Miracles of the Quran - Ayats Are Smaller

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    SurahsofwhichthenumberofayatsareSurahsofwhichthenumberofayatsareSurahsofwhichthenumberofayatsareSurahsofwhichthenumberofayatsaresmallersmallersmallersmaller

    thansequencenumberthansequencenumberthansequencenumberthansequencenumber

    Nowletsperformthesameanalysiswhichwehavemadefor the surahs that have the number of their ayats greater thantheirsequencenumberforthesurahsofwhichhasthenumberofsurahssmallerthanthesequencenumber.

    Thesurahsofwhichtheirnumberofayatsissmallerthan

    the sequence number and the differences are shown in the listbelow:

    No.No.No.No. SurahSurahSurahSurah AyatAyatAyatAyat DifferenceDifferenceDifferenceDifference

    32 Al-Sajdah 30 -245 Al-Jthiyah 37 -846 Al-Aqf 35 -1147 Muammad 38 -948 Al-Fat 29 -1949 Al-ujurt 18 -3150 Qf 45 -552 Al-r 49 -357 Al-add 29 -2858 Al-Mujdalah 22 -3659 Al-ashr 24 -3560 Al-Mumtainah 13 -47

    61 Al-aff 14 -4762 Al-Jumuah 11 -5163 Al-Munfiqn 11 -5264 Al-Taghbun 18 -4665 Al-alq 12 -5366 Al-Tarm 12 -5467 Al-Mulk 30 -3768 Al-Qalam 52 -1669 Al-qqah 52 -17

    70 Al-Marij 44 -26

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    71 N 28 -4372 Al-Jinn 28 -44

    73 Al-Muzzammil 20 -5374 Al-Muddaththir 56 -1875 Al-Qiymah 40 -3576 Al-Insn 31 -4577 Al-Mursalt 50 -2778 Al-Naba 40 -3879 Al-Nzit 46 -3380 Abasa 42 -3881 Al-Takwr 29 -5282 Al-Infir 19 -6383 Al-Muaffifn 36 -4784 Al-Inshiqq 25 -5985 Al-Burj 22 -6386 Al-riq 17 -6987 Al-Al 19 -6888 Al-Ghshiyah 26 -6289 Al-Fajr 30 -59

    90 Al-Balad 20 -7091 Al-Shams 15 -7692 Al-Layl 21 -7193 Al-ua 11 -8294 Al-Inshir 8 -8695 Al-Tn 8 -8796 Al-Alaq 19 -7797 Al-Qadr 5 -9298 Al-Bayyinah 8 -90

    99 Al-Zilzl 8 -91100 Al-diyt 11 -89101 Al-Qriah 11 -90102 Al-Takthur 8 -94103 Al-Asr 3 -100104 Al-Humaza 9 -95105 Al-Fl 5 -100106 Quraysh 4 -102107 Al-Mn 7 -100

    108 Al-Kawthar 3 -105

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    Surahsofwhichthenumberofayatsaresmallerthansequencenumber

    69

    109 Al-Kfirn 6 -103110 Al-Nar 3 -107

    111 Tabbat 5 -106112 Al-Ikhl 4 -108113 Al-Falaq 5 -108114 Al-Ns 6 -108

    List-21Asitcanbeseeninthelisthereinabovethetotalnumber

    ofsuchsurahsis66666666.

    Nowletslookatsurahswhichhaveoddandevennumber

    ofdifferences (numberofayats- sequencenumber),outof such66surahs.

    ThesurahsofwhichtheirnumberoftheayatsisThesurahsofwhichtheirnumberoftheayatsisThesurahsofwhichtheirnumberoftheayatsisThesurahsofwhichtheirnumberoftheayatsissmallersmallersmallersmallerthanthesequencenumbersandhasanoddnumberthanthesequencenumbersandhasanoddnumberthanthesequencenumbersandhasanoddnumberthanthesequencenumbersandhasanoddnumberdifferdifferdifferdifferenceenceenceence

    No.No.No.No. SurahSurahSurahSurah AyatAyatAyatAyat DifferenceDifferenceDifferenceDifference

    46 Al-Aqf 35 -1147 Muammad 38 -948 Al-Fat 29 -1949 Al-ujurt 18 -3150 Qf 45 -552 Al-r 49 -359 Al-ashr 24 -3560 Al-Mumtainah 13 -4761 Al-aff 14 -4762 Al-Jumuah 11 -5165 Al-alq 12 -5367 Al-Mulk 30 -3769 Al-qqah 52 -1771 N 28 -4373 Al-Muzzammil 20 -5375 Al-Qiymah 40 -3576 Al-Insn 31 -45

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    77 Al-Mursalt 50 -2779 Al-Nzit 46 -33

    82 Al-Infir 19 -6383 Al-Muaffifn 36 -4784 Al-Inshiqq 25 -5985 Al-Burj 22 -6386 Al-riq 17 -6989 Al-Fajr 30 -5992 Al-Layl 21 -7195 Al-Tn 8 -8796 Al-Alaq 19 -7799 Al-Zilzl 8 -91100 Al-diyt 11 -89104 Al-Humaza 9 -95108 Al-Kawthar 3 -105109 Al-Kfirn 6 -103110 Al-Nar 3 -107

    List-22Asitcanbeseeninthelisthereinabovethetotalnumber

    ofsuchsurahsis34343434.

    ThesurahsofwhichtheirnumberoftheayatsisThesurahsofwhichtheirnumberoftheayatsisThesurahsofwhichtheirnumberoftheayatsisThesurahsofwhichtheirnumberoftheayatsissmallersmallersmallersmallerthanthesequencenumbersandhasanthanthesequencenumbersandhasanthanthesequencenumbersandhasanthanthesequencenumbersandhasanevenevenevenevennumbernumbernumbernumberdifferencedifferencedifferencedifference

    No.No.No.No. SurahSurahSurahSurah AyatAyatAyatAyat DifferenceDifferenceDifferenceDifference

    32 Al-Sajdah 30 -245 Al-Jthiyah 37 -857 Al-add 29 -2858 Al-Mujdalah 22 -3663 Al-Munfiqn 11 -5264 Al-Taghbun 18 -4666 Al-Tarm 12 -5468 Al-Qalam 52 -1670 Al-Marij 44 -2672 Al-Jinn 28 -44

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    Surahsofwhichthenumberofayatsaresmallerthansequencenumber

    71

    74 Al-Muddaththir 56 -1878 Al-Naba 40 -38

    80 Abasa 42 -3881 Al-Takwr 29 -5287 Al-Al 19 -6888 Al-Ghshiyah 26 -6290 Al-Balad 20 -7091 Al-Shams 15 -7693 Al-ua 11 -8294 Al-Inshir 8 -8697 Al-Qadr 5 -9298 Al-Bayyinah 8 -90101 Al-Qriah 11 -90102 Al-Takthur 8 -94103 Al-Asr 3 -100105 Al-Fl 5 -100106 Quraysh 4 -102107 Al-Mn 7 -100111 Tabbat 5 -106112 Al-Ikhl 4 -108113 Al-Falaq 5 -108114 Al-Ns 6 -108

    List-23Asitcanbeseeninthelisthereinabovethetotalnumber

    ofsuchsurahsis32323232.Nowletslookatthesequencenumbersofthesurahsof

    whichtheirnumberofayatsissmallerthanthesequencenumbers:

    ThesurahsofwhichtheirnumberofayatsisThesurahsofwhichtheirnumberofayatsisThesurahsofwhichtheirnumberofayatsisThesurahsofwhichtheirnumberofayatsissmallersmallersmallersmallerthanthesequencenumberandwhichhaveoddthanthesequencenumberandwhichhaveoddthanthesequencenumberandwhichhaveoddthanthesequencenumberandwhichhaveoddsequencenumberssequencenumberssequencenumberssequencenumbers

    No.No.No.No. SurahSurahSurahSurah AyatAyatAyatAyat No.No.No.No. SurahSurahSurahSurah AyatAyatAyatAyat

    45 Al-Jthiyah 37 83 Al-Muaffifn 3647 Muammad 38 85 Al-Burj 22

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    49 Al-ujurt 18 87 Al-Al 1957 Al-add 29 89 Al-Fajr 30

    59 Al-ashr 24 91 Al-Shams 1561 Al-aff 14 93 Al-ua 1163 Al-Munfiqn 11 95 Al-Tn 865 Al-alq 12 97 Al-Qadr 567 Al-Mulk 30 99 Al-Zilzl 869 Al-qqah 52 101 Al-Qriah 1171 N 28 103 Al-Asr 373 Al-Muzzammil 20 105 Al-Fl 5

    75 Al-Qiymah 40 107 Al-Mn 777 Al-Mursalt 50 109 Al-Kfirn 679 Al-Nzit 46 111 Tabbat 581 Al-Takwr 29 113 Al-Falaq 5

    List-24Asitcanbeseeninthelisthereinabovethetotalnumber

    ofsuchsurahsis32323232.

    ThesurahsofwhichtheirnumberofayatsisThesurahsofwhichtheirnumberofayatsisThesurahsofwhichtheirnumberofayatsisThesurahsofwhichtheirnumberofayatsissmallersmallersmallersmallerthanthesequencenumberandwhichhavethanthesequencenumberandwhichhavethanthesequencenumberandwhichhavethanthesequencenumberandwhichhaveevenevenevenevensequencenumberssequencenumberssequencenumberssequencenumbers

    XX

    No.No.No.No. SurahSurahSurahSurah AyatAyatAyatAyat No.No.No.No. SurahSurahSurahSurah AyatAyatAyatAyat

    32 Al-Sajdah 30 82 Al-Infir 1946 Al-Aqf 35 84 Al-Inshiqq 25

    48 Al-Fat 29 86 Al-riq 1750 Qf 45 88 Al-Ghshiyah 2652 Al-r 49 90 Al-Balad 2058 Al-Mujdalah 22 92 Al-Layl 2160 Al-Mumtainah 13 94 Al-Inshir 862 Al-Jumuah 11 96 Al-Alaq 1964 Al-Taghbun 18 98 Al-Bayyinah 866 Al-Tarm 12 100 Al-diyt 1168 Al-Qalam 52 102 Al-Takthur 870 Al-Marij 44 104 Al-Humaza 9

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    Surahsofwhichthenumberofayatsaresmallerthansequencenumber

    73

    72 Al-Jinn 28 106 Quraysh 474 Al-Muddaththir 56 108 Al-Kawthar 3

    76 Al-Insn 31 110 Al-Nar 378 Al-Naba 40 112 Al-Ikhl 480 Abasa 42 114 Al-Ns 6

    List-25Asitcanbeseeninthelisthereinabovethetotalnumber

    ofsuchsurahsis34343434.EvaluationEvaluationEvaluationEvaluation

    The number of the surahs of which their number of ayats is smaller thanthe sequence number and which have odd sequence number is 32323232. On the other hand,the number of those which have even number difference of (number of ayats-sequence number) is also 32323232.

    The number of the surahs of which their number of ayats is smaller thanthe sequence number and which have even sequence number is 343434 34. On the otherhand, the number of those which have odd number difference of (number of ayats-sequence number) is also 34343434.

    Letsseetheresultswhichoutcomecollectively:

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    74

    1 A l - F t i a 72 A l - B a q a r a h 2863 l I m r n 200

    4 A l - N i s 1765 A l - M i d a h 1206 A l - E n m 1657 A l - A r f 2068 A l - A n f l 759 A l - T a w b a h 129

    10 Y n u s 10911 H d 12312 Y s u f 11113 A l - R a d 4314 I b r h m 5215 A l - i j r 9916 A l - N a l 12817 A l - I s r 11118 A l - K a h f 11019 M a r y a m 9820 h 13521 A l - A n b i y 11222 A l - a j j 7823 A l - M u m i n n 11824 A l - N r 6425 A l - F u r q n 7726 A l - S h u a r 22727 A l - N a m l 9328 A l - Q a a 8829 A l - A n k a b t 6930 A l - R m 60

    31 L u q m n 3432 A l - S a j d a h 3033 A l - A z b 7334 S a b a 5435 F i r 4536 Y s n 8337 A l - a f f t 18238 d 8839 A l - Z u m a r 7540 A l - M u m i n 8541 F u i l a t 5442 A l - S h r 5343 A l - Z u k h r u f 8944 A l - D u k h n 5945 A l - J t h i y a h 3746 A l - A q f 3547 M u a m m a d 3848 A l - F a t 2949 A l - u j u r t 1850 Q f 4551 A l - D h r i y t 6052 A l - r 4953 A l - N a j m 6254 A l - Q a m a r 5555 A l - R a m n 7856 A l - W q i a h 9657 A l - a d d 29

    58 A l - M u j d a l a h 2259 A l - a s h r 2460 A l - M u m t a i n a h 1361 A l - a f f 1462 A l - J u m u a h 1163 A l - M u n f i q n 1164 A l - T a g h b u n 1865 A l - a l q 1266 A l - T a r m 1267 A l - M u l k 3068 A l - Q a l a m 5269 A l - q q a h 5270 A l - M a r i j 4471 N 2872 A l - J i n n 2873 A l - M u z z a m m i l 2074 A l - M u d d a t h t h i r 5675 A l - Q i y m a h 4076 A l - I n s n 3177 A l - M u r s a l t 5078 A l - N a b a 4079 A l - N z i t 4680 A b a s a 4281 A l - T a k w r 2982 A l - I n f i r 1983 A l - M u a f f i f n 3684 A l - I n s h i q q 25

    85 A l - B u r j 2286 A l - r i q 1787 A l - A l 1988 A l - G h s h i y a h 2689 A l - F a j r 3090 A l - B a l a d 2091 A l - S h a m s 1592 A l - L a y l 2193 A l - u a 1194 A l - I n s h i r 895 A l - T n 896 A l - A l a q 19

    97 A l - Q a d r 598 A l - B a y y i n a h 899 A l - Z i l z l 8100 A l - d i y t 11101 A l - Q r i a h 11102 A l - T a k t h u r 8103 A l - A s r 3

    104 A l - H u m a z a 9105 Al-Fl 5106 Q u r a y s h 4107 A l - M n 7108 A l - K a w t h a r 3109 A l - K f i r n 6110 A l - N a r 3

    111 T a b b a t 5

    112 A l - I k h l 4113 A l - F a l a q 5114 A l - N s

    number of ayats < sequence number number of ayats < sequence number

    NO. SURAH AYAT (number of ayatssequence number)ODD NUMBER DIFFERENCE

    (number of ayatssequence number)

    VEN NUMBER DIFFERENCEODD sequence number EVEN sequence number

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X XX X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X XX X

    X X

    Inthefigure,symmetricdistributionforthesurahsofwhichtheir

    numberoftheayatsissmallerthanthesequencenumbersisshown.

    ax

    is

    o

    f

    symme

    try

    34 32 32 34

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    Thenumberswhicharedividedbythreeandnotdividedbytwo

    149

    ThenumberswhicharedividedbyThenumberswhicharedividedbyThenumberswhicharedividedbyThenumberswhicharedividedbythreethreethreethreeandnotandnotandnotandnot

    dividedbytwodividedbytwodividedbytwodividedbytwoInthissectionwewillfirstdetermine thenumberswhich

    arecontainedintheindexofQurnthataredividedbythreeandnot divided by two. Then, we will investigate whether amathematicalharmonyexistsbetweenthemornot.

    Inthefollowinglist,thenumberscontainedintheindexofQurnwhichare divisible by three andnot divisibleby two are

    marked: No.No.No.No. SurahSurahSurahSurah AyatAyatAyatAyat No.No.No.No. SurahSurahSurahSurah AyatAyatAyatAyat

    1 Al-Ftia 7 58 Al-Mujdalah 222 Al-Baqarah 286 59 Al-ashr 243333 lImrn 200 60 Al-Mumtainah 134 Al-Nis 176 61 Al-aff 145

    Al-Midah

    120

    62

    Al-Jumuah

    116 Al-Enm 165165165165 63636363 Al-Munfiqn 117 Al-Arf 206 64 Al-Taghbun 188 Al-Anfl 75757575 65 Al-alq 129999 Al-Tawbah 129129129129 66 Al-Tarm 1210 Ynus 109 67 Al-Mulk 3011 Hd 123123123123 68 Al-Qalam 5212 Ysuf 111111111111 69696969 Al-qqah 5213 Al-Rad 43 70 Al-Marij 4414 Ibrhm 52 71 N 2815151515 Al-ijr 99999999 72 Al-Jinn 2816 Al-Nal 128 73 Al-Muzzammil 2017 Al-Isr 111111111111 74 Al-Muddaththir 5618 Al-Kahf 110 75757575 Al-Qiymah 4019 Maryam 98 76 Al-Insn 3120 h 135135135135 77 Al-Mursalt 5021212121 Al-Anbiy 112 78 Al-Naba 4022 Al-ajj 78 79 Al-Nzit 46

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    23 Al-Muminn 118 80 Abasa 4224 Al-Nr 64 81818181 Al-Takwr 2925 Al-Furqn 77 82 Al-Infir 1926 Al-Shuar 227 83 Al-Muaffifn 3627272727 Al-Naml 93939393 84 Al-Inshiqq 2528 Al-Qaa 88 85 Al-Burj 2229 Al-Ankabt 69696969 86 Al-riq 1730 Al-Rm 60 87878787 Al-Al 1931 Luqmn 34 88 Al-Ghshiyah 2632 Al-Sajdah 30 89 Al-Fajr 3033333333 Al-Azb 73 90 Al-Balad 2034 Saba 54 91 Al-Shams 1515151535 Fir 45454545 92 Al-Layl 2121212136 Ysn 83 93939393 Al-ua 1137 Al-afft 182 94 Al-Inshir 838 d 88 95 Al-Tn 839393939 Al-Zumar 75757575 96 Al-Alaq 1940 Al-Mumin 85 97 Al-Qadr 541

    Fuilat

    54

    98

    Al-Bayyinah

    842 Al-Shr 53 99999999 Al-Zilzl 8

    43 Al-Zukhruf 89 100 Al-diyt 1144 Al-Dukhn 59 101 Al-Qriah 1145454545 Al-Jthiyah 37 102 Al-Takthur 846 Al-Aqf 35 103 Al-Asr 333347 Muammad 38 104 Al-Humaza 999948 Al-Fat 29 105105105105 Al-Fl 549 Al-ujurt 18 106 Quraysh 450 Qf 45454545 107 Al-Mn 751515151 Al-Dhriyt 60 108 Al-Kawthar 333352 Al-r 49 109 Al-Kfirn 653 Al-Najm 62 110 Al-Nar 333354 Al-Qamar 55 111111111111 Tabbat 555 Al-Ramn 78 112 Al-Ikhl 456 Al-Wqiah 96 113 Al-Falaq 557575757 Al-add 29 114 Al-Ns 6

    List-69

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    Thenumberswhicharedividedbythreeandnotdividedbytwo

    151

    Now,letusdividethenumberscontainedintheindexofQurnaccording totheirhomogeneitywithrespect todivisible

    bythreeandbeingnotdivisiblebytwo.

    Example for the surahs with homogeneous sequencenumbersandnumberofayats:

    9 Al-Tawbah 129

    Al-Tawbah is a homogeneous surah. Forwhy, both thesequencenumberandthenumberofayats,meettheconditionof

    divisiblebythreeandnotbeingdivisiblebytwo.Therefore,al-Tawbahsurahishomogeneousinthisrespect.

    1 Al-Ftia 7Surah al-Ftia is also a homogeneous surah. Forwhy,

    neitherthesequencenorthenumberofayats,meetstheconditionofdivisiblebythreeandnotbeingdivisiblebytwo.Therefore,al-Ftiasurahishomogeneousinthisrespect.

    Exampleforthesurahsofwhichtheirsequencenumbersandnumberofayatsarenothomogeneous:

    21 Al-Anbiy 112The sequence number of al-Anbiy surah meets the

    conditionof divisible by three andnot being divisible by two,whereas its number of ayats does not cover this condition.Therefore,al-Anbiysurahisnothomogeneousinthisrespect.

    6 Al-Enm 165

    The number of ayats of al-Enm surah meets theconditionof divisible by three andnot being divisible by two,whereas its sequence number does not cover this condition.Therefore,al-Enmsurahisnothomogeneousinthisrespect.

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    TTTThesetofsurahswhicharehomogeneouswithregardtohesetofsurahswhicharehomogeneouswithregardtohesetofsurahswhicharehomogeneouswithregardtohesetofsurahswhicharehomogeneouswithregardtodivisibilitybydivisibilitybydivisibilitybydivisibilitybythreethreethreethreeandnotbandnotbandnotbandnotbeeeeingdivisiblebyingdivisiblebyingdivisiblebyingdivisiblebytwotwotwotwoofofofofthesequencenumbersandthenumberofayats.thesequencenumbersandthenumberofayats.thesequencenumbersandthenumberofayats.thesequencenumbersandthenumberofayats.

    No.No.No.No. SurSurSurSurahahahah AyatAyatAyatAyat No.No.No.No. SurahSurahSurahSurah AyatAyatAyatAyat

    1 Al-Ftia 7 58 Al-Mujdalah 222 Al-Baqarah 286 59 Al-ashr 244 Al-Nis 176 60 Al-Mumtainah 135

    Al-Midah

    120

    61

    Al-aff

    147 Al-Arf 206 62 Al-Jumuah 119999 Al-Tawbah 129129129129 64 Al-Taghbun 1810 Ynus 109 65 Al-alq 1213 Al-Rad 43 66 Al-Tarm 1214 Ibrhm 52 67 Al-Mulk 3015151515 Al-ijr 99999999 68 Al-Qalam 5216 Al-Nal 128 70 Al-Marij 4418 Al-Kahf 110 71 N 2819 Maryam 98 72 Al-Jinn 2822 Al-ajj 78 73 Al-Muzzammil 2023 Al-Muminn 118 74 Al-Muddaththir 5624 Al-Nr 64 76 Al-Insn 3125 Al-Furqn 77 77 Al-Mursalt 5026 Al-Shuar 227 78 Al-Naba 4027272727 Al-Naml 93939393 79 Al-Nzit 4628 Al-Qaa 88 80 Abasa 4230 Al-Rm 60 82 Al-Infir 1931 Luqmn 34 83 Al-Muaffifn 3632 Al-Sajdah 30 84 Al-Inshiqq 2534 Saba 54 85 Al-Burj 2236 Ysn 83 86 Al-riq 1737 Al-afft 182 88 Al-Ghshiyah 2638 d 88 89 Al-Fajr 3039393939 Al-Zumar 75757575 90 Al-Balad 2040 Al-Mumin 85 94 Al-Inshir 841 Fuilat 54 95 Al-Tn 8

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    Thenumberswhicharedividedbythreeandnotdividedbytwo

    153

    42 Al-Shr 53 96 Al-Alaq 1943 Al-Zukhruf 89 97 Al-Qadr 544 Al-Dukhn 59 98 Al-Bayyinah 846 Al-Aqf 35 100 Al-diyt 1147 Muammad 38 101 Al-Qriah 1148 Al-Fat 29 102 Al-Takthur 849 Al-ujurt 18 106 Quraysh 452 Al-r 49 107 Al-Mn 753 Al-Najm 62 109 Al-Kfirn 654 Al-Qamar 55 112 Al-Ikhl 455

    Al-Ramn

    78

    113

    Al-Falaq

    556 Al-Wqiah 96 114 Al-Ns 6

    List-70Thereare84848484surahsinList-70Letshavealookathowmanyofthesesurahstakeplacein

    thefirsthalfandhowmanyofthemarecontainedinthesecondhalfoftheHolyQurn:

    ThesurahsexistinthefirsthalfoftheHolyThesurahsexistinthefirsthalfoftheHolyThesurahsexistinthefirsthalfoftheHolyThesurahsexistinthefirsthalfoftheHolyQurnQurnQurnQurnwhicharehomogeneouswithregardtodivisibilitybywhicharehomogeneouswithregardtodivisibilitybywhicharehomogeneouswithregardtodivisibilitybywhicharehomogeneouswithregardtodivisibilitybythreethreethreethreeandnotbandnotbandnotbandnotbeeeeingdivisiblebyingdivisiblebyingdivisiblebyingdivisiblebytwotwotwotwoofthesequenceofthesequenceofthesequenceofthesequencenumbersandthenumberofayatnumbersandthenumberofayatnumbersandthenumberofayatnumbersandthenumberofayats.s.s.s.

    No.No.No.No. SurahSurahSurahSurah AyatAyatAyatAyat No.No.No.No. SurahSurahSurahSurah AyatAyatAyatAyat

    1 Al-Ftia 7 31 Luqmn 342 Al-Baqarah 286 32 Al-Sajdah 304 Al-Nis 176 34 Saba 545 Al-Midah 120 36 Ysn 837 Al-Arf 206 37 Al-afft 1829999 Al-Tawbah 129129129129 38 d 8810 Ynus 109 39393939 Al-Zumar 7575757513 Al-Rad 43 40 Al-Mumin 8514 Ibrhm 52 41 Fuilat 5415151515 Al-ijr 99999999 42 Al-Shr 5316 Al-Nal 128 43 Al-Zukhruf 89

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    154

    18 Al-Kahf 110 44 Al-Dukhn 5919 Maryam 98 46 Al-Aqf 3522 Al-ajj 78 47 Muammad 3823 Al-Muminn 118 48 Al-Fat 2924 Al-Nr 64 49 Al-ujurt 1825 Al-Furqn 77 52 Al-r 4926 Al-Shuar 227 53 Al-Najm 6227272727 Al-Naml 93939393 54 Al-Qamar 5528 Al-Qaa 88 55 Al-Ramn 7830 Al-Rm 60 56 Al-Wqiah 96

    List-71Thereare42424242surahsinList-71

    ThesurahsexistinThesurahsexistinThesurahsexistinThesurahsexistinthethethethesecondsecondsecondsecondhalfoftheHolyhalfoftheHolyhalfoftheHolyhalfoftheHolyQurnQurnQurnQurnwhicharehomogeneouswithregardtodivisibilitybywhicharehomogeneouswithregardtodivisibilitybywhicharehomogeneouswithregardtodivisibilitybywhicharehomogeneouswithregardtodivisibilitybythreethreethreethreeandnotbandnotbandnotbandnotbeeeeingdivisiblebyingdivisiblebyingdivisiblebyingdivisiblebytwotwotwotwoofthesequenceofthesequenceofthesequenceofthesequencenumbersandthenumberofayats.numbersandthenumberofayats.numbersandthenumberofayats.numbersandthenumberofayats.

    No.No.No.No. SurahSurahSurahSurah AyatAyatAyatAyat No.No.No.No. SurahSurahSurahSurah AyatAyatAyatAyat58 Al-Mujdalah 22 83 Al-Muaffifn 3659 Al-ashr 24 84 Al-Inshiqq 2560 Al-Mumtainah 13 85 Al-Burj 2261 Al-aff 14 86 Al-riq 1762 Al-Jumuah 11 88 Al-Ghshiyah 2664 Al-Taghbun 18 89 Al-Fajr 3065 Al-alq 12 90 Al-Balad 2066 Al-Tarm 12 94 Al-Inshir 867 Al-Mulk 30 95 Al-Tn 868 Al-Qalam 52 96 Al-Alaq 1970 Al-Marij 44 97 Al-Qadr 571 N 28 98 Al-Bayyinah 872 Al-Jinn 28 100 Al-diyt 1173 Al-Muzzammil 20 101 Al-Qriah 1174

    Al-Muddaththir56

    102

    Al-Takthur876 Al-Insn 31 106 Quraysh 4

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    Thenumberswhicharedividedbythreeandnotdividedbytwo

    155

    77 Al-Mursalt 50 107 Al-Mn 778 Al-Naba 40 109 Al-Kfirn 679 Al-Nzit 46 112 Al-Ikhl 480 Abasa 42 113 Al-Falaq 582 Al-Infir 19 114 Al-Ns 6

    List-72Thereare42424242surahsinList-72

    Figure-12Theequaldistributionofthehomogeneoussurahsisseen.

    EvaluationEvaluationEvaluationEvaluation

    The surahs which are homogeneous with regard to divisibility by threeand not being divisible by two of the sequence numbers and the number of ayats aredistributed in equal numbers in the first and second half ofQuran.

    What about the non-homogeneous surahs?Now,letsexaminethenon-homogeneoussurahswiththe

    sameapproach.

    84 42 42

    Homogenoussurahs

    Thenumberof

    homogenoussurahs

    whichareincluded

    inthefirsthalfof

    theHolyQur'n

    Thenumberof

    homogenoussurahs

    whichareincludedin

    thesecondhalfofthe

    HolyQur'n

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    156

    TTTThesetofsurahswhicharehesetofsurahswhicharehesetofsurahswhicharehesetofsurahswhicharenonnonnonnon----homogeneouswithhomogeneouswithhomogeneouswithhomogeneouswithregardtodivisibilitybyregardtodivisibilitybyregardtodivisibilitybyregardtodivisibilitybythreethreethreethreeandnotbandnotbandnotbandnotbeeeeingingingingdivisiblebydivisiblebydivisiblebydivisiblebytwotwotwotwoofthesequencenumbersandthenumberofayats.ofthesequencenumbersandthenumberofayats.ofthesequencenumbersandthenumberofayats.ofthesequencenumbersandthenumberofayats.

    No.No.No.No. SurahSurahSurahSurah AyatAyatAyatAyat No.No.No.No. SurahSurahSurahSurah AyatAyatAyatAyat

    3333 lImrn 200 63636363 Al-Munfiqn 116 Al-Enm 165165165165 69696969 Al-qqah 528 Al-Anfl 75757575 75757575 Al-Qiymah 4011

    Hd

    123123123123

    81818181

    Al-Takwr

    2912 Ysuf 111111111111 88887777 Al-Al 19

    17 Al-Isr 111111111111 91 Al-Shams 1515151520 h 135135135135 92 Al-Layl 2121212121212121 Al-Anbiy 112 93939393 Al-ua 1129 Al-Ankabt 69696969 99999999 Al-Zilzl 833333333 Al-Azb 73 103 Al-Asr 333335 Fir 45454545 104 Al-Humaza 999945454545 Al-Jthiyah 37 105105105105 Al-Fl 550 Qf 45454545 108 Al-Kawthar 333351515151 Al-Dhriyt 60 110 Al-Nar 333357575757 Al-add 29 111111111111 Tabbat 5

    List-73Thereare30303030surahsinList-73Letshavealookathowmanyofthesesurahstakeplacein

    thefirsthalfandhowmanyofthemarecontainedinthesecondhalfoftheHolyQurn:

    ThesurahswhicharecontainedinthefirsthalfoftheThesurahswhicharecontainedinthefirsthalfoftheThesurahswhicharecontainedinthefirsthalfoftheThesurahswhicharecontainedinthefirsthalfoftheQurnQurnQurnQurn,andregardedasnon,andregardedasnon,andregardedasnon,andregardedasnon----homogeneoushomogeneoushomogeneoushomogeneouswithrespectwithrespectwithrespectwithrespecttodivisibilitybytodivisibilitybytodivisibilitybytodivisibilitybythreethreethreethreeandnotbeingdivisiblebyandnotbeingdivisiblebyandnotbeingdivisiblebyandnotbeingdivisiblebytwotwotwotwoofofofofthesequencenumbersandthenumberofayats:thesequencenumbersandthenumberofayats:thesequencenumbersandthenumberofayats:thesequencenumbersandthenumberofayats:

    No.No.No.No. SurahSurahSurahSurah AyatAyatAyatAyat No.No.No.No. SurahSurahSurahSurah AyatAyatAyatAyat

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    Thenumberswhicharedividedbythreeandnotdividedbytwo

    157

    3333 lImrn 200 29 Al-Ankabt 696969696 Al-Enm 165165165165 33333333 Al-Azb 738 Al-Anfl 75757575 35 Fir 4545454511 Hd 123123123123 45454545 Al-Jthiyah 3712 Ysuf 111111111111 50 Qf 4545454517 Al-Isr 111111111111 51515151 Al-Dhriyt 6020 h 135135135135 57575757 Al-add 2921212121 Al-Anbiy 112

    List-74Thereare15151515surahsinList-74

    ThesurahswhicharecontainedintheThesurahswhicharecontainedintheThesurahswhicharecontainedintheThesurahswhicharecontainedinthesecondsecondsecondsecondhalfofthehalfofthehalfofthehalfoftheQurnQurnQurnQurn,andregardedasnon,andregardedasnon,andregardedasnon,andregardedasnon----homogeneoushomogeneoushomogeneoushomogeneouswithrespectwithrespectwithrespectwithrespecttodivisibilitybytodivisibilitybytodivisibilitybytodivisibilitybythreethreethreethreeandnotbeingdivisiblebyandnotbeingdivisiblebyandnotbeingdivisiblebyandnotbeingdivisiblebytwotwotwotwoofofofofthesequencenumbersandthenumberofayats:thesequencenumbersandthenumberofayats:thesequencenumbersandthenumberofayats:thesequencenumbersandthenumberofayats:

    No.No.No.No. SSSSurahurahurahurah AyatAyatAyatAyat No.No.No.No. SurahSurahSurahSurah AyatAyatAyatAyat

    63636363 Al-Munfiqn 11 99999999 Al-Zilzl 869696969 Al-qqah 52 103 Al-Asr 333375757575 Al-Qiymah 40 104 Al-Humaza 999981818181 Al-Takwr 29 105105105105 Al-Fl 587878787 Al-Al 19 108 Al-Kawthar 333391 Al-Shams 15151515 110 Al-Nar 333392 Al-Layl 21212121 111111111111 Tabbat 593939393

    Al-ua11

    List-75

    Thereare15151515surahsinList-75

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    158

    Figure-13Theequaldistributionofthenon-homogeneoussurahsisseen.

    EvaluationEvaluationEvaluationEvaluation

    The surahs which are not homogeneous with regard to divisibility bythree and not being divisible by two of the sequence numbers and the number ofayats are also distributed in equal numbers in the first and second half ofQuran.

    Letsseetheresultswhichoutcomecollectively:

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    Thenumberswhicharedividedbythreeandnotdividedbytwo

    159

    1 A l - F t i a 72 A l - B a q a r a h 2863 l I m r n 2004 A l - N i s 1765 A l - M i d a h 120

    6 A l - E n m165

    7 A l - A r f 2068 A l - A n f l 759 A l - T a w b a h 129

    10 Y n u s 10911 H d 123

    12 Y s u f 111

    13 A l - R a d 4314 I b r h m 5215 A l - i j r 9916 A l - N a l 12817 A l - I s r 11118 A l - K a h f 11019 M a r y a m 9820 h 13521 A l - A n b i y 11222 A l - a j j 7823 A l - M u m i n n 11824 A l - N r 6425 A l - F u r q n 7726 A l - S h u a r 22727 A l - N a m l 9328 A l - Q a a 8829 A l - A n k a b t 6930 A l - R m 6031 L u q m n 3432 A l - S a j d a h 30

    33 A l - A z b 7334 S a b a 5435 F i r 45

    36 Y s n 8337 A l - a f f t 18238 d 8839 A l - Z u m a r 7540 A l - M u m i n 8541 F u i l a t 5442 A l - S h r 5343 A l - Z u k h r u f 8944 A l - D u k h n 5945 A l - J t h i y a h 3746 A l - A q f 3547 M u a m m a d 3848 A l - F a t 2949 A l - u j u r t 1850 Q f 4551 A l - D h r i y t 6052 A l - r 4953 A l - N a j m 6254 A l - Q a m a r 5555 A l - R a m n 7856 A l - W q i a h 9657 A l - a d d 29

    58 A l - M u j d a l a h 22

    59 A l - a s h r 2460 A l - M u m t a i n a h 1361 A l - a f f 1462 A l - J u m u a h 1163 A l - M u n f i q n 1164 A l - T a g h b u n 1865 A l - a l q 1266 A l - T a r m 1267 A l - M u l k 3068 A l - Q a l a m 5269 A l - q q a h 5270 A l - M a r i j 4471 N 2872 A l - J i n n 2873 A l - M u z z a m m i l 2074 A l - M u d d a t h t h i r 5675 A l - Q i y m a h 4076 A l - I n s n 3177 A l - M u r s a l t 5078 A l - N a b a 4079 A l - N z i t 4680 A b a s a 4281 A l - T a k w r 2982 A l - I n f i r 1983 A l - M u a f f i f n 3684 A l - I n s h i q q 2585 A l - B u r j 22

    86 A l - r i q 1787 A l - A l 1988 A l - G h s h i y a h 2689 A l - F a j r 3090 A l - B a l a d 2091 A l - S h a m s 1592 A l - L a y l 2193 A l - u a 1194 A l - I n s h i r 895 A l - T n 896 A l - A l a q 1997 A l - Q a d r 598 A l - B a y y i n a h 899 A l - Z i l z l 8100 A l - d i y t 11101 A l - Q r i a h 11102 A l - T a k t h u r 8103 A l - A s r 3

    104 A l - H u m a z a 9105 Al-Fl 5106 Q u r a y s h 4107 A l - M n 7108 A l - K a w t h a r 3

    109 A l - K f i r n 6110 A l - N a r 3111 T a b b a t 5112 A l - I k h l 4113 A l - F a l a q 5114 A l - N s 6

    X

    X

    X

    X

    Inthefigure,sym

    metricdistributionofthehomogenousandnon-homogenoussurahstothefirstandsecondha

    lfoftheQur'anisshown.

    X

    X

    NON-HOMOGENOUSNO. SURAH AYAT

    X

    HOMOGENOUS

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

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    X

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    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

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    X

    X

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    X

    X

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    X

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    X

    X

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    X

    X

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    X

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    X

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    X

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    X

    X

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    X

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    X

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    42 15

    42 15

    ax

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    SurahsofwhichthenumberofayatSurahsofwhichthenumberofayatSurahsofwhichthenumberofayatSurahsofwhichthenumberofayatsaregreatersaregreatersaregreatersaregreater

    thansequencenumberthansequencenumberthansequencenumberthansequencenumberIfthereappearsapositivevalueotherthanzerowhenwe

    subtract the sequence number from the number of ayats of asurah, then it means the number of ayats is greater than thesequencenumberinsuchsurah.

    Example:

    DifferenceDifferenceDifferenceDifference=numberofayatssequencenumberDifferenceDifferenceDifferenceDifference=71=6Ifthedifferenceisanegativefigure,thenthismeansthe

    numberoftheayatsissmallerthanthesequencenumber.Thesurahsofwhichtheirnumberofayatsisgreaterthan

    the sequence number and the differences are shown in the list

    below:

    No.No.No.No. SurahSurahSurahSurah AyatAyatAyatAyat DifferenceDifferenceDifferenceDifference

    1 Al-Ftia 7 62 Al-Baqarah 286 2843 lImrn 200 1974 Al-Nis 176 1725 Al-Midah 120 1156 Al-Enm 165 159

    1Al-Ftia

    7

    Thenumber

    ofayatsThesequence

    number

    Thenameof

    thesurah

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    Surahsofwhichthenumberofayatsaregreaterthansequencenumber

    61

    7 Al-Arf 206 1998 Al-Anfl 75 67

    9 Al-Tawbah 129 12010 Ynus 109 9911 Hd 123 11212 Ysuf 111 9913 Al-Rad 43 3014 Ibrhm 52 3815 Al-ijr 99 8416 Al-Nal 128 11217 Al-Isr 111 9418 Al-Kahf 110 9219 Maryam 98 7920 h 135 11521 Al-Anbiy 112 9122 Al-ajj 78 5623 Al-Muminn 118 9524 Al-Nr 64 4025 Al-Furqn 77 5226 Al-Shuar 227 20127 Al-Naml 93 6628 Al-Qaa 88 6029 Al-Ankabt 69 4030 Al-Rm 60 3031 Luqmn 34 333 Al-Azb 73 4034 Saba 54 2035 Fir 45 10

    36 Ysn 83 4737 Al-afft 182 14538 d 88 5039 Al-Zumar 75 3640 Al-Mumin 85 4541 Fuilat 54 1342 Al-Shr 53 1143 Al-Zukhruf 89 4644 Al-Dukhn 59 15

    51 Al-Dhriyt 60 9

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    62

    53 Al-Najm 62 954 Al-Qamar 55 1

    55 Al-Ramn 78 2356 Al-Wqiah 96 40

    List-16Asitcanbeseeninthelisthereinabovethetotalnumber

    ofsuchsurahsis48.

    Nowletslookatsurahswhichhaveoddandevennumberofdifferences (numberofayats- sequencenumber),outof such48surahs.

    ThesurahsofwhThesurahsofwhThesurahsofwhThesurahsofwhichtheirnumberoftheayatsisgreaterichtheirnumberoftheayatsisgreaterichtheirnumberoftheayatsisgreaterichtheirnumberoftheayatsisgreaterthanthesequencenumbersandhasanoddnumberthanthesequencenumbersandhasanoddnumberthanthesequencenumbersandhasanoddnumberthanthesequencenumbersandhasanoddnumberdifferencedifferencedifferencedifference

    No.No.No.No. SurahSurahSurahSurah AyatAyatAyatAyat DifferenceDifferenceDifferenceDifference

    3 lImrn 200 1975 Al-Midah 120 1156 Al-Enm 165 1597 Al-Arf 206 1998 Al-Anfl 75 6710 Ynus 109 9912 Ysuf 111 9919 Maryam 98 7920 h 135 11521 Al-Anbiy 112 9123 Al-Muminn 118 9526 Al-Shuar 227 20131 Luqmn 34 336 Ysn 83 4737 Al-afft 182 14540 Al-Mumin 85 4541 Fuilat 54 1342 Al-Shr 53 1144 Al-Dukhn 59 15

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    Surahsofwhichthenumberofayatsaregreaterthansequencenumber

    63

    51 Al-Dhriyt 60 953 Al-Najm 62 9

    54 Al-Qamar 55 155 Al-Ramn 78 23

    List-17Asitcanbeseeninthelisthereinabovethetotalnumber

    ofsuchsurahsis23232323.

    ThesurahsofwhichtheirnumberoftheayatsisgreaterThesurahsofwhichtheirnumberoftheayatsisgreaterThesurahsofwhichtheirnumberoftheayatsisgreaterThesurahsofwhichtheirnumberoftheayatsisgreaterthanthesequencenumbersandhasanthanthesequencenumbersandhasanthanthesequencenumbersandhasanthanthesequencenumbersandhasanevenevenevenevennumnumnumnumberberberber

    differencedifferencedifferencedifference

    No.No.No.No. SurahSurahSurahSurah AyatAyatAyatAyat DifferenceDifferenceDifferenceDifference

    1 Al-Ftia 7 62 Al-Baqarah 286 2844 Al-Nis 176 1729 Al-Tawbah 129 120

    11 Hd 123 11213 Al-Rad 43 3014 Ibrhm 52 3815 Al-ijr 99 8416 Al-Nal 128 11217 Al-Isr 111 9418 Al-Kahf 110 9222 Al-ajj 78 5624 Al-Nr 64 40

    25 Al-Furqn 77 5227 Al-Naml 93 6628 Al-Qaa 88 6029 Al-Ankabt 69 4030 Al-Rm 60 3033 Al-Azb 73 4034 Saba 54 2035 Fir 45 1038 d 88 5039 Al-Zumar 75 36

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    64

    43 Al-Zukhruf 89 4656 Al-Wqiah 96 40

    List-18Asitcanbeseeninthelisthereinabovethetotalnumber

    ofsuchsurahsis25252525.Nowletslookatthesequencenumbersofthesurahsof

    whichtheirnumberofayatsisgreaterthanthesequencenumbers:

    ThesurahsofwhichtheirnumberofayatsiThesurahsofwhichtheirnumberofayatsiThesurahsofwhichtheirnumberofayatsiThesurahsofwhichtheirnumberofayatsisgreatersgreatersgreatersgreater

    thanthesequencenumberandwhichhaveoddthanthesequencenumberandwhichhaveoddthanthesequencenumberandwhichhaveoddthanthesequencenumberandwhichhaveoddsequencenumberssequencenumberssequencenumberssequencenumbers

    XX

    No.No.No.No. SurahSurahSurahSurah AyatAyatAyatAyat No.No.No.No. SurahSurahSurahSurah AyatAyatAyatAyat

    1 Al-Ftia 7 27 Al-Naml 933 lImrn 200 29 Al-Ankabt 695 Al-Midah 120 31 Luqmn 34

    7 Al-Arf 206 33 Al-Azb 739 Al-Tawbah 129 35 Fir 4511 Hd 123 37 Al-afft 18213 Al-Rad 43 39 Al-Zumar 7515 Al-ijr 99 41 Fuilat 5417 Al-Isr 111 43 Al-Zukhruf 8919 Maryam 98 51 Al-Dhriyt 6021 Al-Anbiy 112 53 Al-Najm 62

    23 Al-Muminn 118 55 Al-Ramn 7825 Al-Furqn 77 List-19

    Asitcanbeseeninthelisthereinabovethetotalnumberofsuchsurahsis25252525.

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    Surahsofwhichthenumberofayatsaregreaterthansequencenumber

    65

    ThesurahsofThesurahsofThesurahsofThesurahsofwhichtheirnumberofayatsisgreaterwhichtheirnumberofayatsisgreaterwhichtheirnumberofayatsisgreaterwhichtheirnumberofayatsisgreaterthanthesequencenumberandwhichhavethanthesequencenumberandwhichhavethanthesequencenumberandwhichhavethanthesequencenumberandwhichhaveevenevenevenevensequencenumberssequencenumberssequencenumberssequencenumbers

    XX

    No.No.No.No. SurahSurahSurahSurah AyatAyatAyatAyat No.No.No.No. SurahSurahSurahSurah AyatAyatAyatAyat

    2 Al-Baqarah 286 26 Al-Shuar 2274 Al-Nis 176 28 Al-Qaa 886 Al-Enm 165 30 Al-Rm 60

    8 Al-Anfl 75 34 Saba 5410 Ynus 109 36 Ysn 8312 Ysuf 111 38 d 8814 Ibrhm 52 40 Al-Mumin 8516 Al-Nal 128 42 Al-Shr 5318 Al-Kahf 110 44 Al-Dukhn 5920 h 135 54 Al-Qamar 5522 Al-ajj 78 56 Al-Wqiah 9624 Al-Nr 64

    List-20Asitcanbeseeninthelisthereinabovethetotalnumber

    ofsuchsurahsis23232323.EvaluationEvaluationEvaluationEvaluation

    The number of the surahs of which their number of ayats is larger than thesequence number and which have odd sequence number is 25252525. On the other hand, the

    number of those which have even number difference of (number of ayats- sequencenumber) is also 25252525.

    The number of the surahs of which their number of ayats is larger than thesequence number and which have even sequence number is 23232323. On the other hand,the number of those which have odd number difference of (number of ayats- sequencenumber) is also 23232323.

    Letsseetheresultswhichoutcomecollectively:

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    66

    1 A l - F t i a 72 A l - B a q a r a h 2863 l I m r n 200

    4 A l - N i s 1765 A l - M i d a h 1206 A l - E n m 1657 A l - A r f 2068 A l - A n f l 759 A l - T a w b a h 129

    10 Y n u s 10911 H d 12312 Y s u f 11113 A l - R a d 4314 I b r h m 5215 A l - i j r 9916 A l - N a l 12817 A l - I s r 11118 A l - K a h f 11019 M a r y a m 9820 h 13521 A l - A n b i y 11222 A l - a j j 7823 A l - M u m i n n 11824 A l - N r 6425 A l - F u r q n 7726 A l - S h u a r 22727 A l - N a m l 9328 A l - Q a a 8829 A l - A n k a b t 6930 A l - R m 60

    31 L u q m n 3432 A l - S a j d a h 3033 A l - A z b 7334 S a b a 5435 F i r 4536 Y s n 8337 A l - a f f t 18238 d 8839 A l - Z u m a r 7540 A l - M u m i n 8541 F u i l a t 5442 A l - S h r 5343 A l - Z u k h r u f 8944 A l - D u k h n 5945 A l - J t h i y a h 3746 A l - A q f 3547 M u a m m a d 3848 A l - F a t 2949 A l - u j u r t 1850 Q f 4551 A l - D h r i y t 6052 A l - r 4953 A l - N a j m 6254 A l - Q a m a r 5555 A l - R a m n 7856 A l - W q i a h 9657 A l - a d d 29

    58 A l - M u j d a l a h 2259 A l - a s h r 2460 A l - M u m t a i n a h 1361 A l - a f f 1462 A l - J u m u a h 1163 A l - M u n f i q n 1164 A l - T a g h b u n 1865 A l - a l q 1266 A l - T a r m 1267 A l - M u l k 3068 A l - Q a l a m 5269 A l - q q a h 5270 A l - M a r i j 4471 N 2872 A l - J i n n 2873 A l - M u z z a m m i l 2074 A l - M u d d a t h t h i r 5675 A l - Q i y m a h 4076 A l - I n s n 3177 A l - M u r s a l t 5078 A l - N a b a 4079 A l - N z i t 4680 A b a s a 4281 A l - T a k w r 2982 A l - I n f i r 1983 A l - M u a f f i f n 3684 A l - I n s h i q q 25

    85 A l - B u r j 2286 A l - r i q 1787 A l - A l 1988 A l - G h s h i y a h 2689 A l - F a j r 3090 A l - B a l a d 2091 A l - S h a m s 1592 A l - L a y l 2193 A l - u a 1194 A l - I n s h i r 895 A l - T n 896 A l - A l a q 1997 A l - Q a d r 598 A l - B a y y i n a h 899 A l - Z i l z l 8

    100 A l - d i y t 11101 A l - Q r i a h 11102 A l - T a k t h u r 8103 A l - A s r 3104 A l - H u m a z a 9105 Al-Fl 5106 Q u r a y s h 4

    107 A l - M n 7108 A l - K a w t h a r 3109 A l - K f i r n 6110 A l - N a r 3111 T a b b a t 5

    112 A l - I k h l 4113 A l - F a l a q 5114 A l - N s

    number of ayats > sequence number number of ayats > sequence number

    NO. SURAH AYAT (number of ayatssequence number)ODD NUMBER DIFFERENCE

    (number of ayatssequence number)

    VEN NUMBER DIFFERENCEODD sequence number EVEN sequence number

    Inthefigu

    re,symmetricdistributionforthesurahsofwhichtheir

    numberoftheayatsisgreaterthanthesequencenumbersisshown.

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    X X

    ax

    is

    o

    f

    symme

    try

    23 25 25 23

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    PPPPerfecterfecterfecterfectNNNNumbersumbersumbersumbers

    n, being a positive integer, the sum of all the positive

    divisorsofnisshownas(n)(n)(n)(n).If,(n)=2n(n)=2n(n)=2n(n)=2n,then,nisaperfectnumber.

    Example:Letusconsiderthenumber28

    Thesetofdivisors={1,2,4,7,14,28}Sumofthemembersofthedivisorsset,(n):(n)=1+2+4+7+14+28=565656562n=2*28=56(n)=2n56=56provides,therefore28isaperfectnumber.Letusconsiderthenumber10Thesetofdivisors={1,2,5,10}

    Sumofthemembersofthedivisorsset,(n):(n)=1+2+5+10=182n=2*10=20Since18isnotequalto20,10isnotaperfectnumber.Perfectnumbers1thru286areshowninthebelowlist.1

    nnnn DDDDivisorsivisorsivisorsivisors (n)(n)(n)(n)

    6 1,2,3,6 1228 1,2,4,7,14,28 56

    List-118

    Letushavealook,howmanyofthesurahswithaperfectnumber of ayats have odd sequence numbers and howmany ofthemhaveeventhereof:

    1 Thereareonlytwoperfectnumbersamongthenumbersfrom1to286.

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    PerfectNumbers

    235

    SurahswithSurahswithSurahswithSurahswithperfectnumberofayatsperfectnumberofayatsperfectnumberofayatsperfectnumberofayats

    No.No.No.No. SurahSurahSurahSurah AyatAyatAyatAyat

    71 N 2872 Al-Jinn 28109 Al-Kfirn 6114 Al-Ns 6

    List-119Thereare4444surahsinList-119

    ThesurahsofwhichtheirnumberofayatsisThesurahsofwhichtheirnumberofayatsisThesurahsofwhichtheirnumberofayatsisThesurahsofwhichtheirnumberofayatsisperfectperfectperfectperfectnumberandwhichhavenumberandwhichhavenumberandwhichhavenumberandwhichhaveananananoddoddoddoddsequencenumbersequencenumbersequencenumbersequencenumber

    No.No.No.No. SurahSurahSurahSurah AyatAyatAyatAyat

    71 N 28109 Al-Kfirn 6

    List-120Thereare2222surahsinList-120

    ThesurahsofwhichtheirnumberofayatsisThesurahsofwhichtheirnumberofayatsisThesurahsofwhichtheirnumberofayatsisThesurahsofwhichtheirnumberofayatsisperfectperfectperfectperfectnumberandwhichhavenumberandwhichhavenumberandwhichhavenumberandwhichhaveananananevenevenevenevensequencenumbersequencenumbersequencenumbersequencenumber

    No.No.No.No. SurahSurahSurahSurah AyatAyatAyatAyat

    72 Al-Jinn 28114 Al-Ns 6

    List-121Thereare2222surahsinList-121Letsseetheresultswhichoutcomecollectively:

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    BinarySymmetricBook ddrr..eenngg..hhaalliissaayyddeemmiirr

    www.symmetricbook.com

    236

    1 A l - F t i a 72 A l - B a q a r a h 2863 l I m r n 200

    4 A l - N i s 1765 A l - M i d a h 1206 A l - E n m 1657 A l - A r f 2068 A l - A n f l 759 A l - T a w b a h 129

    10 Y n u s 10911 H d 12312 Y s u f 11113 A l - R a d 4314 I b r h m 5215 A l - i j r 9916 A l - N a l 12817 A l - I s r 11118 A l - K a h f 11019 M a r y a m 9820 h 13521 A l - A n b i y 11222 A l - a j j 7823 A l - M u m i n n 11824 A l - N r 6425 A l - F u r q n 7726 A l - S h u a r 22727 A l - N a m l 9328 A l - Q a a 8829 A l - A n k a b t 6930 A l - R m 60

    31 L u q m n 3432 A l - S a j d a h 3033 A l - A z b 7334 S a b a 5435 F i r 4536 Y s n 8337 A l - a f f t 18238 d 8839 A l - Z u m a r 7540 A l - M u m i n 8541 F u i l a t 5442 A l - S h r 5343 A l - Z u k h r u f 8944 A l - D u k h n 5945 A l - J t h i y a h 3746 A l - A q f 3547 M u a m m a d 3848 A l - F a t 2949 A l - u j u r t 1850 Q f 4551 A l - D h r i y t 6052 A l - r 4953 A l - N a j m 6254 A l - Q a m a r 5555 A l - R a m n 7856 A l - W q i a h 9657 A l - a d d 29

    58 A l - M u j d a l a h 2259 A l - a s h r 2460 A l - M u m t a i n a h 1361 A l - a f f 1462 A l - J u m u a h 1163 A l - M u n f i q n 1164 A l - T a g h b u n 1865 A l - a l q 1266 A l - T a r m 1267 A l - M u l k 3068 A l - Q a l a m 5269 A l - q q a h 5270 A l - M a r i j 4471 N 2872 A l - J i n n 2873 A l - M u z z a m m i l 2074 A l - M u d d a t h t h i r 5675 A l - Q i y m a h 4076 A l - I n s n 3177 A l - M u r s a l t 5078 A l - N a b a 4079 A l - N z i t 4680 A b a s a 4281 A l - T a k w r 2982 A l - I n f i r 1983 A l - M u a f f i f n 3684 A l - I n s h i q q 25

    85 A l - B u r j 2286 A l - r i q 1787 A l - A l 1988 A l - G h s h i y a h 2689 A l - F a j r 3090 A l - B a l a d 2091 A l - S h a m s 1592 A l - L a y l 2193 A l - u a 1194 A l - I n s h i r 895 A l - T n 896 A l - A l a q 1997 A l - Q a d r 598 A l - B a y y i n a h 899 A l - Z i l z l 8100 A l - d i y t 11101 A l - Q r i a h 11102 A l - T a k t h u r 8103 A l - A s r 3104 A l - H u m a z a 9105 Al-Fl 5106 Q u r a y s h 4107 A l - M n 7108 A l - K a w t h a r 3109 A l - K f i r n 6110 A l - N a r 3111 T a b b a t 5

    112 A l - I k h l 4113 A l - F a l a q 5114 A l - N s 6 X

    X

    X

    X

    NO. SURAH Ayat

    Inthefigure,equaldistributionofthesurahswithperfectnumberofayatsisshown.

    SURAHS WITH PERFECT NUMBER OF AYATS

    AND ODD SEQUENCE NUMBER

    SURAHS WITH PERFECT NUMBER OF AYATS

    AND EVEN SEQUENCE NUMBER

    ax

    is

    o

    f

    symme

    try

    2 2

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    PerfectNumbers

    237

    Now,letsexaminethesurahswithnon-perfectnumberofayatswiththesameapproach.

    SurahswithSurahswithSurahswithSurahswithnonnonnonnon----perfectnumberofayatsperfectnumberofayatsperfectnumberofayatsperfectnumberofayats

    XXXX

    No.No.No.No. SurahSurahSurahSurah AyatAyatAyatAyat No.No.No.No. SurahSurahSurahSurah AyatAyatAyatAyat

    1 Al-Ftia 7 56 Al-Wqiah 962 Al-Baqarah 286 57 Al-add 29

    3 lImrn

    200

    58 Al-Mujdalah

    224 Al-Nis 176 59 Al-ashr 245 Al-Midah 120 60 Al-Mumtainah 137 Al-Arf 206 61 Al-aff 146 Al-Enm 165 62 Al-Jumuah 118 Al-Anfl 75 63 Al-Munfiqn 119 Al-Tawbah 129 64 Al-Taghbun 1810 Ynus 109 65 Al-alq 1211 Hd 123 66 Al-Tarm 12

    12 Ysuf 111 67 Al-Mulk 3013 Al-Rad 43 68 Al-Qalam 5214 Ibrhm 52 69 Al-qqah 5215 Al-ijr 99 70 Al-Marij 4416 Al-Nal 128 73 Al-Muzzammil 2017 Al-Isr 111 74 Al-Muddaththir 5618 Al-Kahf 110 75 Al-Qiymah 4019 Maryam 98 76 Al-Insn 3120 h 135 77 Al-Mursalt 50

    21 Al-Anbiy 112 78 Al-Naba 4022 Al-ajj 78 79 Al-Nzit 4623 Al-Muminn 118 80 Abasa 4224 Al-Nr 64 81 Al-Takwr 2925 Al-Furqn 77 82 Al-Infir 1926 Al-Shuar 227 83 Al-Muaffifn 3627 Al-Naml 93 84 Al-Inshiqq 2528 Al-Qaa 88 85 Al-Burj 2229 Al-Ankabt 69 86 Al-riq 17

    30 Al-Rm 60 87 Al-Al 19

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    BinarySymmetricBook ddrr..eenngg..hhaalliissaayyddeemmiirr

    www.symmetricbook.com

    238

    31 Luqmn 34 88 Al-Ghshiyah 2632 Al-Sajdah 30 89 Al-Fajr 30

    33 Al-Azb 73 90 Al-Balad 2034 Saba 54 91 Al-Shams 1535 Fir 45 92 Al-Layl 2136 Ysn 83 93 Al-ua 1137 Al-afft 182 94 Al-Inshir 838 d 88 95 Al-Tn 839 Al-Zumar 75 96 Al-Alaq 1940 Al-Mumin 85 97 Al-Qadr 541 Fuilat 54 98 Al-Bayyinah 8

    42 Al-Shr 53 99 Al-Zilzl 843 Al-Zukhruf 89 100 Al-diyt 1144 Al-Dukhn 59 101 Al-Qriah 1145 Al-Jthiyah 37 102 Al-Takthur 846 Al-Aqf 35 103 Al-Asr 347 Muammad 38 104 Al-Humaza 948 Al-Fat 29 105 Al-Fl 549 Al-ujurt 18 106 Quraysh 450 Qf 45 107 Al-Mn 751 Al-Dhriyt 60 108 Al-Kawthar 352 Al-r 49 110 Al-Nar 353 Al-Najm 62 111 Tabbat 554 Al-Qamar 55 112 Al-Ikhl 455 Al-Ramn 78 113 Al-Falaq 5

    List-122Thereare110110110110surahsinList-122

    ThesurahsofwhichtheirnumberofayatsisThesurahsofwhichtheirnumberofayatsisThesurahsofwhichtheirnumberofayatsisThesurahsofwhichtheirnumberofayatsisnonnonnonnon----perfectperfectperfectperfectnumberandwhichhavenumberandwhichhavenumberandwhichhavenumberandwhichhaveananananoddoddoddoddsequencsequencsequencsequencenumberenumberenumberenumber

    XXXX

    No.No.No.No. SurahSurahSurahSurah AyatAyatAyatAyat No.No.No.No. SurahSurahSurahSurah AyatAyatAyatAyat

    1 Al-Ftia 7 57 Al-add 293 lImrn 200 59 Al-ashr 245 Al-Midah 120 61 Al-aff 14

    7 Al-Arf 206 63 Al-Munfiqn 11

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    PerfectNumbers

    239

    9 Al-Tawbah 129 65 Al-alq 1211 Hd 123 67 Al-Mulk 30

    13 Al-Rad 43 69 Al-qqah 5215 Al-ijr 99 73 Al-Muzzammil 2017 Al-Isr 111 75 Al-Qiymah 4019 Maryam 98 77 Al-Mursalt 5021 Al-Anbiy 112 79 Al-Nzit 4623 Al-Muminn 118 81 Al-Takwr 2925 Al-Furqn 77 83 Al-Muaffifn 3627 Al-Naml 93 85 Al-Burj 2229 Al-Ankabt 69 87 Al-Al 19

    31 Luqmn 34 89 Al-Fajr 3033 Al-Azb 73 91 Al-Shams 1535 Fir 45 93 Al-ua 1137 Al-afft 182 95 Al-Tn 839 Al-Zumar 75 97 Al-Qadr 541 Fuilat 54 99 Al-Zilzl 843 Al-Zukhruf 89 101 Al-Qriah 1145 Al-Jthiyah 37 103 Al-Asr 347 Muammad 38 105 Al-Fl 549 Al-ujurt 18 107 Al-Mn 751 Al-Dhriyt 60 111 Tabbat 553 Al-Najm 62 113 Al-Falaq 555 Al-Ramn 78

    List-123Thereare55555555surahsinList-123

    ThesurahsofwhichtheThesurahsofwhichtheThesurahsofwhichtheThesurahsofwhichtheirnumberofayatsisirnumberofayatsisirnumberofayatsisirnumberofayatsisnonnonnonnon----perfectperfectperfectperfect

    numberandwhichhavenumberandwhichhavenumberandwhichhavenumberandwhichhaveananananevenevenevenevensequencenumbersequencenumbersequencenumbersequencenumber

    XXXXNo.No.No.No. SurahSurahSurahSurah AyatAyatAyatAyat No.No.No.No. SurahSurahSurahSurah AyatAyatAyatAyat

    2 Al-Baqarah 286 58 Al-Mujdalah 224 Al-Nis 176 60 Al-Mumtainah 136 Al-Enm 165 62 Al-Jumuah 118 Al-Anfl 75 64 Al-Taghbun 18

    10 Ynus 109 66 Al-Tarm 12

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    BinarySymmetricBook ddrr..eenngg..hhaalliissaayyddeemmiirr

    www.symmetricbook.com

    240

    12 Ysuf 111 68 Al-Qalam 5214 Ibrhm 52 70 Al-Marij 44

    16 Al-Nal 128 74 Al-Muddaththir 5618 Al-Kahf 110 76 Al-Insn 3120 h 135 78 Al-Naba 4022 Al-ajj 78 80 Abasa 4224 Al-Nr 64 82 Al-Infir 1926 Al-Shuar 227 84 Al-Inshiqq 2528 Al-Qaa 88 86 Al-riq 1730 Al-Rm 60 88 Al-Ghshiyah 2632 Al-Sajdah 30 90 Al-Balad 20

    34 Saba 54 92 Al-Layl 2136 Ysn 83 94 Al-Inshir 838 d 88 96 Al-Alaq 1940 Al-Mumin 85 98 Al-Bayyinah 842 Al-Shr 53 100 Al-diyt 1144 Al-Dukhn 59 102 Al-Takthur 846 Al-Aqf 35 104 Al-Humaza 948 Al-Fat 29 106 Quraysh 450 Qf 45 108 Al-Kawthar 352 Al-r 49 110 Al-Nar 354 Al-Qamar 55 112 Al-Ikhl 456 Al-Wqiah 96

    List-124Thereare55555555surahsinList-124Letsseetheresultswhichoutcomecollectively:

    Dare to behave viciously against to what is being ignorant of isDare to behave viciously against to what is being ignorant of isDare to behave viciously against to what is being ignorant of isDare to behave viciously against to what is being ignorant of isincongruous with human attitude!incongruous with human attitude!incongruous with human attitude!incongruous with human attitude!

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    PerfectNumbers

    241

    1 A l - F t i a 72 A l - B a q a r a h 2863 l I m r n 200

    4 A l - N i s 1765 A l - M i d a h 1206 A l - E n m 1657 A l - A r f 2068 A l - A n f l 759 A l - T a w b a h 129

    10 Y n u s 10911 H d 12312 Y s u f 11113 A l - R a d 4314 I b r h m 5215 A l - i j r 9916 A l - N a l 12817 A l - I s r 11118 A l - K a h f 11019 M a r y a m 9820 h 13521 A l - A n b i y 11222 A l - a j j 7823 A l - M u m i n n 11824 A l - N r 6425 A l - F u r q n 7726 A l - S h u a r 22727 A l - N a m l 9328 A l - Q a a 8829 A l - A n k a b t 6930 A l - R m 60

    31 L u q m n 3432 A l - S a j d a h 3033 A l - A z b 7334 S a b a 5435 F i r 4536 Y s n 8337 A l - a f f t 18238 d 8839 A l - Z u m a r 7540 A l - M u m i n 8541 F u i l a t 5442 A l - S h r 5343 A l - Z u k h r u f 8944 A l - D u k h n 5945 A l - J t h i y a h 3746 A l - A q f 3547 M u a m m a d 3848 A l - F a t 2949 A l - u j u r t 1850 Q f 4551 A l - D h r i y t 6052 A l - r 4953 A l - N a j m 6254 A l - Q a m a r 5555 A l - R a m n 7856 A l - W q i a h 9657 A l - a d d 29

    58 A l - M u j d a l a h 2259 A l - a s h r 2460 A l - M u m t a i n a h 1361 A l - a f f 1462 A l - J u m u a h 1163 A l - M u n f i q n 1164 A l - T a g h b u n 1865 A l - a l q 1266 A l - T a r m 1267 A l - M u l k 3068 A l - Q a l a m 5269 A l - q q a h 5270 A l - M a r i j 4471 N 2872 A l - J i n n 2873 A l - M u z z a m m i l 2074 A l - M u d d a t h t h i r 5675 A l - Q i y m a h 4076 A l - I n s n 3177 A l - M u r s a l t 5078 A l - N a b a 4079 A l - N z i t 4680 A b a s a 4281 A l - T a k w r 2982 A l - I n f i r 1983 A l - M u a f f i f n 3684 A l - I n s h i q q 25

    85 A l - B u r j 2286 A l - r i q 1787 A l - A l 1988 A l - G h s h i y a h 2689 A l - F a j r 3090 A l - B a l a d 2091 A l - S h a m s 1592 A l - L a y l 2193 A l - u a 1194 A l - I n s h i r 895 A l - T n 896 A l - A l a q 1997 A l - Q a d r 598 A l - B a y y i n a h 899 A l - Z i l z l 8100 A l - d i y t 11101 A l - Q r i a h 11102 A l - T a k t h u r 8103 A l - A s r 3104 A l - H u m a z a 9105 Al-Fl 5106 Q u r a y s h 4107 A l - M n 7108 A l - K a w t h a r 3109 A l - K f i r n 6110 A l - N a r 3111 T a b b a t 5

    112 A l - I k h l 4113 A l - F a l a q 5114 A l - N s 6

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

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    X

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    X

    X

    X

    X

    X

    X

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    X

    X

    X

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    X

    X

    X

    X

    X

    X

    X

    X

    X

    X

    NO. SURAH Ayat

    Inthefigure,equaldistributionofthesura

    hswithnon-perfectnumberofayatsisshown.

    X

    X

    X

    SURAHS WITH NON-PERFECT NUMBER OF

    AYATS AND ODD SEQUENCE NUMBER

    SURAHS WITH NON-PERFECT NUMBER OF

    AYATS AND EVEN SEQUENCE NUMBER

    ax

    is

    o

    f

    symme

    try

    55 55

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    BinarySymmetricBook ddrr..eenngg..hhaalliissaayyddeemmiirr

    www.symmetricbook.com

    242

    NowletusdividethenumbersintheindexofQurnas

    homogeneous and non-homogeneous with respect to beingperfect.

    Example for the surahs with homogeneous sequencenumbersandnumberofayats:

    1 Al-Ftia 7Surahal-Ftiaisahomogeneoussurah.Forewhyneither

    the sequence number, nor the number of ayats are perfectnumbers. Therefore, al-Ftia surah is homogeneous in thisrespect.2

    Exampleforthesurahsofwhichtheirsequencenumbersandnumberofayatsarenothomogeneous:

    6 Al-Enm 165The sequence number of surah al-Enm is a perfect

    number;however,thenumberofayatsisnot.Therefore,surahal-Enmisconsideredasnon-homogeneous.

    71 N 28

    The number of ayats of surahN is a perfect number;however, the sequence number is not. Therefore, surah N isconsideredasnon-homogeneous.

    ThesetofThesetofThesetofThesetofhomogeneoushomogeneoushomogeneoushomogeneoussurahswithrespecttobeingsurahswithrespecttobeingsurahswithrespecttobeingsurahswithrespecttobeingperfectinthesequencenumberandthenumberofayatsperfectinthesequencenumberandthenumberofayatsperfectinthesequencenumberandthenumberofayatsperfectinthesequencenumberandthenumberofayats

    No.No.No.No. SurahSurahSurahSurah AyatAyatAyatAyat No.No.No.No. SurahSurahSurahSurah AyatAyatAyatAyat

    1 Al-Ftia 7 57 Al-add 29

    2 ThereisnotanysurahinQurnhavingboththesequencenumberandthenumberof

    ayatsareperfectnumbers.

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    PerfectNumbers

    243

    2 Al-Baqarah 286 58 Al-Mujdalah 223 lImrn 200 59 Al-ashr 24

    4 Al-Nis 176 60 Al-Mumtainah 135 Al-Midah 120 61 Al-aff 147 Al-Arf 206 62 Al-Jumuah 118 Al-Anfl 75 63 Al-Munfiqn 119 Al-Tawbah 129 64 Al-Taghbun 1810 Ynus 109 65 Al-alq 1211 Hd 123 66 Al-Tarm 1212 Ysuf 111 67 Al-Mulk 30

    13 Al-Rad 43 68 Al-Qalam 5214 Ibrhm 52 69 Al-qqah 5215 Al-ijr 99 70 Al-Marij 4416 Al-Nal 128 73 Al-Muzzammil 2017 Al-Isr 111 74 Al-Muddaththir 5618 Al-Kahf 110 75 Al-Qiymah 4019 Maryam 98 76 Al-Insn 3120 h 135 77 Al-Mursalt 5021 Al-Anbiy 112 78 Al-Naba 40

    22 Al-ajj 78 79 Al-Nzit 4623 Al-Muminn 118 80 Abasa 4224 Al-Nr 64 81 Al-Takwr 2925 Al-Furqn 77 82 Al-Infir 1926 Al-Shuar 227 83 Al-Muaffifn 3627 Al-Naml 93 84 Al-Inshiqq 2529 Al-Ankabt 69 85 Al-Burj 2230 Al-Rm 60 86 Al-riq 17

    31 Luqmn 34 87 Al-Al 1932 Al-Sajdah 30 88 Al-Ghshiyah 2633 Al-Azb 73 89 Al-Fajr 3034 Saba 54 90 Al-Balad 2035 Fir 45 91 Al-Shams 1536 Ysn 83 92 Al-Layl 2137 Al-afft 182 93 Al-ua 1138 d 88 94 Al-Inshir 839 Al-Zumar 75 95 Al-Tn 8

    40 Al-Mumin 85 96 Al-Alaq 19

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    PerfectNumbers

    245

    13 Al-Rad 43 42 Al-Shr 5314 Ibrhm 52 43 Al-Zukhruf 89

    15 Al-ijr 99 44 Al-Dukhn 5916 Al-Nal 128 45 Al-Jthiyah 3717 Al-Isr 111 46 Al-Aqf 3518 Al-Kahf 110 47 Muammad 3819 Maryam 98 48 Al-Fat 2920 h 135 49 Al-ujurt 1821 Al-Anbiy 112 50 Qf 4522 Al-ajj 78 51 Al-Dhriyt 60

    23 Al-Muminn 118 52 Al-r 4924 Al-Nr 64 53 Al-Najm 6225 Al-Furqn 77 54 Al-Qamar 5526 Al-Shuar 227 55 Al-Ramn 7827 Al-Naml 93 56 Al-Wqiah 9629 Al-Ankabt 69 57 Al-add 2930 Al-Rm 60

    List-126Thereare55555555surahsinList-126

    55555555isnotaprimenumber!

    ThesetofThesetofThesetofThesetofhomogeneoushomogeneoushomogeneoushomogeneoussurahswhicharecontainedinsurahswhicharecontainedinsurahswhicharecontainedinsurahswhicharecontainedinthethethethesecondsecondsecondsecondhalfofhalfofhalfofhalfofQurnQurnQurnQurnwithrespecttobeingpewithrespecttobeingpewithrespecttobeingpewithrespecttobeingperrrrfectfectfectfectinthesequencenumberandthenumberofayatsinthesequencenumberandthenumberofayatsinthesequencenumberandthenumberofayatsinthesequencenumberandthenumberofayats

    No.No.No.No. SurahSurahSurahSurah AyatAyatAyatAyat No.No.No.No. SurahSurahSurahSurah AyatAyatAyatAyat

    58 Al-Mujdalah 22 87 Al-Al 1959 Al-ashr 24 88 Al-Ghshiyah 2660 Al-Mumtainah 13 89 Al-Fajr 3061 Al-aff 14 90 Al-Balad 2062 Al-Jumuah 11 91 Al-Shams 1563 Al-Munfiqn 11 92 Al-Layl 2164 Al-Taghbun 18 93 Al-ua 1165 Al-alq 12 94 Al-Inshir 866 Al-Tarm 12 95 Al-Tn 8

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    BinarySymmetricBook ddrr..eenngg..hhaalliissaayyddeemmiirr

    www.symmetricbook.com

    246

    67 Al-Mulk 30 96 Al-Alaq 1968 Al-Qalam 52 97 Al-Qadr 5

    69 Al-qqah 52 98 Al-Bayyinah 870 Al-Marij 44 99 Al-Zilzl 873 Al-Muzzammil 20 100 Al-diyt 1174 Al-Muddaththir 56 101 Al-Qriah 1175 Al-Qiymah 40 102 Al-Takthur 876 Al-Insn 31 103 Al-Asr 377 Al-Mursalt 50 104 Al-Humaza 978 Al-Naba 40 105 Al-Fl 5

    79 Al-Nzit 46 106 Quraysh 480 Abasa 42 107 Al-Mn 781 Al-Takwr 29 108 Al-Kawthar 382 Al-Infir 19 110 Al-Nar 383 Al-Muaffifn 36 111 Tabbat 584 Al-Inshiqq 25 112 Al-Ikhl 485 Al-Burj 22 113 Al-Falaq 586 Al-riq 17

    List-127

    Thereare53535353surahsinList-12753535353isaprimenumber!

    ThesetofThesetofThesetofThesetofnonnonnonnon----homogeneoushomogeneoushomogeneoushomogeneoussurahswithrespecttosurahswithrespecttosurahswithrespecttosurahswithrespecttobeingperfectinthesequencbeingperfectinthesequencbeingperfectinthesequencbeingperfectinthesequencenumberandthenumberenumberandthenumberenumberandthenumberenumberandthenumberofayatsofayatsofayatsofayats

    No.No.No.No. SurahSurahSurahSurah AyatAyatAyatAyat No.No.No.No. SurahSurahSurahSurah AyatAyatAyatAyat

    6 Al-Enm 165 72 Al-Jinn 2828 Al-Qaa 88 109 Al-Kfirn 671 N 28 114 Al-Ns 6

    List-128Thereare6666surahsinList-128

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    BinarySymmetricBook ddrr..eenngg..hhaalliissaayyddeemmiirr

    www.symmetricbook.com

    248

    1 A l - F t i a 72 A l - B a q a r a h 2863 l I m r n 2004 A l - N i s 1765 A l - M i d a h 120

    6 A l - E n m 1657 A l - A r f 2068 A l - A n f l 759 A l - T a w b a h 129

    10 Y n u s 10911 H d 12312 Y s u f 11113 A l - R a d 4314 I b r h m 5215 A l - i j r 9916 A l - N a l 12817 A l - I s r 11118 A l - K a h f 11019 M a r y a m 9820 h 13521 A l - A n b i y 11222 A l - a j j 7823 A l - M u m i n n 11824 A l - N r 6425 A l - F u r q n 7726 A l - S h u a r 22727 A l - N a m l 9328 A l - Q a a 8829 A l - A n k a b t 6930 A l - R m 6031 L u q m n 3432 A l - S a j d a h 30

    33 A l - A z b 7334 S a b a 5435 F i r 4536 Y s n 8337 A l - a f f t 18238 d 8839 A l - Z u m a r 7540 A l - M u m i n 8541 F u i l a t 5442 A l - S h r 5343 A l - Z u k h r u f 8944 A l - D u k h n 5945 A l - J t h i y a h 3746 A l - A q f 3547 M u a m m a d 3848 A l - F a t 2949 A l - u j u r t 1850 Q f 4551 A l - D h r i y t 6052 A l - r 4953 A l - N a j m 6254 A l - Q a m a r 5555 A l - R a m n 7856 A l - W q i a h 9657 A l - a d d 29

    58 A l - M u j d a l a h 22

    59 A l - a s h r 2460 A l - M u m t a i n a h 1361 A l - a f f 1462 A l - J u m u a h 1163 A l - M u n f i q n 1164 A l - T a g h b u n 1865 A l - a l q 1266 A l - T a r m 1267 A l - M u l k 3068 A l - Q a l a m 5269 A l - q q a h 5270 A l - M a r i j 4471 N 2872 A l - J i n n 2873 A l - M u z z a m m i l 2074 A l - M u d d a t h t h i r 5675 A l - Q i y m a h 4076 A l - I n s n 3177 A l - M u r s a l t 5078 A l - N a b a 4079 A l - N z i t 4680 A b a s a 4281 A l - T a k w r 2982 A l - I n f i r 1983 A l - M u a f f i f n 3684 A l - I n s h i q q 2585 A l - B u r j 22

    86 A l - r i q 1787 A l - A l 1988 A l - G h s h i y a h 2689 A l - F a j r 3090 A l - B a l a d 2091 A l - S h a m s 1592 A l - L a y l 2193 A l - u a 1194 A l - I n s h i r 895 A l - T n 896 A l - A l a q 1997 A l - Q a d r 598 A l - B a y y i n a h 899 A l - Z i l z l 8100 A l - d i y t 11101 A l - Q r i a h 11102 A l - T a k t h u r 8103 A l - A s r 3104 A l - H u m a z a 9105 Al-Fl 5106 Q u r a y s h 4107 A l - M n 7108 A l - K a w t h a r 3109 A l - K f i r n 6110 A l - N a r 3111 T a b b a t 5112 A l - I k h l 4113 A l - F a l a q 5114 A l - N s 6

    NO. SURAH Ayat HOMOGENOUS NON-HOMOGENOUS

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    mmetricdistributionofthehomogenousandno

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    alfoftheQur'anisshown.

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    PerfectNumbers

    249

    1 A l - F t i a 72 A l - B a q a r a h 2863 l I m r n 2004 A l - N i s 1765 A l - M i d a h 120

    6 A l - E n m 1657 A l - A r f 2068 A l - A n f l 759 A l - T a w b a h 129

    10 Y n u s 10911 H d 12312 Y s u f 11113 A l - R a d 4314 I b r h m 5215 A l - i j r 9916 A l - N a l 12817 A l - I s r 11118 A l - K a h f 11019 M a r y a m 9820 h 13521 A l - A n b i y 11222 A l - a j j 7823 A l - M u m i n n 11824 A l - N r 6425 A l - F u r q n 7726 A l - S h u a r 22727 A l - N a m l 9328 A l - Q a a 8829 A l - A n k a b t 6930 A l - R m 6031 L u q m n 3432 A l - S a j d a h 30

    33 A l - A z b 7334 S a b a 5435 F i r 4536 Y s n 8337 A l - a f f t 18238 d 8839 A l - Z u m a r 7540 A l - M u m i n 8541 F u i l a t 5442 A l - S h r 5343 A l - Z u k h r u f 8944 A l - D u k h n 5945 A l - J t h i y a h 3746 A l - A q f 3547 M u a m m a d 3848 A l - F a t 2949 A l - u j u r t 1850 Q f 4551 A l - D h r i y t 6052 A l - r 4953 A l - N a j m 6254 A l - Q a m a r 5555 A l - R a m n 7856 A l - W q i a h 9657 A l - a d d 29

    58 A l - M u j d a l a h 22

    59 A l - a s h r 2460 A l - M u m t a i n a h 1361 A l - a f f 1462 A l - J u m u a h 1163 A l - M u n f i q n 1164 A l - T a g h b u n 1865 A l - a l q 1266 A l - T a r m 1267 A l - M u l k 3068 A l - Q a l a m 5269 A l - q q a h 5270 A l - M a r i j 4471 N 2872 A l - J i n n 2873 A l - M u z z a m m i l 2074 A l - M u d d a t h t h i r 5675 A l - Q i y m a h 4076 A l - I n s n 3177 A l - M u r s a l t 5078 A l - N a b a 4079 A l - N z i t 4680 A b a s a 4281 A l - T a k w r 2982 A l - I n f i r 1983 A l - M u a f f i f n 3684 A l - I n s h i q q 2585 A l - B u r j 22

    86 A l - r i q 1787 A l - A l 1988 A l - G h s h i y a h 2689 A l - F a j r 3090 A l - B a l a d 2091 A l - S h a m s 1592 A l - L a y l 2193 A l - u a 1194 A l - I n s h i r 895 A l - T n 896 A l - A l a q 1997 A l - Q a d r 598 A l - B a y y i n a h 899 A l - Z i l z l 8100 A l - d i y t 11101 A l - Q r i a h 11102 A l - T a k t h u r 8103 A l - A s r 3104 A l - H u m a z a 9105 Al-Fl 5106 Q u r a y s h 4107 A l - M n 7108 A l - K a w t h a r 3109 A l - K f i r n 6110 A l - N a r 3111 T a b b a t 5112 A l - I k h l 4113 A l - F a l a q 5114 A l - N s 6

    Inthefigure,sy

    mmetricdistributionofthehomogenousandno

    n-homogenoussurahstothefirstandsecondh

    alfoftheQur'anisshown.

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    NO. SURAH Ayat HOMOGENOUS NON-HOMOGENOUS

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    BinarySymmetricBook ddrr..eenngg..hhaalliissaayyddeemmiirr

    www.symmetricbook.com

    250

    AmongtheAmongtheAmongtheAmongthehomogeneoushomogeneoushomogeneoushomogeneoussurahswithrespecttobeingsurahswithrespecttobeingsurahswithrespecttobeingsurahswithrespecttobeingperfectinthesequencenumberandthenumberofperfectinthesequencenumberandthenumberofperfectinthesequencenumberandthenumberofperfectinthesequencenumberandthenumberofayats,thesetofsurahswhichareayats,thesetofsurahswhichareayats,thesetofsurahswhichareayats,thesetofsurahswhicharehomogeneoushomogeneoushomogeneoushomogeneouswithwithwithwithrespecttooddnessandevennessrespecttooddnessandevennessrespecttooddnessandevennessrespecttooddnessandevenness

    No.No.No.No. SurahSurahSurahSurah AyatAyatAyatAyat No.No.No.No. SurahSurahSurahSurah AyatAyatAyatAyat

    1 Al-Ftia 7 58 Al-Mujdalah 222 Al-Baqarah 286 63 Al-Munfiqn 11

    4 Al-Nis 176 64 Al-Taghbun 189 Al-Tawbah 129 66 Al-Tarm 1211 Hd 123 68 Al-Qalam 5213 Al-Rad 43 70 Al-Marij 4414 Ibrhm 52 74 Al-Muddaththir 5615 Al-ijr 99 78 Al-Naba 4016 Al-Nal 128 80 Abasa 4217 Al-Isr 111 81 Al-Takwr 2918 Al-Kahf 110 87 Al-Al 19

    22 Al-ajj 78 88 Al-Ghshiyah 2624 Al-Nr 64 90 Al-Balad 2025 Al-Furqn 77 91 Al-Shams 1527 Al-Naml 93 93 Al-ua 1129 Al-Ankabt 69 94 Al-Inshir 830 Al-Rm 60 97 Al-Qadr 532 Al-Sajdah 30 98 Al-Bayyinah 833 Al-Azb 73 101 Al-Qriah 11

    34 Saba 54 102 Al-Takthur 835 Fir 45 103 Al-Asr 338 d 88 105 Al-Fl 539 Al-Zumar 75 106 Quraysh 443 Al-Zukhruf 89 107 Al-Mn 745 Al-Jthiyah 37 111 Tabbat 556 Al-Wqiah 96 112 Al-Ikhl 457 Al-add 29 113 Al-Falaq 5

    List-131

    Thereare54545454surahsinList-131

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    PerfectNumbers

    251

    AmongtheAmongtheAmongtheAmongthehomogeneoushomogeneoushomogeneoushomogeneoussurahswithrespecttobeingsurahswithrespecttobeingsurahswithrespecttobeingsurahswithrespecttobeingperfectinthperfectinthperfectinthperfectinthesequencenumberandthenumberofesequencenumberandthenumberofesequencenumberandthenumberofesequencenumberandthenumberofayats,thesetofsurahswhichareayats,thesetofsurahswhichareayats,thesetofsurahswhichareayats,thesetofsurahswhicharenothomogeneousnothomogeneousnothomogeneousnothomogeneouswithwithwithwithrespecttooddnessandevennessrespecttooddnessandevennessrespecttooddnessandevennessrespecttooddnessandevenness

    No.No.No.No. SurahSurahSurahSurah AyatAyatAyatAyat No.No.No.No. SurahSurahSurahSurah AyatAyatAyatAyat

    3 lImrn 200 55 Al-Ramn 785 Al-Midah 120 59 Al-ashr 24

    7 Al-Arf 206 60 Al-Mumtainah 138 Al-Anfl 75 61 Al-aff 1410 Ynus 109 62 Al-Jumuah 1112 Ysuf 111 65 Al-alq 1219 Maryam 98 67 Al-Mulk 3020 h 135 69 Al-qqah 5221 Al-Anbiy 112 73 Al-Muzzammil 2023 Al-Muminn 118 75 Al-Qiymah 4026 Al-Shuar 227 76 Al-Insn 31

    31 Luqmn 34 77 Al-Mursalt 5036 Ysn 83 79 Al-Nzit 4637 Al-afft 182 82 Al-Infir 1940 Al-Mumin 85 83 Al-Muaffifn 3641 Fuilat 54 84 Al-Inshiqq 2542 Al-Shr 53 85 Al-Burj 2244 Al-Dukhn 59 86 Al-riq 1746 Al-Aqf 35 89 Al-Fajr 30

    47 Muammad 38 92 Al-Layl 2148 Al-Fat 29 95 Al-Tn 849 Al-ujurt 18 96 Al-Alaq 1950 Qf 45 99 Al-Zilzl 851 Al-Dhriyt 60 100 Al-diyt 1152 Al-r 49 104 Al-Humaza 953 Al-Najm 62 108 Al-Kawthar 354 Al-Qamar 55 110 Al-Nar 3

    List-132

    Thereare54545454surahsinList-132

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    BinarySymmetricBook ddrr..eenngg..hhaalliissaayyddeemmiirr

    www.symmetricbook.com

    252

    1 A l - F t i a 72 A l - B a q a r a h 2863 l I m r n 200

    4 A l - N i s 1765 A l - M i d a h 1206 A l - E n m 1657 A l - A r f 2068 A l - A n f l 759 A l - T a w b a h 129

    10 Y n u s 10911 H d 12312 Y s u f 11113 A l - R a d 4314 I b r h m 5215 A l - i j r 9916 A l - N a l 12817 A l - I s r 11118 A l - K a h f 11019 M a r y a m 9820 h 13521 A l - A n b i y 11222 A l - a j j 7823 A l - M u m i n n 11824 A l - N r 6425 A l - F u r q n 7726 A l - S h u a r 22727 A l - N a m l 9328 A l - Q a a 8829 A l - A n k a b t 6930 A l - R m 60

    31 L u q m n 3432 A l - S a j d a h 3033 A l - A z b 7334 S a b a 5435 F i r 4536 Y s n 8337 A l - a f f t 18238 d 8839 A l - Z u m a r 7540 A l - M u m i n 8541 F u i l a t 5442 A l - S h r 5343 A l - Z u k h r u f 8944 A l - D u k h n 5945 A l - J t h i y a h 3746 A l - A q f 3547 M u a m m a d 3848 A l - F a t 2949 A l - u j u r t 1850 Q f 4551 A l - D h r i y t 6052 A l - r 4953 A l - N a j m 6254 A l - Q a m a r 5555 A l - R a m n 7856 A l - W q i a h 9657 A l - a d d 29

    58 A l - M u j d a l a h 2259 A l - a s h r 2460 A l - M u m t a i n a h 1361 A l - a f f 1462 A l - J u m u a h 1163 A l - M u n f i q n 1164 A l - T a g h b u n 1865 A l - a l q 1266 A l - T a r m 1267 A l - M u l k 3068 A l - Q a l a m 5269 A l - q q a h 5270 A l - M a r i j 4471 N 2872 A l - J i n n 2873 A l - M u z z a m m i l 2074 A l - M u d d a t h t h i r 5675 A l - Q i y m a h 4076 A l - I n s n 3177 A l - M u r s a l t 5078 A l - N a b a 4079 A l - N z i t 4680 A b a s a 4281 A l - T a k w r 2982 A l - I n f i r 1983 A l - M u a f f i f n 3684 A l - I n s h i q q 25

    85 A l - B u r j 2286 A l - r i q 1787 A l - A l 1988 A l - G h s h i y a h 2689 A l - F a j r 3090 A l - B a l a d 2091 A l - S h a m s 1592 A l - L a y l 2193 A l - u a 1194 A l - I n s h i r 895 A l - T n 896 A l - A l a q 1997 A l - Q a d r 598 A l - B a y y i n a h 899 A l - Z i l z l 8100 A l - d i y t 11101 A l - Q r i a h 11102 A l - T a k t h u r 8103 A l - A s r 3104 A l - H u m a z a 9105 Al-Fl 5106 Q u r a y s h 4107 A l - M n 7108 A l - K a w t h a r 3109 A l - K f i r n 6110 A l - N a r 3111 T a b b a t 5

    112 A l - I k h l 4113 A l - F a l a q 5114 A l - N s 6

    Inthefigure,equaldistributionofthehomogenoussurahswithrespecttobeingperfectissho

    wn.

    X

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    NO. SURAH Ayat

    AMONG THE HOMOGENOUS SURAHS WITH RESPECT TO

    BEING PERFECT, THE SURAHS WHICH ARE HOMOGENOUS

    WITH RESPECT TO ODDNESS AND EVENNESS

    AMONG THE HOMOGENOUS SURAHS WITH RESPECT TO

    BEING PERFECT, THE SURAHS WHICH ARE NOT

    HOMOGENOUS WITH RESPECT TO ODDNESS AND

    EVENNESS

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    PerfectNumbers

    253

    AmongtheAmongtheAmongtheAmongthenonnonnonnon----homogeneoushomogeneoushomogeneoushomogeneoussurahswithrespecttosurahswithrespecttosurahswithrespecttosurahswithrespecttobeingperfectinthesequencenumberandthenumberbeingperfectinthesequencenumberandthenumberbeingperfectinthesequencenumberandthenumberbeingperfectinthesequencenumberandthenumberofayats,thesetofsurahswhichareofayats,thesetofsurahswhichareofayats,thesetofsurahswhichareofayats,thesetofsurahswhicharehomogeneoushomogeneoushomogeneoushomogeneouswithwithwithwithrespecttooddnessandevennrespecttooddnessandevennrespecttooddnessandevennrespecttooddnessandevennessessessess

    No.No.No.No. SurahSurahSurahSurah AyatAyatAyatAyat

    28 Al-Qaa 8872 Al-Jinn 28

    114 Al-Ns 6List-133Thereare3333surahsinList-133

    AmongtheAmongtheAmongtheAmongthenonnonnonnon----homogeneoushomogeneoushomogeneoushomogeneoussurahswithrespecttosurahswithrespecttosurahswithrespecttosurahswithrespecttobeingperfectinthesequencenumberandthenumberbeingperfectinthesequencenumberandthenumberbeingperfectinthesequencenumberandthenumberbeingperfectinthesequencenumberandthenumberofayats,thesetofsurahswhichareofayats,thesetofsurahswhichareofayats,thesetofsurahswhichareofayats,thesetofsurahswhicharenothnothnothnothomogeneousomogeneousomogeneousomogeneous

    withrespecttooddnessandevennesswithrespecttooddnessandevennesswithrespecttooddnessandevennesswithrespecttooddnessandevenness

    No.No.No.No. SurahSurahSurahSurah AyatAyatAyatAyat

    6 Al-Enm 16571 N 28109 Al-Kfirn 6

    List-134

    Thereare3333surahsinList-134Letsseetheresultswhichoutcomecollectively:

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    SequenceNumSequenceNumSequenceNumSequenceNumbersSetandNumberofAyatsSetbersSetandNumberofAyatsSetbersSetandNumberofAyatsSetbersSetandNumberofAyatsSet

    InthissectionwewillanalyzethesequencenumbersandthenumberofayatssetsofthesurahsofQurn.

    SequencenumbersetofsurahsofHolySequencenumbersetofsurahsofHolySequencenumbersetofsurahsofHolySequencenumbersetofsurahsofHolyQurnQurnQurnQurn

    Thissetconsistsoftheconsecutivenumbersstartingfrom

    1andendswith114;thereforethenumberofmembersis114.SequencenumbersetofsurahsofHolyQurn={1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114}

    ThenumberofayatssetofthesurahsofThenumberofayatssetofthesurahsofThenumberofayatssetofthesurahsofThenumberofayatssetofthesurahsofQurQurQurQurnnnnThesmallestnumberinthissetis3andthelargestnumber

    is286.Thenumberofmembersofthissetis77.ThenumberofayatssetofthesurahsofQurn={3,4,5,6,7,8,9,11,12,13,14,15,17,18,19,20,21,22,24,25,26,28,29,30,31,34,35,36,37,38,40,42,43,44,45,46,49,50,52,53,54,55,56,59,60,62,64,69,73,75,77,78,83,85,88,89,93,96,98,99,109,110,

    111,112,118,120,123,128,129,135,165,176,182,200,206,227,286}

    Afterspecifyingthesetwosetslikethis,wemaynowstarttomaketheanalysis.Firstofall,letushavealookatthecommonmembersofthesequencenumberandthenumberofayatssets.

    QuestionQuestionQuestionQuestion:Howmanyoftheoddnumbersthatconsistin

    thesequencenumbersarealsocontainedinthenumbersofayats?

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    Sequencenumberssetandnumberofayatsset

    113

    Inordertogiveananswertothisquestion,firstweshould

    havetoconstitutethesetwosetsandthencomparethem.

    Odd numbers set contained in thesequence numbers Odd numbers set contained in thenumber of ayats

    OddOddOddOddnumberssetcontainedinthesequencenumbersnumberssetcontainedinthesequencenumbersnumberssetcontainedinthesequencenumbersnumberssetcontainedinthesequencenumbers

    Themembersofthissetaretheoddnumbersfrom1to114.

    {1,3,5,7,9,..,113}LetthisgivethenameNtothisset.

    s(N)=57

    OddnumberssetcontainedinthenumberofayatsOddnumberssetcontainedinthenumberofayatsOddnumberssetcontainedinthenumberofayatsOddnumberssetcontainedinthenumberofayatsWeknowthatthetotalofoddnumbersinthenumberof

    ayatsis54.Inordertodeterminethemembersoftheset,ifweremove the repeated numbers (they are 17 in total), 37 oddnumbersleft:

    {7,165,129,109,123,111,43,99,135,77,227,93,69,73,83,75,85,53,89,59,37,35,45,49,55,13,31,29,25,17,15,21,11,19,9,3,5}

    LetthisgivethenameAtothisset.

    N

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    BinarySymmetricBook ddrr..eenngg..hhaalliissaayyddeemmiirr

    www.symmetricbook.com

    114

    s(A)=37

    OddsequencenumbersetOddsequencenumbersetOddsequencenumbersetOddsequencenumbersetoddnumberofayaoddnumberofayaoddnumberofayaoddnumberofayatssettssettssettsset

    Letuslookatthecommonmembersofthesesets:

    NA={7,109,111,43,99,77,93,69,73,83,75,85,53,89,59,37,35,45,49,55,13,31,29,25,17,15,21,11,19,9,3,5}

    s(NA)=32323232Nowwemayreplyourquestion.ResponseResponseResponseResponse: 32 of the odd numbers contained in the

    sequencenumbersusedinthenumbersofayats.

    QuestionQuestionQuestionQuestion:Howmanyoftheevennumbersthatconsistinthesequencenumbersarealsocontainedinthenumbersofayats?

    Inordertogiveananswertothisquestion,firstweshould

    havetoconstitutethesetwosetsandthencomparethem.

    Even numbers set contained in the

    sequence numbers

    A

    N ANA

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    Sequencenumberssetandnumberofayatsset

    115

    Even numbers set contained in thenumber of ayats

    EvennumberssetcontainediEvennumberssetcontainediEvennumberssetcontainediEvennumberssetcontainedinthesequencenumbersnthesequencenumbersnthesequencenumbersnthesequencenumbers

    Themembersofthissetaretheevennumbersfrom1to114.

    {2,4,6,8,10,..,114}LetthisgivethenameRtothisset.

    s(R)=57

    EvennumberssetcontainedinthenumberofayatsEvennumberssetcontainedinthenumberofayatsEvennumberssetcontainedinthenumberofayatsEvennumberssetcontainedinthenumberofayatsWeknowthatthetotalofevennumberscontainedinthe

    numberofayats is60.Inordertodeterminethemembersof the

    set,ifweremovetherepeatednumbers(theyare20intotal),then40evennumbersleft:

    {286,200,176,120,206,128,110,98,112,118,64,88,34,30,182,54,38,60,62,78,96,24,14,18,12,52,44,28,20,56,50,40,46,42,36,22,26,8,4,6}

    LetthisgivethenameMtothisset.

    s(M)=40

    evenevenevenevensequencenumbersetsequencenumbersetsequencenumbersetsequencenumbersetevennumberofayaevennumberofayaeve