Abundant Numbers - Simetrik Kitap

Abundant␣bundant␣Numbersumbers␣␣n,␣ being␣ a␣ positive␣ integer,␣ the␣ sum␣ of␣ all␣ the␣ positive␣divisors␣of␣n␣is␣shown␣as␣σ(n)σ(n).␣␣If,␣σ(n)␣>␣2n␣␣␣then,␣n␣is␣an␣abundant␣number.␣␣␣ Example:␣␣Let␣us␣consider␣the␣number␣12␣The␣set␣of␣divisors␣={1,␣2,␣3,␣4,␣6,␣12}␣Sum␣of␣the␣members␣of␣the␣divisors␣set,␣σ(n):␣σ(n)␣=␣1+␣2+␣3+␣4+␣6+␣12␣=␣2828␣2n␣=␣2␣*␣12␣=␣24␣σ(n)␣>␣2n␣28␣>␣24␣␣␣␣provides,␣therefore␣28␣is␣an␣abundant␣number.␣␣Let␣us␣consider␣the␣number␣16␣The␣set␣of␣divisors␣={1,␣2,␣4,␣8,␣16␣}␣Sum␣of␣the␣members␣of␣the␣divisors␣set,␣σ(n):␣σ(n)␣=␣1+␣2+␣4+␣8+␣16␣=␣3131␣2n␣=␣2␣*␣16␣=␣32␣Since␣the␣figure␣31␣is␣not␣greater␣then␣the␣figure␣32,␣16␣is␣not␣an␣abundant␣number.␣␣␣Abundant␣numbers␣1␣thru␣286␣are␣shown␣in␣the␣below␣list.␣␣nDivisorsσ(n)␣12 1,␣2,␣3,␣4,␣6,␣12 28␣18 1,␣2,␣3,␣6,␣9,␣18 39␣20 1,␣2,␣4,␣5,␣10,␣20 42␣24 1,␣2,␣3,␣4,␣6,␣8,␣12,␣24 60␣30 1,␣2,␣3,␣5,␣6,␣10,␣15,␣30 72␣36 1,␣2,␣3,␣4,␣6,␣9,␣12,␣18,␣36 91␣40 1,␣2,␣4,␣5,␣8,␣10,␣20,␣40 90␣42 1,␣2,␣3,␣6,␣7,␣14,␣21,␣42 96␣

Binary␣Symmetric␣Book␣␣␣␣␣␣␣␣ ␣ ␣ ␣ ␣dr.␣eng.␣halis␣aydemir␣www.symmetricbook.com␣48 1,␣2,␣3,␣4,␣6,␣8,␣12,␣16,␣24,␣48 124␣54 1,␣2,␣3,␣6,␣9,␣18,␣27,␣54 120␣56 1,␣2,␣4,␣7,␣8,␣14,␣28,␣56 120␣60 1,␣2,␣3,␣4,␣5,␣6,␣10,␣12,␣15,␣20,␣30,␣60 168␣66 1,␣2,␣3,␣6,␣11,␣22,␣33,␣66 144␣70 1,␣2,␣5,␣7,␣10,␣14,␣35,␣70 144␣72 1,␣2,␣3,␣4,␣6,␣8,␣9,␣12,␣18,␣24,␣36,␣72 195␣78 1,␣2,␣3,␣6,␣13,␣26,␣39,␣78 168␣80 1,␣2,␣4,␣5,␣8,␣10,␣16,␣20,␣40,␣80 186␣84 1,␣2,␣3,␣4,␣6,␣7,␣12,␣14,␣21,␣28,␣42,␣84 224␣88 1,␣2,␣4,␣8,␣11,␣22,␣44,␣88 180␣90 1,␣2,␣3,␣5,␣6,␣9,␣10,␣15,␣18,␣30,␣45,␣90 234␣96 1,␣2,␣3,␣4,␣6,␣8,␣12,␣16,␣24,␣32,␣48,␣96 252␣100 1,␣2,␣4,␣5,␣10,␣20,␣25,␣50,␣100 217␣102 1,␣2,␣3,␣6,␣17,␣34,␣51,␣102 216␣104 1,␣2,␣4,␣8,␣13,␣26,␣52,␣104 210␣108 1,␣2,␣3,␣4,␣6,␣9,␣12,␣18,␣27,␣36,␣54,␣108 280␣112 1,␣2,␣4,␣7,␣8,␣14,␣16,␣28,␣56,␣112 248␣114 1,␣2,␣3,␣6,␣19,␣38,␣57,␣114 240␣120 1,␣2,␣3,␣4,␣5,␣6,␣8,␣10,␣12,␣15,␣20,␣24,␣30,␣40,␣60,␣120 360␣126 1,␣2,␣3,␣6,␣7,␣9,␣14,␣18,␣21,␣42,␣63,␣126 312␣132 1,␣2,␣3,␣4,␣6,␣11,␣12,␣22,␣33,␣44,␣66,␣132 336␣138 1,␣2,␣3,␣6,␣23,␣46,␣69,␣138 288␣140 1,␣2,␣4,␣5,␣7,␣10,␣14,␣20,␣28,␣35,␣70,␣140 336␣144 1,␣2,␣3,␣4,␣6,␣8,␣9,␣12,␣16,␣18,␣24,␣36,␣48,␣72,␣144 403␣150 1,␣2,␣3,␣5,␣6,␣10,␣15,␣25,␣30,␣50,␣75,␣150 372␣156 1,␣2,␣3,␣4,␣6,␣12,␣13,␣26,␣39,␣52,␣78,␣156 392␣160 1,␣2,␣4,␣5,␣8,␣10,␣16,␣20,␣32,␣40,␣80,␣160 378␣162 1,␣2,␣3,␣6,␣9,␣18,␣27,␣54,␣81,␣162 363␣168 1,␣2,␣3,␣4,␣6,␣7,␣8,␣12,␣14,␣21,␣24,␣28,␣42,␣56,␣84,␣168 480␣174 1,␣2,␣3,␣6,␣29,␣58,␣87,␣174 360␣176 1,␣2,␣4,␣8,␣11,␣16,␣22,␣44,␣88,␣176 372␣1,␣2,␣3,␣4,␣5,␣6,␣9,␣10,␣12,␣15,␣18,␣20,␣30,␣36,␣45,␣60,␣90,␣180 546␣180186 1,␣2,␣3,␣6,␣31,␣62,␣93,␣186 384␣192 1,␣2,␣3,␣4,␣6,␣8,␣12,␣16,␣24,␣32,␣48,␣64,␣96,␣192 508␣196 1,␣2,␣4,␣7,␣14,␣28,␣49,␣98,␣196 399␣198 1,␣2,␣3,␣6,␣9,␣11,␣18,␣22,␣33,␣66,␣99,␣198 468␣256

␣Abundant␣numbers␣200 1,␣2,␣4,␣5,␣8,␣10,␣20,␣25,␣40,␣50,␣100,␣200 465␣204 1,␣2,␣3,␣4,␣6,␣12,␣17,␣34,␣51,␣68,␣102,␣204 504␣208 1,␣2,␣4,␣8,␣13,␣16,␣26,␣52,␣104,␣208 434␣210 1,␣2,␣3,␣5,␣6,␣7,␣10,␣14,␣15,␣21,␣30,␣35,␣42,␣70,␣105,␣210 576␣216 1,␣2,␣3,␣4,␣6,␣8,␣9,␣12,␣18,␣24,␣27,␣36,␣54,␣72,␣108,␣216 600␣220 1,␣2,␣4,␣5,␣10,␣11,␣20,␣22,␣44,␣55,␣110,␣220 504␣222 1,␣2,␣3,␣6,␣37,␣74,␣111,␣222 456␣224 1,␣2,␣4,␣7,␣8,␣14,␣16,␣28,␣32,␣56,␣112,␣224 504␣228 1,␣2,␣3,␣4,␣6,␣12,␣19,␣38,␣57,␣76,␣114,␣228 560␣234 1,␣2,␣3,␣6,␣9,␣13,␣18,␣26,␣39,␣78,␣117,␣234 546␣2401,␣2,␣3,␣4,␣5,␣6,␣8,␣10,␣12,␣15,␣16,␣20,␣24,␣30,␣40,␣48,␣60,␣80,␣120,␣240744␣246 1,␣2,␣3,␣6,␣41,␣82,␣123,␣246 504␣1,␣2,␣3,␣4,␣6,␣7,␣9,␣12,␣14,␣18,␣21,␣28,␣36,␣42,␣63,␣84,␣126,␣252252 728␣258 1,␣2,␣3,␣6,␣43,␣86,␣129,␣258 528␣260 1,␣2,␣4,␣5,␣10,␣13,␣20,␣26,␣52,␣65,␣130,␣260 588␣264 1,␣2,␣3,␣4,␣6,␣8,␣11,␣12,␣22,␣24,␣33,␣44,␣66,␣88,␣132,␣264 720␣270 1,␣2,␣3,␣5,␣6,␣9,␣10,␣15,␣18,␣27,␣30,␣45,␣54,␣90,␣135,␣270 720␣272 1,␣2,␣4,␣8,␣16,␣17,␣34,␣68,␣136,␣272 558␣276 1,␣2,␣3,␣4,␣6,␣12,␣23,␣46,␣69,␣92,␣138,␣276 672␣280 1,␣2,␣4,␣5,␣7,␣8,␣10,␣14,␣20,␣28,␣35,␣40,␣56,␣70,␣140,␣280 720␣282 1,␣2,␣3,␣6,␣47,␣94,␣141,␣282 576␣List-135␣␣ Let␣ us␣ have␣ a␣ look,␣ how␣ many␣ of␣ the␣ surahs␣ with␣ an␣abundant␣ number␣ of␣ ayats␣ have␣odd␣ sequence␣ numbers␣ and␣how␣many␣of␣them␣have␣even␣thereof:␣␣Surahs␣with␣abundant␣number␣of␣ayats␣number␣of␣ayats␣␣XXNo.SurahAyatNo.SurahAyat␣3 Āl␣‘Imrān 200 56 Al-Wāqi‘ah 96␣4 Al-Nisā 176 59 Al-ashr 24␣5 Al-Māidah 120 64 Al-Taghābun 18␣21 Al-Anbiyā 112 65 Al-alāq 12␣257

Binary␣Symmetric␣Book␣␣␣␣␣␣␣␣ ␣ ␣ ␣ ␣dr.␣eng.␣halis␣aydemir␣www.symmetricbook.com␣22 Al-ajj 78 66 Al-Tarīm 12␣28 Al-Qaa 88 67 Al-Mulk 30␣30 Al-Rūm 60 73 Al-Muzzammil 20␣32 Al-Sajdah 30 74 Al-Muddaththir 56␣34 Saba 54 75 Al-Qiyāmah 40␣38␣ ād 88 78 Al-Naba’ 40␣41 Fuilat 54 80 ‘Abasa 42␣49 Al-ujurāt 18 83 Al-Muaffifīn 36␣51 Al-Dhāriyāt 60 89 Al-Fajr 30␣55 Al-Ramān 78 90 Al-Balad 20␣List-136␣There␣are␣2828␣surahs␣in␣List-136␣␣The␣surahs␣of␣which␣their␣number␣of␣ayats␣is␣abundantabundant␣number␣and␣which␣haved␣which␣have␣an␣an␣oddodd␣sequence␣number␣sequence␣number␣␣XXNo.SurahAyatNo.SurahAyat␣3 Āl␣‘Imrān 200 59 Al-ashr 24␣5 Al-Māidah 120 65 Al-alāq 12␣21 Al-Anbiyā 112 67 Al-Mulk 30␣41 Fuilat 54 73 Al-Muzzammil 20␣49 Al-ujurāt 18 75 Al-Qiyāmah 40␣51 Al-Dhāriyāt 60 83 Al-Muaffifīn 36␣55 Al-Ramān 78 89 Al-Fajr 30␣List-137␣There␣are␣1414␣surahs␣in␣List-137␣␣The␣surahs␣of␣which␣their␣number␣of␣ayats␣is␣abundantabundant␣number␣and␣which␣have␣an␣an␣eveneven␣sequence␣number␣sequence␣number␣␣XXNo.SurahAyatNo.SurahAyat␣4 Al-Nisā 176 56 Al-Wāqi‘ah 96␣22 Al-ajj 78 64 Al-Taghābun 18␣258

␣Abundant␣numbers␣28 Al-Qaa 88 66 Al-Tarīm 12␣30 Al-Rūm 60 74 Al-Muddaththir 56␣32 Al-Sajdah 30 78 Al-Naba’ 40␣34 Saba 54 80 ‘Abasa 42␣38␣ ād 88 90 Al-Balad 20␣List-138␣There␣are␣1414␣surahs␣in␣List-138␣␣␣

Binary␣Symmetric␣Book␣␣␣␣␣␣␣␣ ␣ ␣ ␣ ␣dr.␣eng.␣halis␣aydemir␣www.symmetricbook.com␣NO. SURAH Ayat1 A l - F ā t i ḥ a 72 A l - B a q a r a h 2863 Ā l ‘ I m r ā n 2004 A l - N i s ā 1765 A l - M ā i d a h 1206 A l - E n ‘ ā m 1657 A l - A ‘ r ā f 2068 A l - A n f ā l 759 A l - T a w b a h 12910 Y ū n u s 10911 H ū d 12312 Y ū s u f 11113 A l - R a ‘ d 4314 I b r ā h ī m 5215 A l - Ḥ i j r 9916 A l - N a ḥ l 12817 A l - ’ I s r ā 11118 A l - K a h f 11019 M a r y a m 9820 Ṭ ā h ā 13521 A l - A n b i y ā 11222 A l - Ḥ a j j 7823 A l - M u ’ m i n ū n 11824 A l - N ū r 6425 A l - F u r q ā n 7726 A l - S h u ‘ a r ā 22727 A l - N a m l 9328 A l - Q a ṣ a ṣ 8829 A l - ‘ A n k a b ū t 6930 A l - R ū m 6031 L u q m ā n 3432 A l - S a j d a h 3033 A l - A ḥ z ā b 7334 S a b a 5435 F ā ṭ i r 4536 Y ā s ī n 8337 A l - Ṣ a f f ā t 18238 Ṣ ā d 8839 A l - Z u m a r 7540 A l - M u ’ m i n 8541 F u ṣ ṣ i l a t 5442 A l - S h ū r ā 5343 A l - Z u k h r u f 8944 A l - D u k h ā n 5945 A l - J ā t h i y a h 3746 A l - A ḥ q ā f 3547 M u ḥ a m m a d 3848 A l - F a t ḥ 2949 A l - Ḥ u j u r ā t 1850 Q ā f 4551 A l - D h ā r i y ā t 6052 A l - Ṭ ū r 4953 A l - N a j m 6254 A l - Q a m a r 5555 A l - R a ḥ m ā n 7856 A l - W ā q i ‘ a h 9657 A l - Ḥ a d ī d 2958 A l - M u j ā d a l a h 2259 A l - Ḥ a s h r 2460 A l - M u m t a ḥ i n a h 1361 A l - Ṣ a f f 1462 A l - J u m u ‘ a h 1163 A l - M u n ā f i q ū n 1164 A l - T a g h ā b u n 1865 A l - Ṭ a l ā q 1266 A l - T a ḥ r ī m 1267 A l - M u l k 3068 A l - Q a l a m 5269 A l - Ḥ ā q q a h 5270 A l - M a ‘ ā r i j 4471 N ū ḥ 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 ā m a h 4076 A l - I n s ā n 3177 A l - M u r s a l ā t 5078 A l - N a b a’ 4079 A l - N ā z i ‘ ā t 4680 ‘A b a s a 4281 A l - T a k w ī r 2982 A l - I n f i ṭ ā r 1983 A l - M u ṭ a f f i f ī n 3684 A l - I n s h i q ā q 2585 A l - B u r ū j 2286 A l - Ṭ ā r i q 1787 A l - A ‘ l ā 1988 A l - G h ā 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 - Ḍ u ḥ a 1194 A l - I n s h i r ā ḥ 895 A l - T ī 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 ā l 8100 A l - ‘ Ā d i y ā t 11101 A l - Q ā r i ‘a h 11102 A l - T a k ā t h u r 8103 A l - ‘A s r 3104 A l - H u m a z a 9105 Al-Fīl 5106 Q u r a y s h 4107 A l - M ā ‘ ū n 7108 A l - K a w t h a r 3109 A l - K ā f i r ū n 6110 A l - N a ṣ r 3111 T a b b a t 5112 A l - I k h l ā ṣ 4113 A l - F a l a q 5114 A l - N ā s 6SURAHS WITH ABUNDANT NUMBER OFAYATS AND ODD SEQUENCE NUMBERXXXXX14 14XXXXXXXXXXXXa x i s o f s y m m e t r ySURAHS WITH ABUNDANT NUMBER OFAYATS AND EVEN SEQUENCE NUMBERXXXXXXXXXXXIn the figure, equal distribution of the surahs with abundant number of ayats is shown.␣260

Binary␣Symmetric␣Book␣␣␣␣␣␣␣␣ ␣ ␣ ␣ ␣dr.␣eng.␣halis␣aydemir␣www.symmetricbook.com␣42 Al-Shūrā 53 102 Al-Takāthur 8␣43 Al-Zukhruf 89 103 Al-‘Asr 3␣44 Al-Dukhān 59 104 Al-Humaza 9␣45 Al-Jāthiyah 37 105 Al-Fīl 5␣46 Al-Aqāf 35 106 Quraysh 4␣47 Muammad 38 107 Al-Mā‘ūn 7␣48 Al-Fat 29 108 Al-Kawthar 3␣50 Qāf 45 109 Al-Kāfirūn 6␣52 Al-ūr 49 110 Al-Nar 3␣53 Al-Najm 62 111 Tabbat 5␣54 Al-Qamar 55 112 Al-Ikhlā 4␣57 Al-adīd 29 113 Al-Falaq 5␣58 Al-Mujādalah 22 114 Al-Nās 6␣List-139␣There␣are␣8686␣surahs␣in␣List-139␣␣The␣surahs␣of␣which␣their␣number␣of␣ayats␣is␣nonnon-abundant␣number␣and␣which␣havenumber␣and␣which␣have␣an␣an␣oddodd␣sequence␣number␣␣XXXNo.SurahAyatNo.SurahAyat␣1 Al-Fātia 7 61 Al-aff 14␣7 Al-A‘rāf 206 63 Al-Munāfiqūn 11␣9 Al-Tawbah 129 69 Al-āqqah 52␣11 Hūd 123 71 Nū 28␣13 Al-Ra‘d 43 77 Al-Mursalāt 50␣15 Al-ijr 99 79 Al-Nāzi‘āt 46␣17 Al-’Isrā 111 81 Al-Takwīr 29␣19 Maryam 98 85 Al-Burūj 22␣23 Al-Mu’minūn 118 87 Al-A‘lā 19␣25 Al-Furqān 77 91 Al-Shams 15␣27 Al-Naml 93 93 Al-ua 11␣29 Al-‘Ankabūt 69 95 Al-Tīn 8␣31 Luqmān 34 97 Al-Qadr 5␣33 Al-Azāb 73 99 Al-Zilzāl 8␣35 Fāir 45 101 Al-Qāri‘ah 11␣262

␣Abundant␣numbers␣37 Al-affāt 182 103 Al-‘Asr 3␣39 Al-Zumar 75 105 Al-Fīl 5␣43 Al-Zukhruf 89 107 Al-Mā‘ūn 7␣45 Al-Jāthiyah 37 109 Al-Kāfirūn 6␣47 Muammad 38 111 Tabbat 5␣53 Al-Najm 62 113 Al-Falaq 5␣57 Al-adīd 29 ␣List-140␣There␣are␣4343␣surahs␣in␣List-140␣␣The␣surahs␣of␣which␣their␣number␣of␣ayats␣is␣nonnon-abundant␣number␣and␣which␣havenumber␣and␣which␣have␣an␣an␣eveneven␣sequence␣number␣␣XXNo.SurahAyatNo.SurahAyat␣2 Al-Baqarah 286 62 Al-Jumu‘ah 11␣6 Al-En‘ām 165 68 Al-Qalam 52␣8 Al-Anfāl 75 70 Al-Ma‘ārij 44␣10 Yūnus 109 72 Al-Jinn 28␣12 Yūsuf 111 76 Al-Insān 31␣14 Ibrāhīm 52 82 Al-Infiār 19␣16 Al-Nal 128 84 Al-Inshiqāq 25␣18 Al-Kahf 110 86 Al-āriq 17␣20␣ āhā 135 88 Al-Ghāshiyah 26␣24 Al-Nūr 64 92 Al-Layl 21␣26 Al-Shu‘arā 227 94 Al-Inshirā 8␣36 Yāsīn 83 96 Al-‘Alaq 19␣40 Al-Mu’min 85 98 Al-Bayyinah 8␣42 Al-Shūrā 53 100 Al-‘Ādiyāt 11␣44 Al-Dukhān 59 102 Al-Takāthur 8␣46 Al-Aqāf 35 104 Al-Humaza 9␣48 Al-Fat 29 106 Quraysh 4␣50 Qāf 45 108 Al-Kawthar 3␣52 Al-ūr 49 110 Al-Nar 3␣54 Al-Qamar 55 112 Al-Ikhlā 4␣58 Al-Mujādalah 22 114 Al-Nās 6␣263

Binary␣Symmetric␣Book␣␣␣␣␣␣␣␣ ␣ ␣ ␣ ␣dr.␣eng.␣halis␣aydemir␣www.symmetricbook.com␣60 Al-Mumtainah 13 ␣List-141␣There␣are␣4343␣surahs␣in␣List-141␣␣Let’s␣see␣the␣results␣which␣outcome␣collectively:␣␣␣␣

␣Abundant␣numbers␣NO. SURAH AyatSURAHS WITH NON-ABUNDANT NUMBER OFAYATS AND ODD SEQUENCE NUMBER1 A l - F ā t i ḥ a 7X2 A l - B a q a r a h 286X3 Ā l ‘ I m r ā n 2004 A l - N i s ā 1765 A l - M ā i d a h 1206 A l - E n ‘ ā m 165X7 A l - A ‘ r ā f 206X8 A l - A n f ā l 75X9 A l - T a w b a h 129X10 Y ū n u s 109X11 H ū d 123X12 Y ū s u f 111X13 A l - R a ‘ d 43X14 I b r ā h ī m 52X15 A l - Ḥ i j r 99X16 A l - N a ḥ l 128X17 A l - ’ I s r ā 111X18 A l - K a h f 110X19 M a r y a m 98X20 Ṭ ā h ā 135X21 A l - A n b i y ā 11222 A l - Ḥ a j j 7823 A l - M u ’ m i n ū n 118X24 A l - N ū r 64X25 A l - F u r q ā n 77X26 A l - S h u ‘ a r ā 227X27 A l - N a m l 93X28 A l - Q a ṣ a ṣ 8829 A l - ‘ A n k a b ū t 69X30 A l - R ū m 6031 L u q m ā n 34X32 A l - S a j d a h 3033 A l - A ḥ z ā b 73X34 S a b a 5435 F ā ṭ i r 45X36 Y ā s ī n 83X37 A l - Ṣ a f f ā t 182X38 Ṣ ā d 8839 A l - Z u m a r 75X40 A l - M u ’ m i n 85X41 F u ṣ ṣ i l a t 5442 A l - S h ū r ā 53X43 A l - Z u k h r u f 89X44 A l - D u k h ā n 59X45 A l - J ā t h i y a h 37X46 A l - A ḥ q ā f 35X47 M u ḥ a m m a d 38X48 A l - F a t ḥ 29X49 A l - Ḥ u j u r ā t 1850 Q ā f 4543 43X51 A l - D h ā r i y ā t 6052 A l - Ṭ ū r 49X53 A l - N a j m 62X54 A l - Q a m a r 55X55 A l - R a ḥ m ā n 7856 A l - W ā q i ‘ a h 9657 A l - Ḥ a d ī d 29X58 A l - M u j ā d a l a h 22X59 A l - Ḥ a s h r 2460 A l - M u m t a ḥ i n a h 13X61 A l - Ṣ a f f 14X62 A l - J u m u ‘ a h 11X63 A l - M u n ā f i q ū n 11X64 A l - T a g h ā b u n 1865 A l - Ṭ a l ā q 1266 A l - T a ḥ r ī m 1267 A l - M u l k 3068 A l - Q a l a m 52X69 A l - Ḥ ā q q a h 52X70 A l - M a ‘ ā r i j 44X71 N ū ḥ 28X72 A l - J i n n 28X73 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 ā m a h 4076 A l - I n s ā n 31X77 A l - M u r s a l ā t 50X78 A l - N a b a’ 4079 A l - N ā z i ‘ ā t 46X80 ‘A b a s a 4281 A l - T a k w ī r 29X82 A l - I n f i ṭ ā r 19X83 A l - M u ṭ a f f i f ī n 3684 A l - I n s h i q ā q 25X85 A l - B u r ū j 22X86 A l - Ṭ ā r i q 17X87 A l - A ‘ l ā 19X88 A l - G h ā s h i y a h 26X89 A l - F a j r 3090 A l - B a l a d 2091 A l - S h a m s 15X92 A l - L a y l 21X93 A l - Ḍ u ḥ a 11X94 A l - I n s h i r ā ḥ 8X95 A l - T ī n 8X96 A l - ‘ A l a q 19X97 A l - Q a d r 5X98 A l - B a y y i n a h 8X99 A l - Z i l z ā l 8X100 A l - ‘ Ā d i y ā t 11X101 A l - Q ā r i ‘a h 11X102 A l - T a k ā t h u r 8X103 A l - ‘A s r 3X104 A l - H u m a z a 9X105 Al-Fīl 5X106 Q u r a y s h 4X107 A l - M ā ‘ ū n 7X108 A l - K a w t h a r 3X109 A l - K ā f i r ū n 6X110 A l - N a ṣ r 3X111 T a b b a t 5X112 A l - I k h l ā ṣ 4X113 A l - F a l a q 5X114 A l - N ā s 6 Xa x i s o f s y m m e t r ySURAHS WITH NON-ABUNDANT NUMBER OFAYATS AND EVEN SEQUENCE NUMBERIn the figure, equal distribution of the surahs with non-abundant number of ayats is shown.␣265

Binary␣Symmetric␣Book␣␣␣␣␣␣␣␣ ␣ ␣ ␣ ␣dr.␣eng.␣halis␣aydemir␣www.symmetricbook.com␣␣ Now␣let␣us␣divide␣the␣numbers␣in␣the␣index␣of␣Qur’ān␣as␣homogeneous␣ and␣ non-homogeneous␣ with␣ respect␣ to␣ “being␣abundant”.␣␣␣ Example␣ for␣ the␣ surahs␣ with␣ homogeneous␣ sequence␣numbers␣and␣number␣of␣ayats:␣␣30␣ Al-Rūm␣ 60␣The␣sequence␣number␣and␣also␣the␣number␣of␣ayats␣of␣the␣surah␣ of␣ al-Rūm␣ are␣ abundant␣ numbers.␣ Consequently,␣ surah␣ of␣al-Rūm␣is␣a␣homogeneoushomogeneous␣surah␣in␣this␣sense.␣␣1␣ Al-Fātia␣ 7␣Surah␣al-Fātia␣is␣a␣homogeneous␣surah.␣Forewhy␣neither␣the␣ sequence␣ number,␣ nor␣ the␣ number␣ of␣ ayats␣ are␣ abundant␣numbers.␣ Therefore,␣ al-Fātia␣ surah␣ is␣ homogeneous␣ in␣ this␣respect.␣␣␣ Example␣for␣the␣surahs␣of␣which␣their␣sequence␣numbers␣and␣number␣of␣ayats␣are␣not␣homogeneous:␣␣12␣ Yūsuf␣ 111␣The␣ sequence␣ number␣ of␣ surah␣ Yūsuf␣ is␣ an␣ abundant␣number;␣ however,␣ the␣ number␣ of␣ ayats␣ is␣ not.␣ Therefore,␣ surah␣Yūsuf␣is␣considered␣as␣non-homogeneous.␣␣␣4␣ Al-Nisā␣ 176␣The␣ number␣ of␣ ayats␣ of␣ surah␣ al-Nisā␣ is␣ an␣ abundant␣number;␣ however,␣ the␣ sequence␣ number␣ is␣ not.␣Therefore,␣ surah␣al-Nisā␣is␣considered␣as␣non-homogeneous.␣␣␣The␣set␣of␣homogeneoushomogeneous␣surahs␣with␣respect␣to␣being␣abundant␣in␣the␣sequence␣number␣and␣the␣number␣of␣ayats␣␣266

␣Abundant␣numbers␣No.SurahAyatNo.SurahAyat␣1 Al-Fātia 7 61 Al-aff 14␣2 Al-Baqarah 286 62 Al-Jumu‘ah 11␣6 Al-En‘ām 165 63 Al-Munāfiqūn 11␣7 Al-A‘rāf 206 66 Al-Tarīm 12␣8 Al-Anfāl 75 68 Al-Qalam 52␣9 Al-Tawbah 129 69 Al-āqqah 52␣10 Yūnus 109 71 Nū 28␣11 Hūd 123 76 Al-Insān 31␣13 Al-Ra‘d 43 77 Al-Mursalāt 50␣14 Ibrāhīm 52 78 Al-Naba’ 40␣15 Al-ijr 99 79 Al-Nāzi‘āt 46␣16 Al-Nal 128 80 ‘Abasa 42␣17 Al-’Isrā 111 81 Al-Takwīr 29␣19 Maryam 98 82 Al-Infiār 19␣23 Al-Mu’minūn 118 85 Al-Burūj 22␣25 Al-Furqān 77 86 Al-āriq 17␣26 Al-Shu‘arā 227 87 Al-A‘lā 19␣27 Al-Naml 93 90 Al-Balad 20␣29 Al-‘Ankabūt 69 91 Al-Shams 15␣30 Al-Rūm 60 92 Al-Layl 21␣31 Luqmān 34 93 Al-ua 11␣33 Al-Azāb 73 94 Al-Inshirā 8␣35 Fāir 45 95 Al-Tīn 8␣37 Al-affāt 182 97 Al-Qadr 5␣39 Al-Zumar 75 98 Al-Bayyinah 8␣43 Al-Zukhruf 89 99 Al-Zilzāl 8␣44 Al-Dukhān 59 101 Al-Qāri‘ah 11␣45 Al-Jāthiyah 37 103 Al-‘Asr 3␣46 Al-Aqāf 35 105 Al-Fīl 5␣47 Muammad 38 106 Quraysh 4␣50 Qāf 45 107 Al-Mā‘ūn 7␣52 Al-ūr 49 109 Al-Kāfirūn 6␣53 Al-Najm 62 110 Al-Nar 3␣56 Al-Wāqi‘ah 96 111 Tabbat 5␣57 Al-adīd 29 113 Al-Falaq 5␣58 Al-Mujādalah 22 ␣267

Binary␣Symmetric␣Book␣␣␣␣␣␣␣␣ ␣ ␣ ␣ ␣dr.␣eng.␣halis␣aydemir␣www.symmetricbook.com␣List-142␣If␣we␣count␣the␣members␣of␣the␣List-142,␣we␣find␣that␣the␣total␣members␣of␣this␣set␣are␣7171.␣71␣is␣a␣prime␣number!␣The␣set␣of␣nonnon-homogeneoushomogeneous␣surahs␣with␣respect␣to␣being␣abundantabundant␣in␣the␣sequence␣in␣the␣sequence␣number␣and␣the␣␣number␣and␣the␣number␣of␣ayats␣␣No.SurahAyatNo.SurahAyat␣3 Āl␣‘Imrān 200 59 Al-ashr 24␣4 Al-Nisā 176 60 Al-Mumtainah 13␣5 Al-Māidah 120 64 Al-Taghābun 18␣12 Yūsuf 111 65 Al-alāq 12␣18 Al-Kahf 110 67 Al-Mulk 30␣20␣ āhā 135 70 Al-Ma‘ārij 44␣21 Al-Anbiyā 112 72 Al-Jinn 28␣22 Al-ajj 78 73 Al-Muzzammil 20␣24 Al-Nūr 64 74 Al-Muddaththir 56␣28 Al-Qaa 88 75 Al-Qiyāmah 40␣32 Al-Sajdah 30 83 Al-Muaffifīn 36␣34 Saba 54 84 Al-Inshiqāq 25␣36 Yāsīn 83 88 Al-Ghāshiyah 26␣38␣ ād 88 89 Al-Fajr 30␣40 Al-Mu’min 85 96 Al-‘Alaq 19␣41 Fuilat 54 100 Al-‘Ādiyāt 11␣42 Al-Shūrā 53 102 Al-Takāthur 8␣48 Al-Fat 29 104 Al-Humaza 9␣49 Al-ujurāt 18 108 Al-Kawthar 3␣51 Al-Dhāriyāt 60 112 Al-Ikhlā 4␣54 Al-Qamar 55 114 Al-Nās 6␣55 Al-Ramān 78 ␣List-143␣If␣we␣count␣the␣members␣of␣the␣List-143,␣we␣find␣that␣the␣total␣members␣of␣this␣set␣are␣4343.␣43␣is␣a␣prime␣number!268

␣Abundant␣numbers␣NO. SURAH Ayat HOMOGENOUS NON-HOMOGENOUS1 A l - F ā t i ḥ a 72 A l - B a q a r a h 2863 Ā l ‘ I m r ā n 2004 A l - N i s ā 1765 A l - M ā i d a h 1206 A l - E n ‘ ā m 1657 A l - A ‘ r ā f 2068 A l - A n f ā l 759 A l - T a w b a h 12910 Y ū n u s 10911 H ū d 12312 Y ū s u f 11113 A l - R a ‘ d 4314 I b r ā h ī m 5215 A l - Ḥ i j r 9916 A l - N a ḥ l 12817 A l - ’ I s r ā 11118 A l - K a h f 11019 M a r y a m 9820 Ṭ ā h ā 13521 A l - A n b i y ā 11222 A l - Ḥ a j j 7823 A l - M u ’ m i n ū n 11824 A l - N ū r 6425 A l - F u r q ā n 7726 A l - S h u ‘ a r ā 22727 A l - N a m l 9328 A l - Q a ṣ a ṣ 8829 A l - ‘ A n k a b ū t 6930 A l - R ū m 6031 L u q m ā n 3432 A l - S a j d a h 3033 A l - A ḥ z ā b 7334 S a b a 5435 F ā ṭ i r 4536 Y ā s ī n 8337 A l - Ṣ a f f ā t 18238 Ṣ ā d 8839 A l - Z u m a r 7540 A l - M u ’ m i n 8541 F u ṣ ṣ i l a t 5442 A l - S h ū r ā 5343 A l - Z u k h r u f 8944 A l - D u k h ā n 5945 A l - J ā t h i y a h 3746 A l - A ḥ q ā f 3547 M u ḥ a m m a d 3848 A l - F a t ḥ 2949 A l - Ḥ u j u r ā t 1850 Q ā f 4551 A l - D h ā r i y ā t 6052 A l - Ṭ ū r 4953 A l - N a j m 6254 A l - Q a m a r 5555 A l - R a ḥ m ā n 7856 A l - W ā q i ‘ a h 9657 A l - Ḥ a d ī d 2958 A l - M u j ā d a l a h 2259 A l - Ḥ a s h r 2460 A l - M u m t a ḥ i n a h 1361 A l - Ṣ a f f 1462 A l - J u m u ‘ a h 1163 A l - M u n ā f i q ū n 1164 A l - T a g h ā b u n 1865 A l - Ṭ a l ā q 1266 A l - T a ḥ r ī m 1267 A l - M u l k 3068 A l - Q a l a m 5269 A l - Ḥ ā q q a h 5270 A l - M a ‘ ā r i j 4471 N ū ḥ 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 ā m a h 4076 A l - I n s ā n 3177 A l - M u r s a l ā t 5078 A l - N a b a’ 4079 A l - N ā z i ‘ ā t 4680 ‘A b a s a 4281 A l - T a k w ī r 2982 A l - I n f i ṭ ā r 1983 A l - M u ṭ a f f i f ī n 3684 A l - I n s h i q ā q 2585 A l - B u r ū j 2286 A l - Ṭ ā r i q 1787 A l - A ‘ l ā 1988 A l - G h ā 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 - Ḍ u ḥ a 1194 A l - I n s h i r ā ḥ 895 A l - T ī 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 ā l 8100 A l - ‘ Ā d i y ā t 11101 A l - Q ā r i ‘a h 11102 A l - T a k ā t h u r 8103 A l - ‘A s r 3104 A l - H u m a z a 9105 Al-Fīl 5106 Q u r a y s h 4107 A l - M ā ‘ ū n 7108 A l - K a w t h a r 3109 A l - K ā f i r ū n 6110 A l - N a ṣ r 3111 T a b b a t 5112 A l - I k h l ā ṣ 4113 A l - F a l a q 5114 A l - N ā s 6XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX71X43XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXa x i s o f s y m m e t r yIn the figure, (prime-prime) distribution of the homogenous and non-homogenous surahs is shown.␣269

Binary␣Symmetric␣Book␣␣␣␣␣␣␣␣ ␣ ␣ ␣ ␣dr.␣eng.␣halis␣aydemir␣www.symmetricbook.com␣NO. SURAH Ayat HOMOGENOUS NON-HOMOGENOUS1 A l - F ā t i ḥ a 72 A l - B a q a r a h 2863 Ā l ‘ I m r ā n 2004 A l - N i s ā 1765 A l - M ā i d a h 1206 A l - E n ‘ ā m 1657 A l - A ‘ r ā f 2068 A l - A n f ā l 759 A l - T a w b a h 12910 Y ū n u s 10911 H ū d 12312 Y ū s u f 11113 A l - R a ‘ d 4314 I b r ā h ī m 5215 A l - Ḥ i j r 9916 A l - N a ḥ l 12817 A l - ’ I s r ā 11118 A l - K a h f 11019 M a r y a m 9820 Ṭ ā h ā 13521 A l - A n b i y ā 11222 A l - Ḥ a j j 7823 A l - M u ’ m i n ū n 11824 A l - N ū r 6425 A l - F u r q ā n 7726 A l - S h u ‘ a r ā 22727 A l - N a m l 9328 A l - Q a ṣ a ṣ 8829 A l - ‘ A n k a b ū t 6930 A l - R ū m 6031 L u q m ā n 3432 A l - S a j d a h 3033 A l - A ḥ z ā b 7334 S a b a 5435 F ā ṭ i r 4536 Y ā s ī n 8337 A l - Ṣ a f f ā t 18238 Ṣ ā d 8839 A l - Z u m a r 7540 A l - M u ’ m i n 8541 F u ṣ ṣ i l a t 5442 A l - S h ū r ā 5343 A l - Z u k h r u f 8944 A l - D u k h ā n 5945 A l - J ā t h i y a h 3746 A l - A ḥ q ā f 3547 M u ḥ a m m a d 3848 A l - F a t ḥ 2949 A l - Ḥ u j u r ā t 1850 Q ā f 4551 A l - D h ā r i y ā t 6052 A l - Ṭ ū r 4953 A l - N a j m 6254 A l - Q a m a r 5555 A l - R a ḥ m ā n 7856 A l - W ā q i ‘ a h 9657 A l - Ḥ a d ī d 2958 A l - M u j ā d a l a h 2259 A l - Ḥ a s h r 2460 A l - M u m t a ḥ i n a h 1361 A l - Ṣ a f f 1462 A l - J u m u ‘ a h 1163 A l - M u n ā f i q ū n 1164 A l - T a g h ā b u n 1865 A l - Ṭ a l ā q 1266 A l - T a ḥ r ī m 1267 A l - M u l k 3068 A l - Q a l a m 5269 A l - Ḥ ā q q a h 5270 A l - M a ‘ ā r i j 4471 N ū ḥ 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 ā m a h 4076 A l - I n s ā n 3177 A l - M u r s a l ā t 5078 A l - N a b a’ 4079 A l - N ā z i ‘ ā t 4680 ‘A b a s a 4281 A l - T a k w ī r 2982 A l - I n f i ṭ ā r 1983 A l - M u ṭ a f f i f ī n 3684 A l - I n s h i q ā q 2585 A l - B u r ū j 2286 A l - Ṭ ā r i q 1787 A l - A ‘ l ā 1988 A l - G h ā 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 - Ḍ u ḥ a 1194 A l - I n s h i r ā ḥ 895 A l - T ī 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 ā l 8100 A l - ‘ Ā d i y ā t 11101 A l - Q ā r i ‘a h 11102 A l - T a k ā t h u r 8103 A l - ‘A s r 3104 A l - H u m a z a 9105 Al-Fīl 5106 Q u r a y s h 4107 A l - M ā ‘ ū n 7108 A l - K a w t h a r 3109 A l - K ā f i r ū n 6110 A l - N a ṣ r 3111 T a b b a t 5112 A l - I k h l ā ṣ 4113 A l - F a l a q 5114 A l - N ā s 6PrimeXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXa x i s o f s y m m e t r yPrimeIn the figure, (prime-prime) distribution of the homogenous and non-homogenous surahs is shown.␣270