from a single quite mundane coincidence: Total ayats in the odd s+a group = total surah numbers in the even s+a group. Specifically, that number is 3303. And no, 3303 is not divisible by 19 in case you were wondering! 😉

It’s worth noticing that it makes no difference whether you define the two groups based on odd and even numbers or any other selection criteria so long as the total ayats in one group of surahs = total surah numbers for the rest of the surahs. The two apparent coincidences follow simply from that fact.

Incidentally, it is sometimes claimed that the distribution of ayats has to be exactly as it is for the “miracle” to work, and thus it supposedly has a useful function as a sort of checksum against change (in the numbering at least). However, there are many ways that the total number and distribution of ayat numbers could be different without affecting this property. For example, you could add or subtract any multiple of 2 to the number of ayats of any surah in the even s+a group. Another is that for 2 even numbered surahs, you could swap their number of ayats if both are even or both are odd. The same for 2 odd numbered surahs. I have created an Excel spreadsheet so you can try this for yourself if you wish.

How remarkable is this coincidence?

Even by the most basic consideration at the start of the previous section we saw that one half of the “miracle” automatically implies the other. We further saw by putting it another way that its proponents unwittingly count the same quantity within both sides of each equation so it is in fact just two versions of the same equation, the same single coincidence. And as we shall see due to various factors, the likelihood of its occurance by chance is not so low that anyone should be impressed by it and proclaim it a miracle!

The sum of the ayats (which range from 3 to 286, skewed such that the higher numbers are less frequent) is approximately the same as the sum of the surah numbers (which range from 1 to 114, uniformly distributed), 6236 and 6555 respectively. Thus (and as further explained below) it is not particularly remarkable that you can use some criteria to select approximately half the surahs (as this process does – exactly half as it happens), and find that the sum of those surah numbers = the sum of the other half’s ayats (3303 is approximately half of 6236 or 6555).

Even if your selection turns out to be weighted toward the higher numbered surahs, then the ayats of the other surahs will similarly be weighted toward the higher numbers (since the surahs tend to be ordered such that as the surah number increases, the number of ayats per surah decreases). So there is a rough correlation – they are not independant variables. Almost whatever your selection of half the surahs, the sum of their numbers will roughly correlate with the sum of the other surahs’ ayats.

If the selection criteria that is used by the miracle seekers hadn’t found a coincidence, there are many other options for selecting around half the surahs and people could have tried them instead (for example odd numbered surahs, surahs with an odd number of ayats, odd letters in the surah name, odd surah number multiplied by ayats etc.).

We should also bear in mind that for each way of dividing the surahs into two halves, you have two chances to find a match: your “odd” group might = the sum of all surahs and the “even” group = the sum of all ayats, or alternatively, your “odd” group might = the sum of all ayats and the “even” group = the sum of all surahs.

Using computer simulations with random numbers and a similar distribution of ayats as we have in the Qur’an, I found that the odds of finding a match after randomly selecting half the surahs are approximately 1 in 170. See the endnotes for the vbscript I used.[3] If there is a 169 in 170 chance that a selection criteria will not give a match, then 1 – (169/170)^n  gives the probability that you will find a match with n attempts using random selection criteria. For example, there is a 0.057 probablity (1 in 17 chance) of getting a match trying 10 selection criteria. Of course, if you succeed that does not mean that there is a 16 in 17 chance that you have found a miracle. Otherwise every unlikely event would be a miracle. Unlikely things happen all the time.

We must consider that huge amounts of man-hours have been spent looking for numerical patterns in religious books, so try hundreds or thousands of possible patterns and coincidences, including this kind, and it is likely that you will find some. If the numbering had been very different, then obsessive numerologists would have found some different numerical “miracles” instead. One should bare in mind that miracle seekers do not have any prior hypothesis predicting a specific pattern, but rather just that there will be *some* kind of numerical pattern, fulfilled prophecy etc., and thus they commit the Texas Sharpshooter Fallacy.

Martin Taverille

Addendum:Some of the commenters below completely misunderstood the point in this article and went off on a tangent that is beside the point, suggesting that it would be extremely complex for someone to have intentionally given the numbering of the Qur’an this feature. In fact, I actually said this feature of the Qur’an was simply an unintentional coincidence, (and explained factors that boost its likelihood of occurance) so the difficulty or otherwise of deliberately manufacturing it is therefore irrelevant. However, for the interest of these people I have explained below in a comment dated June 17 2012 a simple process that someone could follow to deliberately implement these properties, which as I demonstrated in the article, both follow trivially from a match between just a single pair of numbers. I explain in the comment a simple process (without at all changing the text itself) to adjust the number of ayats into which the surahs are divided to make the single pair of numbers match if they didn’t already, which would in turn thus give that Qur’an the 2 pairs of matching number feature.

I have just added this explanation in the comment for interested readers since all the comments that have attempted to contest the article have for some reason focused on how it could have been done by a human deliberately. I don’t argue that it was deliberate in my article. I regard that question as an interesting, but distracting irrelevance. If, as I argued, this property of the numbering system was an unintended coincidence, which is very plausible due to various conducive factors that I explained, then it is utterly irrelevant how hard it would have been for a human to implement it deliberately (though as I explain in the comment, it would be a surprisingly simple process).


Other articles on this site

Dhu’l Qarnayn and the muddy spring in Qur’an 18:86 – New Evidence
Dhu’l Qarnayn and the muddy spring – Shorter version
Greek and Jewish ideas about reproduction in the Qur’an and Hadith


Endnotes and references

[1]It seems to have come originally from a book in Arabic by a Jordanian researcher named Abdullah Jalghoom.
[3] Here’s my (probably inefficient) vbscript code. You can control how many selection criteria you want to test with numPasses. With 10000 it takes around 20 seconds on my slow computer.
dim i
dim s
dim selection(56)
dim ayats(113)
dim c
dim randomSura
dim sumSelectedSuras
dim totalAyats
dim sumUnselectedAyats
dim pass
dim matches
dim numPasses
dim stats(3248)

totalAyats = 0
matches = 0
numPasses = 10000

'populate array with similar skewed
'distribution of ayats to that of the Quran

for i = 0 to UBound(ayats)
   'ayats(i)=114-i   'uncomment to test that there are 100%
                     'matches when ayats are a mirror image of suras
   totalAyats = totalAyats + ayats(i)

'see if we get a match using random selection of suras
for pass = 1 to numPasses
   s = 0
   sumSelectedSuras = 0
   sumUnselectedAyats = 0

   'populate array with random distinct sura numbers
   do while s < 57
      randomSura = Int(114 * Rnd())+1

      'check through array to avoid adding duplicates
      c = 0
      do while c <= s - 1
         if randomSura = selection(c) then
            exit do
         end if
         c = c + 1
      if c = s then
         selection(s) = randomSura
         sumSelectedSuras = sumSelectedSuras + randomSura
         s = s + 1
      end if

   s = 0
   sumUnselectedAyats = totalAyats

   'subtract ayats in the selected suras from the total
   'to get the sum of ayats in unselected suras
   do while s  0 then
   wscript.echo matches & " matches out of " & numPasses & _
   " = 1 in " & numPasses/matches
   wscript.echo "0 matches out of " & numPasses
end if
  1. Rahimtullah.M.Bijaputre

    Excellent information

  2. Hi
    There are now many many websites showing the miracle of the Quran. In my opinion is the most accuarate, ie they are include what they are 100% sure about, and where no one has challenged them (maybe you would like to?!)
    The Quran is unlike ANY book in the universe, For 1400 plus years, it was ‘simply’ the language, poetry, style, then it was the science in the Quran, then on further Studying, we noticed incrediable (beyond human capability) Symmetrical wonders, THEN the Miracle 19. AND going back to the language, all this done in the most beautiful poetic way!!

    Please can you give me ONE book that (i will not be unfair) has 1, yes ONE percent of what the Quran has?

    ‘there is no compulsion in religon’ you may be happy being whatever you are?? but trying to deny the Qurans miracle is not going to do you any good., happy reading!

    • “, happy reading!”

      Isn’t that Rashad Khalifa’s deal? Didn’t he have to cut and paste a bit of the Quran to make that work?

      Didn’t see a list of science miracles over there, but most of that stuff is so vague you could find it in any writing that uses metaphorical imagery. They’re just naked eye observations.

      —-“all this done in the most beautiful poetic way!”
      That depends on who you ask.

      —-“ONE percent of what the Quran has?”
      I’m sure you’ll find fault with anything presented. Depends on what people want to believe is true. The average person isn’t going to piddle their whole life away looking for miracles in a throwaway romance novel.

      “Some even exclaim that (God) is no longer alive (Nietzche, p. 275, Vol. 10).”…Umm, it doesn’t mean God croaked. Religion has become obsolete. We need to move beyond it.

  3. Nice breakdown. I was noticing how some ayats ended mid sentence, so that an ayat by itself had no coherent statement in it. Poetic purposes? Then why does it sound so bad?

  4. Regarding the odd and even numbers. ( the 6236 and 6555 thing ) Nope, there’s just NO way this thing is just a coincidence. I tried experimenting it myself by using just 5 or 6 imaginary chapters and tried to give some random amount of verses no. to it too and then tried to make everything tally. And i still need to use the calculaters for many minutes to make everything tally. and i havent even put any stories to it yet. And Quran was based on ACTUAL HISTORICAL EVENTS, witnessed by thousands during Prophet Muhammad’s lifetime, spanning more than TWENTY YEARS too! There’s just no way human being could do that, even with a computer too, it would be impossible to do it if you want to base it according to actual events spanning many years. You would have to wait for tomorrow to to know what will happen tomorrow. And then there’s also many other very complicated mathematical patterns too based on one or two chapters only, here and there in the Quran.

  5. ( You said : It is sometimes claimed that if the distribution of ayats was changed in any way, the pattern will disappear. However, there are many ways you could alter the distribution of ayat numbers without affecting this property and which you can easily verify with the spreadsheet……)

    Lol, SPREADSHEET!! Ya, I guess there were many of those SPREADSHEET 1400 years ago!

    • From your comments I think you have completely misunderstood. I am not saying that this coincidence was carefully arranged or designed by anybody, but rather that it happened unintentionally when the suras were arranged and divided into verses. So if it was an unintended coincidence, then it is utterly irrelevant how hard you or anyone would find it to implement deliberately. I explained why it is nowhere near as unlikely as it might first seem, and that an unlikely coincidence is unremarkable given the vast possiblities of patterns that people spend vast amounts of time searching for. My point that you can alter the numbers is to show that contrary to the claim that this “miracle” has some sort of useful function of showing preservation in ordering, number of verses etc., this “miracle” cannot in fact show any such preservation.

      Judging by your first comment, you also seem to have missed that the division into 6236 verses was not “revealed” to Muhammad, but rather was decided by a group of people decades later, and was one of many systems that were used (6000, 6204 etc.), but the 6236 divisions of Kufah became the most popular.

      Incidentally, while I think the coincidence was unintentional, it could easily have been implemented by design after the Qur’an had been completed. Remember, both parts of the “miracle” simply follow from a match between the total ayats in the odd s+a group and the total sura numbers in the even s+a group. If you checked for this property in a Qur’an and found that the two numbers had not matched (3303 = 3303 as it happens), but rather there had been a gap between them, it would actually have been very easy to intentionally alter the number of ayats into which some suras were divided in order to close the gap so that there is a match. As explained in the article, the gap would probably be relatively small to start with. Btw, I am not talking about changing the text or its ordering at all, just how it is numbered.

      If the gap was an even number, you would simply add an even number of ayats to some suras in one group (either the odd or even sura+ayat group), and/or subtract an even number of ayats to suras in the other group until the gap is closed. You could spread the changes across many suras. Note that because the change is an even number, it does not affect which group any sura is in. Note also that I don’t mean changing the text of the Qur’an or its ordering at all, but rather just how many ayats a sura is divided into, which is easy since 1 ayah does not generally = 1 sentence.

      If the gap was an odd number, you would first do an additional step to make the gap even: You would add/subtract one ayah to a sura whose sura number and number of ayats were both odd. You would then add/subtract one ayah to a sura whose sura number was even but whose number of ayats was odd. The gap will now be even because you have changed the total of sura numbers in the even s+a group by an odd number, and you have changed the total ayats in the odd s+a group by zero or an even number.

  6. Peace & blessings Martin,

    As for your statement that these “coincidences” are not remarkable, please note that Quran was revealed over a period of almost 23 years, in a hap hazard manner, at various places, during war and peace, as a guidance for the whole mankind, covering a variety of topics like life, death & hereafter. Not every Surah was revealed and completed before moving to the next one. Sometimes a few verses would be revealed from one Surah then other verses from another Surah, with several incomplete Surahs at one point or another, but when the revelation was completed every Surah was completed.

    There are chapters named after Mary (Mother of Jesus) and cow. How “great” a book would it be if the verses for Mary and cow were switched to cook up a numeric miracle? Point is, you can’t just move around a few verses here & there just because they are both odd or even and claim the pattern holds true. You are completely missing the essence of Qur’an if you just look at it as a book on maths.


    Regarding 6,000, 6,204, 6,219, and 6,236 verses, what’s the proof on this? Britannica just mentions this as a passing comment. You’ve not offered any proof either. How do you prove Qur’an, as taught by Prophet (saws), had many versions and Kufic version was any different from what he taught?. Kufa, as a city, was founded during the time of second caliph Umar ibn Khattab (R.A). All four righteous caliphs were huffaz themselves. They were all contemporaries of prophet (saws) and prayed along with him. Since they had direct access to prophet (saws) himself and learnt Qur’an directly from him, what would be the reason for them to change or alter the sequence of suras or ayas?

    If you are insinuating that Qur’anic verses were not codified during the life of Prophet (saws) then you are wrong. Or, can you please back up your claim? This is what Muslims believe which is backed up by sahih hadith, books on sunnah and seerah:

    Order of Verses:

    Muslim scholars agree that the order of the verses in every chapter was done or commanded by the Prophet (saws) himself following the commands of Almighty Allah.The Prophet (saws) once told his Companions after he had received a certain revelation that the arch-angel Gabriel had specified for him the particular order of verses (Ahmad). There are also many incidents narrated in the books of Sunnah regarding the Prophet’s (saws) recitation during prayer. The Companions used to pray every day behind the Prophet (saws) and he used to recite the Qur’an in the order given to him by Allah, and they used to learn and memorize from his recitation. There have never been any incident in which any of the Companions reciting in any order that violated the order of the verses showed to us by the Prophet (saws).

    Order of Surahs:

    As for the order of the surahs (chapters), the most accepted view is that it was also applied following an instruction given by Almighty Allah. It has been recorded that the Prophet (saws) reviewed the Qur’an with the arch-angel Gabriel 24 times all within his life. Every year, he used to review it once during the month of Ramadan with Gabriel. During the final year of the Prophet’s life, Gabriel revised the Qur’an twice with the Prophet (saws) as a way of confirming it. The Prophet (saws), in turn, used to follow this order in teaching his Companions and communicating the message to them.


    Your statement “While I think this feature of the Qur’an was simply an unintentional coincidence, I have explained in a comment dated June 17 2012 below how it would actually be a simple process to manufacture this pattern.”

    No, you haven’t shown how to manufacture this pattern, far less show how simple it is. All you’ve done is show that if you move around a couple of verses (ayats) that satisfies a certain criteia it will STILL hold the pattern. That’s FAR from manufacturing the pattern. It is easy, NOW (with the help of a compuer program), to spot the pattern once it has already been built. More importantly, you also need to take care of the contents of the suras, you can’t just mix & match verses from different suras just to manufacture a pattern or a create a miracle.

    I wish you had spent 1/10th the time you spent on writing the VB script on actually reading Qur’an, maybe you’d seen something of value. And if ever you choose to do so, try getting Muahmmad Asad’s translation. 🙂

    Peace be unto you & your family, may God guide us all in the right path !



    • Dear Texan,

      Thankyou for your comment, but your points are actually irrelevant and/or incorrect.

      You said:
      “No, you haven’t shown how to manufacture this pattern, far less show how simple it is. All you’ve done is show that if you move around a couple of verses (ayats) that satisfies a certain criteia it will STILL hold the pattern.”

      That part of the article is nothing to do with how to manufacture this pattern. If you read my comment dated June 17 (which I referred to in the update, which you quoted), that comment is where I address how to manufacture it and you will see that you are wrong. You would NOT be starting with the pattern already in place. All you’d need to start with is that the suras are arranged roughly in reverse length order and you’d probably start from one of the existing division systems with around 6000 verses. It wouldn’t need a computer to add each sura number to the number of its verses and add up some numbers, just someone with a numerology obsession! Then once you’ve thought of the process I described in the comment above which gives it the interesting properties, implementing it is very simple.

      But all this is beside the point. For these purposes, it is really irrelevant how long it took for the Qur’an to be revealed or the topics it covers. While I don’t for a second imagine that anyone actually sat down and implemented this pattern deliberately, a human who wanted to implement such a numbering system would start work from a finished Qur’an and not need to change the text at all. And if I’m right that it was an unintentional coincidence, not deliberate, then the difficulty for a human is completely irrelevant in that case anyway. My explanation of how to do it deliberately is a side issue just for interest as most comments for some reason seem concerned with how it could be done deliberately. Perhaps I shouldn’t have bothered to discuss that in the comments as it is beside the point of the article. This is really a distracting and irrelevant side issue.

      As for your other comments, I am NOT talking about anyone changing the words or their order. Rather I’m just talking about how they were numbered, i.e. how many verses they are divided up into. Similarly, the different numbering systems that were used may well have all been with identical Qur’anic texts.

      But regarding ordering of the text itself, it is possibly that there is evidence that the present word ordering goes back to Muhammad. That’s beyond the scope of my article. My point in the main text of the article is just that this “miracle” is not part of that evidence.

      Peace to you and your family also


  7. I don’t understand the point of your article, you are simply explaining the mathematics of why it works, and then you are stating that it has a probability to happen, but those are things we already know, and then the title of the article is “debunked” which is not reflecting the nature of the article at all.

    I think the point that you are missing, is this symmetry that is present in the Qu’ran, in the context of what the Qu’ran is (the claim that it is the unaltered word of god), alongside with dozens of other unlikely “coincidences”, means it is more logical to say that the Qu’ran is of divine origin rather than a piece of work engineered over many years to be what it is, especially when we look at when these “coincidences” were discovered, why would a person, or a group of people go to so much effort loading the qu’ran chock full of these “coincidences” and not inform the world.

    I guess it just comes down to a matter of personal stand point, personally, after much research of the Qu’ran, of what we know of the life of the prophet, and of Islamic history, I just find it very very unlikely that a man wrote this book, and much more likely that god wrote it, it just fit together so well. That is my reason for leaving my atheistic beliefs anyway, but as we know people will defend what they think right down to the day they die, even if they know they are wrong.


    • Thanks for your comment, but I don’t think anyone intentionally loaded the Qur’an with the various numerical properties that some Muslims believe to be miracles. I think they are there by chance (and some are not quite what they seem, or depend on whether 2 verses are removed from surah 9). The main point of my article and explaining the mathematics behind it is to show that this particular one isn’t anywhere near as improbable to occur by chance as it might at first seem, due to both parts being rewordings of a single coincidence, and various factors that are condusive to such an occurance. So it is very plausible as just a coincidence given that there are countless possible numerical properties that could arise by chance and could seem remarkable to a religious person. If the numbering of the Qur’an was different, people with a lot of time on their hands would have found other interesting numerical properties instead and proclaimed those to be miracles (in fact, even with the particular property that my article addresses, one of the minor points in my article is that there are many different ways this Qur’an could have been numbered that would have this exact property).


%d bloggers like this: