binary symmetric book 1 luluya giden · 72 23·3 2 12 215 5·43 48 73 773373 73 216 2 3·3 15 74...

37
Sum of the Prime Factors Sum of the Prime Factors Sum of the Prime Factors Sum of the Prime Factors In this section, we will make some determinations by separating the index of Qur’ān into prime factors. What do prime factors of a number mean? Non-prime numbers can be separated into multipliers by using the appropriate prime numbers among the preceding. Let us explain it with a few examples: Example: Let us consider the number 6 Prime factors of this number: 6=2*3 Let us consider the number 8 Prime factors of this number: 8=2*2*2 Let us consider the number 75 Prime factors of this number: 75 = 3 * 5 * 5 Let us consider the number 100 Prime factors of this number: 100 = 2 * 2 * 5 * 5 In separation of factors, if exponential notation is used for the repeated multipliers, 8=2 3 75 = 3 * 5 2 100 = 2 2 *5 2 Then the acquired notation is called as separating such number into prime factors, and the transaction is called the separation into prime factors (the integer prime integer prime integer prime integer prime-factorization) factorization) factorization) factorization). n, being a positive integer, the sum of the primer

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Page 1: Binary Symmetric Book 1 luluya giden · 72 23·3 2 12 215 5·43 48 73 773373 73 216 2 3·3 15 74 2·37 39 217 7·31 38 75 3·5 2 13 218 2·109 111 76 22·19 23 219 3·73 76 77 7·11
Page 2: Binary Symmetric Book 1 luluya giden · 72 23·3 2 12 215 5·43 48 73 773373 73 216 2 3·3 15 74 2·37 39 217 7·31 38 75 3·5 2 13 218 2·109 111 76 22·19 23 219 3·73 76 77 7·11

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198

a0(100)�=�2�+�2�+�5�+�5�a0(100)�=�14141414��The�largest�number�in�the�index�of�Holy�Qur’ān�is�286.�In�

the� following� list,� prime� factors� of� the� numbers� 1� thru� 286� and�their�sums�are�given:�

�PrimePrimePrimePrime PrimePrimePrimePrime

nnnn FactorsFactorsFactorsFactors

aaaa0000((((nnnn))))

nnnn FactorsFactorsFactorsFactors

aaaa0000((((nnnn))))����

1 1111 1 144 24·32 14�2 2222 2 145 5·29 34�3 3333 3 146 2·73 75�4 22 4 147 3·72 17�5 5555 5 148 22·37 41�6 2.3 5 149 149149149149 149�7 7777 7 150 2·3·52 15�8 23 6 151 151151151151 151�9 32 6 152 23·19 25�

10 2·5 7 153 32·17 23�11 11111111 11 154 2·7·11 20�12 22·3 7 155 5·31 36�13 13131313 13 156 22·3·13 20�14 2·7 9 157 157157157157 157�15 3·5 8 158 2·79 81�16 24 8 159 3·53 56�17 17171717 17 160 25·5 15�18 2·32 8 161 7·23 30�19 19191919 19 162 2·34 14�20 22·5 9 163 163163163163 163�21 3·7 10 164 22·41 45�22 2·11 13 165 3·5·11 19�23 23232323 23 166 2·83 85�24 23·3 9 167 167167167167 167�25 52 10 168 23·3·7 16�

Page 3: Binary Symmetric Book 1 luluya giden · 72 23·3 2 12 215 5·43 48 73 773373 73 216 2 3·3 15 74 2·37 39 217 7·31 38 75 3·5 2 13 218 2·109 111 76 22·19 23 219 3·73 76 77 7·11

�Sum�of�the�Prime�Factors�

199

26 2·13 15 169 132 26�27 33 9 170 2·5·17 24�28 22·7 11 171 32·19 25�29 29292929 29 172 22·43 47�30 2·3·5 10 173 173173173173 173�31 31313131 31 174 2·3·29 34�32 25 10 175 52·7 17�33 3·11 14 176 24·11 19�34 2·17 19 177 3·59 62�35 5·7 12 178 2·89 91�36 22·32 10 179 179179179179 179�37 37373737 37 180 22·32·5 15�38 2·19 21 181 181181181181 181�39 3·13 16 182 2·7·13 22�40 23·5 11 183 3·61 64�41 41414141 41 184 23·23 29�42 2·3·7 12 185 5·37 42�43 43434343 43 186 2·3·31 36�44 22·11 15 187 11·17 28�45 32·5 11 188 22·47 51�46 2·23 25 189 33·7 16�47 47474747 47 190 2·5·19 26�48 24·3 11 191 191191191191 191�49 72 14 192 26·3 15�50 2·52 12 193 193193193193 193�51 3·17 20 194 2·97 99�52 22·13 17 195 3·5·13 21�53 53535353 53 196 22·72 18�54 2·33 11 197 197197197197 197�55 5·11 16 198 2·32·11 19�56 23·7 13 199 191919199999 199�57 3·19 22 200 23·52 16�58 2·29 31 201 3·67 70�59 59595959 59 202 2·101 103�

Page 4: Binary Symmetric Book 1 luluya giden · 72 23·3 2 12 215 5·43 48 73 773373 73 216 2 3·3 15 74 2·37 39 217 7·31 38 75 3·5 2 13 218 2·109 111 76 22·19 23 219 3·73 76 77 7·11

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200

60 22·3·5 12 203 7·29 36�61 61616161 61 204 22·3·17 24�62 2·31 33 205 5·41 46�63 32·7 13 206 2·103 105�64 26 12 207 32·23 29�65 5·13 18 208 24·13 21�66 2·3·11 16 209 11·19 30�67 67676767 67 210 2·3·5·7 17�68 22·17 21 211 211211211211 211�69 3·23 26 212 22·53 57�70 2·5·7 14 213 3·71 74�71 71717171 71 214 2·107 109�72 23·32 12 215 5·43 48�73 73737373 73 216 23·33 15�74 2·37 39 217 7·31 38�75 3·52 13 218 2·109 111�76 22·19 23 219 3·73 76�77 7·11 18 220 22·5·11 20�78 2·3·13 18 221 13·17 30�79 79797979 79 222 2·3·37 42�80 24·5 13 223 223223223223 223�81 34 12 224 25·7 17�82 2·41 43 225 32·52 16�83 83838383 83 226 2·113 115�84 22·3·7 14 227 227227227227 227�85 5·17 22 228 22·3·19 26�86 2·43 45 229 229229229229 229�87 3·29 32 230 2·5·23 30�88 23·11 17 231 3·7·11 21�89 89898989 89 232 23·29 35�90 2·32·5 13 233 233233233233 233�91 7·13 20 234 2·32·13 21�92 22·23 27 235 5·47 52�93 3·31 34 236 22·59 63�

Page 5: Binary Symmetric Book 1 luluya giden · 72 23·3 2 12 215 5·43 48 73 773373 73 216 2 3·3 15 74 2·37 39 217 7·31 38 75 3·5 2 13 218 2·109 111 76 22·19 23 219 3·73 76 77 7·11

�Sum�of�the�Prime�Factors�

201

94 2·47 49 237 3·79 82�95 5·19 24 238 2·7·17 26�96 25·3 13 239 239239239239 239�97 97979797 97 240 24·3·5 16�98 2·72 16 241 241241241241 241�99 32·11 17 242 2·112 24�

100 22·52 14 243 35 15�101 101101101101 101 244 22·61 65�102 2·3·17 22 245 5·72 19�103 103103103103 103 246 2·3·41 46�104 23·13 19 247 13·19 32�105 3·5·7 15 248 23·31 37�106 2·53 55 249 3·83 86�107 107107107107 107 250 2·53 17�108 22·33 13 251 251251251251 251�109 109109109109 109 252 22·32·7 17�110 2·5·11 18 253 11·23 34�111 3·37 40 254 2·127 129�112 24·7 15 255 3·5·17 25�113 113113113113 113 256 28 16�114 2·3·19 24 257 257257257257 257�115 5·23 28 258 2·3·43 48�116 22·29 33 259 7·37 44�117 32·13 19 260 22·5·13 22�118 2·59 61 261 32·29 35�119 7·17 24 262 2·131 133�120 23·3·5 14 263 263263263263 263�121 112 22 264 23·3·11 20�122 2·61 63 265 5·53 58�123 3·41 44 266 2·7·19 28�124 22·31 35 267 3·89 92�125 53 15 268 22·67 71�126 2·32·7 15 269 269269269269 269�127 127127127127 127 270 2·33·5 16�

Page 6: Binary Symmetric Book 1 luluya giden · 72 23·3 2 12 215 5·43 48 73 773373 73 216 2 3·3 15 74 2·37 39 217 7·31 38 75 3·5 2 13 218 2·109 111 76 22·19 23 219 3·73 76 77 7·11

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202

128 27 14 271 271271271271 271�129 3·43 46 272 24·17 25�130 2·5·13 20 273 3·7·13 23�131 131131131131 131 274 2·137 139�132 22·3·11 18 275 52·11 21�133 7·19 26 276 22·3·23 30�134 2·67 69 277 277277277277 277�135 33·5 14 278 2·139 141�136 23·17 23 279 32·31 37�137 137137137137 137 280 23·5·7 18�138 2·3·23 28 281 281281281281 281�139 139139139139 139 282 2·3·47 52�140 22·5·7 16 283 283283283283 283�141 3·47 50 284 22·71 75�142 2·71 73 285 3·5·19 27�143 11·13 24 286 2·11·13 26�

List–99�

Sum�of�the�Prime�Sum�of�the�Prime�Sum�of�the�Prime�Sum�of�the�Prime�FactorsFactorsFactorsFactors�of�the�Sequence�Number�of��of�the�Sequence�Number�of��of�the�Sequence�Number�of��of�the�Sequence�Number�of�the�Surahs�the�Surahs�the�Surahs�the�Surahs�����

�Instead�of�the�sequence�number�of�the�surahs�let�us�write�

down�the�sum�of�the�prime�factors�of�them:����

aaaa0000((((No.No.No.No.)))) SurahSurahSurahSurah

aaaa0000((((No.No.No.No.)))) SurahSurahSurahSurah

aaaa0000((((No.No.No.No.)))) SurahSurahSurahSurah����

1 Al-Fāti@a 16 Al-Zumar 18 Al-

Mursalāt�

2 Al-

Baqarah 11 Al-Mu’min 18 Al-Naba’�

3 Āl�‘Imrān 41 FuEEilat 79 Al-Nāzi‘āt�4 Al-Nisā 12 Al-Shūrā 13 ‘Abasa�

5 Al-

Māidah 43 Al-Zukhruf 12 Al-Takwīr�

5 Al-En‘ām 15 Al-Dukhān 43 Al-InfiIār�7 Al-A‘rāf 11 Al-Jāthiyah 83 Al-

Page 7: Binary Symmetric Book 1 luluya giden · 72 23·3 2 12 215 5·43 48 73 773373 73 216 2 3·3 15 74 2·37 39 217 7·31 38 75 3·5 2 13 218 2·109 111 76 22·19 23 219 3·73 76 77 7·11

�Sum�of�the�Prime�Factors�

203

MuIaffifīn�

6 Al-Anfāl 25 Al-A@qāf 14 Al-

Inshiqāq�

6 Al-

Tawbah 47 Mu@ammad 22 Al-Burūj�

7 Yūnus 11 Al-Fat@ 45 Al-Māriq�11 Hūd 14 Al-Nujurāt 32 Al-A‘lā�

7 Yūsuf 12 Qāf 17 Al-

Ghāshiyah�13 Al-Ra‘d 20 Al-Dhāriyāt 89 Al-Fajr�9 Ibrāhīm 17 Al-Mūr 13 Al-Balad�8 Al-Nijr 53 Al-Najm 20 Al-Shams�

8 Al-Na@l 11 Al-Qamar 27 Al-Layl�17 Al-’Isrā 16 Al-Ra@mān 34 Al-Qu@a�

8 Al-Kahf 13 Al-Wāqi‘ah 49 Al-

Inshirā@�19 Maryam 22 Al-Nadīd 24 Al-Tīn�

9� Māhā 31 Al-

Mujādalah 13 Al-‘Alaq�

10 Al-Anbiyā 59 Al-Nashr 97 Al-Qadr�

13 Al-Najj 12 Al-

Mumta@inah 16 Al-

Bayyinah�

23 Al-

Mu’minūn 61 Al-Saff 17 Al-Zilzāl�

9 Al-Nūr 33 Al-Jumu‘ah 14 Al-‘Ādiyāt�

10 Al-

Furqān 13 Al-

Munāfiqūn 101 Al-

Qāri‘ah�

15 Al-

Shu‘arā 12 Al-

Taghābun 22 Al-

Takāthur�9 Al-Naml 18 Al-Malāq 103 Al-‘Asr�

11 Al-QaEaE 16 Al-Ta@rīm 19 Al-

Humaza�

29 Al-

‘Ankabūt 67 Al-Mulk 15 Al-Fīl�

10 Al-Rūm 21 Al-Qalam 55 Quraysh�31 Luqmān 26 Al-Nāqqah 107 Al-Mā‘ūn�

10 Al-Sajdah 14 Al-Ma‘ārij 13 Al-

Kawthar�

14 Al-A@zāb 71 Nū@ 109 Al-

Kāfirūn�19 Saba 12 Al-Jinn 18 Al-NaEr�

Page 8: Binary Symmetric Book 1 luluya giden · 72 23·3 2 12 215 5·43 48 73 773373 73 216 2 3·3 15 74 2·37 39 217 7·31 38 75 3·5 2 13 218 2·109 111 76 22·19 23 219 3·73 76 77 7·11
Page 9: Binary Symmetric Book 1 luluya giden · 72 23·3 2 12 215 5·43 48 73 773373 73 216 2 3·3 15 74 2·37 39 217 7·31 38 75 3·5 2 13 218 2·109 111 76 22·19 23 219 3·73 76 77 7·11

�Sum�of�the�Prime�Factors�

205

Al-’Isrā 40 Al-Ra@mān 18 Al-Qu@a 11�

Al-Kahf 18 Al-Wāqi‘ah 13 Al-

Inshirā@ 6�

Maryam 16 Al-Nadīd 29 Al-Tīn 6�

Māhā 14 Al-

Mujādalah 13 Al-‘Alaq 19�

Al-Anbiyā 15 Al-Nashr 9 Al-Qadr 5�

Al-Najj 18 Al-

Mumta@inah 13

Al-Bayyinah

6�

Al-Mu’minūn

61 Al-Saff 9 Al-Zilzāl 6�

Al-Nūr 12 Al-Jumu‘ah 11 Al-‘Ādiyāt 11�Al-

Furqān 18

Al-Munāfiqūn

11 Al-

Qāri‘ah 11�

Al-Shu‘arā

227 Al-

Taghābun 8

Al-Takāthur

6�

Al-Naml 34 Al-Malāq 7 Al-‘Asr 3�

Al-QaEaE 17 Al-Ta@rīm 7 Al-

Humaza 6�

Al-‘Ankabūt

26 Al-Mulk 10 Al-Fīl 5�

Al-Rūm 12 Al-Qalam 17 Quraysh 4�Luqmān 19 Al-Nāqqah 17 Al-Mā‘ūn 7�

Al-Sajdah 10 Al-Ma‘ārij 15 Al-

Kawthar 3�

Al-A@zāb 73 Nū@ 11 Al-

Kāfirūn 5�

Saba 11 Al-Jinn 11 Al-NaEr 3�

FāIir 11 Al-

Muzzammil 9 Tabbat 5�

Yāsīn 83 Al-

Muddaththir 13 Al-IkhlāE 4�

Al-Saffāt 22 Al-Qiyāmah 11 Al-Falaq 5�

Sād 17 Al-Insān 31 Al-Nās 5�List–101�

�After�specifying� these� two�sets,�now�we�can�proceed�with�

the�determination�of�the�subsets.����

Page 10: Binary Symmetric Book 1 luluya giden · 72 23·3 2 12 215 5·43 48 73 773373 73 216 2 3·3 15 74 2·37 39 217 7·31 38 75 3·5 2 13 218 2·109 111 76 22·19 23 219 3·73 76 77 7·11

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206

The�set�of�surahs�with�odd�The�set�of�surahs�with�odd�The�set�of�surahs�with�odd�The�set�of�surahs�with�odd�aaaa0000�(number�of�ayats)�(number�of�ayats)�(number�of�ayats)�(number�of�ayats)����

� XX

No.No.No.No. SurahSurahSurahSurah aaaa0000((((AyatAyatAyatAyat))))

No.No.No.No. SurahSurahSurahSurah

aaaa0000((((AyatAyatAyatAyat))))����

1 Al-Fāti@a 7 63 Al-

Munāfiqūn 11�

4 Al-Nisā 19 65 Al-Malāq 7�6 Al-En‘ām 19 66 Al-Ta@rīm 7�7 Al-A‘rāf 105 68 Al-Qalam 17�8 Al-Anfāl 13 69 Al-Nāqqah 17�

10 Yūnus 109 70 Al-Ma‘ārij 15�13 Al-Ra‘d 43 71 Nū@ 11�14 Ibrāhīm 17 72 Al-Jinn 11�15 Al-Nijr 17 73 Al-Muzzammil 9�

21 Al-Anbiyā 15 74 Al-Muddaththir 13�

23 Al-

Mu’minūn 61 75 Al-Qiyāmah 11�

26 Al-Shu‘arā 227 76 Al-Insān 31�28 Al-QaEaE 17 78 Al-Naba’ 11�31 Luqmān 19 79 Al-Nāzi‘āt 25�33 Al-A@zāb 73 81 Al-Takwīr 29�34 Saba 11 82 Al-InfiIār 19�35 FāIir 11 85 Al-Burūj 13�36 Yāsīn 83 86 Al-Māriq 17�38� Sād 17 87 Al-A‘lā 19�

39 Al-Zumar 13 88 Al-

Ghāshiyah 15�

41 FuEEilat 11 90 Al-Balad 9�42 Al-Shūrā 53 93 Al-Qu@a 11�43 Al-Zukhruf 89 96 Al-‘Alaq 19�44 Al-Dukhān 59 97 Al-Qadr 5�45 Al-Jāthiyah 37 100 Al-‘Ādiyāt 11�47 Mu@ammad 21 101 Al-Qāri‘ah 11�48 Al-Fat@ 29 103 Al-‘Asr 3�50 Qāf 11 105 Al-Fīl 5�53 Al-Najm 33 107 Al-Mā‘ūn 7�

Page 11: Binary Symmetric Book 1 luluya giden · 72 23·3 2 12 215 5·43 48 73 773373 73 216 2 3·3 15 74 2·37 39 217 7·31 38 75 3·5 2 13 218 2·109 111 76 22·19 23 219 3·73 76 77 7·11

�Sum�of�the�Prime�Factors�

207

56 Al-Wāqi‘ah 13 108 Al-Kawthar 3�57 Al-Nadīd 29 109 Al-Kāfirūn 5�

58 Al-

Mujādalah 13 110 Al-NaEr 3�

59 Al-Nashr 9 111 Tabbat 5�

60 Al-

Mumta@inah 13 113 Al-Falaq 5�

61 Al-Saff 9 114 Al-Nās 5�62 Al-Jumu‘ah 11 �

List–102�As�it�is�seen�from�the�List-102,�the�number�of�members�of�

the� set� of� surahs�with� an� odd� numbered� sum� of� prime� factors� of�the�number�of�ayats�is�71717171.���

71717171�is�a�prime�number!��

The�set�of�surahs�with�odd�The�set�of�surahs�with�odd�The�set�of�surahs�with�odd�The�set�of�surahs�with�odd�aaaa0000�(�(�(�(Sequence�NumberSequence�NumberSequence�NumberSequence�Number))))����

� aaaa0000((((No.No.No.No.)))) SurahSurahSurahSurah

aaaa0000((((No.No.No.No.)))) SurahSurahSurahSurah����

1 Al-Fāti@a 31 Al-Mujādalah�3 Āl�‘Imrān 59 Al-Nashr�5 Al-Māidah 61 Al-Saff�5 Al-En‘ām 33 Al-Jumu‘ah�7 Al-A‘rāf 13 Al-Munāfiqūn�7 Yūnus 67 Al-Mulk�

11 Hūd 21 Al-Qalam�7 Yūsuf 71 Nū@�

13 Al-Ra‘d 73 Al-Muzzammil�9 Ibrāhīm 39 Al-Muddaththir�

17 Al-’Isrā 13 Al-Qiyāmah�19 Maryam 23 Al-Insān�9� Māhā 79 Al-Nāzi‘āt�

13 Al-Najj 13 ‘Abasa�23 Al-Mu’minūn 43 Al-InfiIār�9 Al-Nūr 83 Al-MuIaffifīn�

15 Al-Shu‘arā 45 Al-Māriq�9 Al-Naml 17 Al-Ghāshiyah�

Page 12: Binary Symmetric Book 1 luluya giden · 72 23·3 2 12 215 5·43 48 73 773373 73 216 2 3·3 15 74 2·37 39 217 7·31 38 75 3·5 2 13 218 2·109 111 76 22·19 23 219 3·73 76 77 7·11

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208

11 Al-QaEaE 89 Al-Fajr�29 Al-‘Ankabūt 13 Al-Balad�31 Luqmān 27 Al-Layl�19 Saba 49 Al-Inshirā@�37 Al-Saffāt 13 Al-‘Alaq�21� Sād 97 Al-Qadr�11 Al-Mu’min 17 Al-Zilzāl�41 FuEEilat 101 Al-Qāri‘ah�43 Al-Zukhruf 103 Al-‘Asr�15 Al-Dukhān 19 Al-Humaza�11 Al-Jāthiyah 15 Al-Fīl�25 Al-A@qāf 55 Quraysh�47 Mu@ammad 107 Al-Mā‘ūn�11 Al-Fat@ 13 Al-Kawthar�17 Al-Mūr 109 Al-Kāfirūn�53 Al-Najm 15 Al-IkhlāE�11 Al-Qamar 113 Al-Falaq�13 Al-Wāqi‘ah �

List–103�

�As�it�is�seen�from�the�List-103,�the�number�of�members�of�

the�set�of�surahs�with�an�odd�numbered�sum�of�the�prime�factors�of�the�sequence�number�of�the�surahs�also�is�71717171.���

71717171�is�a�prime�number!��EvaluationEvaluationEvaluationEvaluation

Can this happen by coincidence? �Let’s�see�the�results�which�outcome�collectively:���

Page 13: Binary Symmetric Book 1 luluya giden · 72 23·3 2 12 215 5·43 48 73 773373 73 216 2 3·3 15 74 2·37 39 217 7·31 38 75 3·5 2 13 218 2·109 111 76 22·19 23 219 3·73 76 77 7·11

�Sum�of�the�Prime�Factors�

209

1 A l - F ā t i ḥ a 72 A l - B a q a r a h 26

3 Ā l ‘ I m r ā n 164 A l - N i s ā 195 A l - M ā i d a h 145 A l - E n ‘ ā m 197 A l - A ‘ r ā f 1056 A l - A n f ā l 136 A l - T a w b a h 46

7 Y ū n u s 10911 H ū d 447 Y ū s u f 4013 A l - R a ‘ d 43

9 I b r ā h ī m 178 A l - Ḥ i j r 178 A l - N a ḥ l 1417 A l - ’ I s r ā 408 A l - K a h f 18

19 M a r y a m 169 Ṭ ā h ā 1410 A l - A n b i y ā 1513 A l - Ḥ a j j 1823 A l - M u ’ m i n ū n 619 A l - N ū r 1210 A l - F u r q ā n 1815 A l - S h u ‘ a r ā 227

9 A l - N a m l 3411 A l - Q a ṣ a ṣ 1729 A l - ‘ A n k a b ū t 2610 A l - R ū m 1231 L u q m ā n 19

10 A l - S a j d a h 1014 A l - A ḥ z ā b 73

19 S a b a 1112 F ā ṭ i r 1110 Y ā s ī n 83

37 A l - Ṣ a f f ā t 2221 Ṣ ā d 1716 A l - Z u m a r 1311 A l - M u ’ m i n 2241 F u ṣ ṣ i l a t 1112 A l - S h ū r ā 5343 A l - Z u k h r u f 8915 A l - D u k h ā n 5911 A l - J ā t h i y a h 3725 A l - A ḥ q ā f 1247 M u ḥ a m m a d 2111 A l - F a t ḥ 2914 A l - Ḥ u j u r ā t 812 Q ā f 1120 A l - D h ā r i y ā t 1217 A l - Ṭ ū r 1453 A l - N a j m 3311 A l - Q a m a r 1616 A l - R a ḥ m ā n 1813 A l - W ā q i ‘ a h 1322 A l - Ḥ a d ī d 2931 A l - M u j ā d a l a h 1359 A l - Ḥ a s h r 912 A l - M u m t a ḥ i n a h 1361 A l - Ṣ a f f 933 A l - J u m u ‘ a h 1113 A l - M u n ā f i q ū n 1112 A l - T a g h ā b u n 818 A l - Ṭ a l ā q 716 A l - T a ḥ r ī m 767 A l - M u l k 1021 A l - Q a l a m 1726 A l - Ḥ ā q q a h 1714 A l - M a ‘ ā r i j 1571 N ū ḥ 1112 A l - J i n n 1173 A l - M u z z a m m i l 939 A l - M u d d a t h t h i r 1313 A l - Q i y ā m a h 1123 A l - I n s ā n 3118 A l - M u r s a l ā t 1218 A l - N a b a’ 1179 A l - N ā z i ‘ ā t 2513 ‘A b a s a 1212 A l - T a k w ī r 2943 A l - I n f i ṭ ā r 1983 A l - M u ṭ a f f i f ī n 1014 A l - I n s h i q ā q 1022 A l - B u r ū j 1345 A l - Ṭ ā r i q 1732 A l - A ‘ l ā 1917 A l - G h ā s h i y a h 1589 A l - F a j r 1013 A l - B a l a d 920 A l - S h a m s 827 A l - L a y l 1034 A l - Ḍ u ḥ a 1149 A l - I n s h i r ā ḥ 624 A l - T ī n 613 A l - ‘ A l a q 1997 A l - Q a d r 516 A l - B a y y i n a h 617 A l - Z i l z ā l 614 A l - ‘ Ā d i y ā t 11101 A l - Q ā r i ‘a h 1122 A l - T a k ā t h u r 6103 A l - ‘A s r 319 A l - H u m a z a 615 Al-Fīl 555 Q u r a y s h 4107 A l - M ā ‘ ū n 713 A l - K a w t h a r 3109 A l - K ā f i r ū n 518 A l - N a ṣ r 340 T a b b a t 515 A l - I k h l ā ṣ 4113 A l - F a l a q 524 A l - N ā s 5

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1 A l - F ā t i ḥ a 72 A l - B a q a r a h 263 Ā l ‘ I m r ā n 164 A l - N i s ā 195 A l - M ā i d a h 14

5 A l - E n ‘ ā m 197 A l - A ‘ r ā f 105

6 A l - A n f ā l 136 A l - T a w b a h 467 Y ū n u s 10911 H ū d 447 Y ū s u f 40

13 A l - R a ‘ d 439 I b r ā h ī m 178 A l - Ḥ i j r 178 A l - N a ḥ l 1417 A l - ’ I s r ā 408 A l - K a h f 1819 M a r y a m 169 Ṭ ā h ā 1410 A l - A n b i y ā 1513 A l - Ḥ a j j 1823 A l - M u ’ m i n ū n 619 A l - N ū r 1210 A l - F u r q ā n 1815 A l - S h u ‘ a r ā 2279 A l - N a m l 34

11 A l - Q a ṣ a ṣ 1729 A l - ‘ A n k a b ū t 2610 A l - R ū m 1231 L u q m ā n 1910 A l - S a j d a h 1014 A l - A ḥ z ā b 7319 S a b a 1112 F ā ṭ i r 1110 Y ā s ī n 83

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16 A l - Z u m a r 1311 A l - M u ’ m i n 2241 F u ṣ ṣ i l a t 1112 A l - S h ū r ā 5343 A l - Z u k h r u f 8915 A l - D u k h ā n 5911 A l - J ā t h i y a h 3725 A l - A ḥ q ā f 1247 M u ḥ a m m a d 2111 A l - F a t ḥ 2914 A l - Ḥ u j u r ā t 812 Q ā f 1120 A l - D h ā r i y ā t 1217 A l - Ṭ ū r 1453 A l - N a j m 3311 A l - Q a m a r 1616 A l - R a ḥ m ā n 1813 A l - W ā q i ‘ a h 1322 A l - Ḥ a d ī d 2931 A l - M u j ā d a l a h 1359 A l - Ḥ a s h r 912 A l - M u m t a ḥ i n a h 1361 A l - Ṣ a f f 933 A l - J u m u ‘ a h 1113 A l - M u n ā f i q ū n 1112 A l - T a g h ā b u n 818 A l - Ṭ a l ā q 716 A l - T a ḥ r ī m 767 A l - M u l k 1021 A l - Q a l a m 1726 A l - Ḥ ā q q a h 1714 A l - M a ‘ ā r i j 1571 N ū ḥ 1112 A l - J i n n 1173 A l - M u z z a m m i l 939 A l - M u d d a t h t h i r 1313 A l - Q i y ā m a h 1123 A l - I n s ā n 3118 A l - M u r s a l ā t 1218 A l - N a b a’ 1179 A l - N ā z i ‘ ā t 2513 ‘A b a s a 1212 A l - T a k w ī r 2943 A l - I n f i ṭ ā r 1983 A l - M u ṭ a f f i f ī n 1014 A l - I n s h i q ā q 1022 A l - B u r ū j 1345 A l - Ṭ ā r i q 1732 A l - A ‘ l ā 1917 A l - G h ā s h i y a h 1589 A l - F a j r 1013 A l - B a l a d 920 A l - S h a m s 827 A l - L a y l 1034 A l - Ḍ u ḥ a 1149 A l - I n s h i r ā ḥ 624 A l - T ī n 613 A l - ‘ A l a q 1997 A l - Q a d r 516 A l - B a y y i n a h 617 A l - Z i l z ā l 614 A l - ‘ Ā d i y ā t 11101 A l - Q ā r i ‘a h 1122 A l - T a k ā t h u r 6103 A l - ‘A s r 319 A l - H u m a z a 615 Al-Fīl 555 Q u r a y s h 4107 A l - M ā ‘ ū n 713 A l - K a w t h a r 3109 A l - K ā f i r ū n 518 A l - N a ṣ r 340 T a b b a t 515 A l - I k h l ā ṣ 4113 A l - F a l a q 524 A l - N ā s 5

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�Sum�of�the�Prime�Factors�

211

The�set�of�surahs�with�The�set�of�surahs�with�The�set�of�surahs�with�The�set�of�surahs�with�eveneveneveneven����aaaa0000�(number��(number��(number��(number�of�ayats)of�ayats)of�ayats)of�ayats)����

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2 Al-

Baqarah 26 51 Al-Dhāriyāt 12�

3 Āl�‘Imrān 16 52 Al-Mūr 14�5 Al-Māidah 14 54 Al-Qamar 16�9 Al-Tawbah 46 55 Al-Ra@mān 18�

11 Hūd 44 64 Al-Taghābun 8�12 Yūsuf 40 67 Al-Mulk 10�16 Al-Na@l 14 77 Al-Mursalāt 12�17 Al-’Isrā 40 80 ‘Abasa 12�18 Al-Kahf 18 83 Al-MuIaffifīn 10�19 Maryam 16 84 Al-Inshiqāq 10�20� Māhā 14 89 Al-Fajr 10�22 Al-Najj 18 91 Al-Shams 8�24 Al-Nūr 12 92 Al-Layl 10�25 Al-Furqān 18 94 Al-Inshirā@ 6�27 Al-Naml 34 95 Al-Tīn 6�

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30 Al-Rūm 12 99 Al-Zilzāl 6�32 Al-Sajdah 10 102 Al-Takāthur 6�37 Al-Saffāt 22 104 Al-Humaza 6�40 Al-Mu’min 22 106 Quraysh 4�46 Al-A@qāf 12 112 Al-IkhlāE 4�49 Al-Nujurāt 8 �

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the�set�of�surahs�with�an�even�numbered�sum�of�prime�factors�of�the�number�of�ayats�is�43434343.���

43434343�is�a�prime�number!�

Page 16: Binary Symmetric Book 1 luluya giden · 72 23·3 2 12 215 5·43 48 73 773373 73 216 2 3·3 15 74 2·37 39 217 7·31 38 75 3·5 2 13 218 2·109 111 76 22·19 23 219 3·73 76 77 7·11

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212

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Figure-20�Distribution�of�the�surahs�(as�prime�and�prime)�is�shown.�

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2 Al-Baqarah 12 Al-Taghābun�4 Al-Nisā 18 Al-Malāq�6 Al-Anfāl 16 Al-Ta@rīm�6 Al-Tawbah 26 Al-Nāqqah�8 Al-Nijr 14 Al-Ma‘ārij�8 Al-Na@l 12 Al-Jinn�8 Al-Kahf 18 Al-Mursalāt�

10 Al-Anbiyā 18 Al-Naba’�10 Al-Furqān 12 Al-Takwīr�10 Al-Rūm 14 Al-Inshiqāq�10 Al-Sajdah 22 Al-Burūj�14 Al-A@zāb 32 Al-A‘lā�12 FāIir 20 Al-Shams�10 Yāsīn 34 Al-Qu@a�16 Al-Zumar 24 Al-Tīn�12 Al-Shūrā 16 Al-Bayyinah�14 Al-Nujurāt 14 Al-‘Ādiyāt�12 Qāf 22 Al-Takāthur�

114 � � �

71 43�

The�total�number�of�surahs�

The�number�of�surahs�

with�odd�a0�(number�

of�ayats)�

The�number�of�surahs�

with�even�a0�(number�of�

ayats)�

Page 17: Binary Symmetric Book 1 luluya giden · 72 23·3 2 12 215 5·43 48 73 773373 73 216 2 3·3 15 74 2·37 39 217 7·31 38 75 3·5 2 13 218 2·109 111 76 22·19 23 219 3·73 76 77 7·11

�Sum�of�the�Prime�Factors�

213

20 Al-Dhāriyāt 18 Al-NaEr�16 Al-Ra@mān 40 Tabbat�22 Al-Nadīd 24 Al-Nās�12 Al-Mumta@inah �

List-105�

�As�it�is�seen�from�the�List-105,�the�number�of�members�of�

the�set�of�surahs�with�an�even�numbered�sum�of�the�prime�factors�of�the�sequence�number�of�the�surahs�also�is�43434343.���

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Figure-21�Distribution�of�the�surahs�(as�prime�and�prime)�is�shown.�

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In a single word, it is incredible… �Let’s�see�the�results�which�outcome�collectively:��

114 � � �

71 43�

The�total�number�of�surahs�

The�number�of�surahs�

with�odd�a0�(sequence�

number)�

The�number�of�surahs�

with�even�a0�(sequence�

number)�

Page 18: Binary Symmetric Book 1 luluya giden · 72 23·3 2 12 215 5·43 48 73 773373 73 216 2 3·3 15 74 2·37 39 217 7·31 38 75 3·5 2 13 218 2·109 111 76 22·19 23 219 3·73 76 77 7·11
Page 19: Binary Symmetric Book 1 luluya giden · 72 23·3 2 12 215 5·43 48 73 773373 73 216 2 3·3 15 74 2·37 39 217 7·31 38 75 3·5 2 13 218 2·109 111 76 22·19 23 219 3·73 76 77 7·11

�Sum�of�the�Prime�Factors�

215

1 A l - F ā t i ḥ a 72 A l - B a q a r a h 263 Ā l ‘ I m r ā n 164 A l - N i s ā 195 A l - M ā i d a h 145 A l - E n ‘ ā m 197 A l - A ‘ r ā f 1056 A l - A n f ā l 136 A l - T a w b a h 467 Y ū n u s 10911 H ū d 447 Y ū s u f 4013 A l - R a ‘ d 439 I b r ā h ī m 178 A l - Ḥ i j r 178 A l - N a ḥ l 1417 A l - ’ I s r ā 408 A l - K a h f 1819 M a r y a m 169 Ṭ ā h ā 1410 A l - A n b i y ā 1513 A l - Ḥ a j j 1823 A l - M u ’ m i n ū n 619 A l - N ū r 1210 A l - F u r q ā n 1815 A l - S h u ‘ a r ā 2279 A l - N a m l 3411 A l - Q a ṣ a ṣ 1729 A l - ‘ A n k a b ū t 2610 A l - R ū m 1231 L u q m ā n 1910 A l - S a j d a h 1014 A l - A ḥ z ā b 7319 S a b a 1112 F ā ṭ i r 1110 Y ā s ī n 8337 A l - Ṣ a f f ā t 2221 Ṣ ā d 1716 A l - Z u m a r 13

11 A l - M u ’ m i n 2241 F u ṣ ṣ i l a t 1112 A l - S h ū r ā 5343 A l - Z u k h r u f 8915 A l - D u k h ā n 5911 A l - J ā t h i y a h 3725 A l - A ḥ q ā f 1247 M u ḥ a m m a d 2111 A l - F a t ḥ 29

14 A l - Ḥ u j u r ā t 812 Q ā f 11

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Page 20: Binary Symmetric Book 1 luluya giden · 72 23·3 2 12 215 5·43 48 73 773373 73 216 2 3·3 15 74 2·37 39 217 7·31 38 75 3·5 2 13 218 2·109 111 76 22·19 23 219 3·73 76 77 7·11

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216

� QuestionQuestionQuestionQuestion:� How� many� of� the� numbers� in� the� sum� of� the�prime� factors� of� the� number� of� ayats� of� the� surahs� are� prime�numbers�and�how�many�of�them�are�not?�

In�order�to�give�an�answer�to�this�question,�we�should�have�to�constitute�these�two�sets:�

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Al-Fāti@a 7 Al-Munāfiqūn 11�Al-Nisā 19 Al-Malāq 7�

Al-En‘ām 19 Al-Ta@rīm 7�Al-Anfāl 13 Al-Qalam 17�Yūnus 109 Al-Nāqqah 17�

Al-Ra‘d 43 Nū@ 11�Ibrāhīm 17 Al-Jinn 11�Al-Nijr 17 Al-Muddaththir 13�

Al-Mu’minūn 61 Al-Qiyāmah 11�Al-Shu‘arā 227 Al-Insān 31�Al-QaEaE 17 Al-Naba’ 11�Luqmān 19 Al-Takwīr 29�

Al-A@zāb 73 Al-InfiIār 19�Saba 11 Al-Burūj 13�FāIir 11 Al-Māriq 17�Yāsīn 83 Al-A‘lā 19�Sād 17 Al-Qu@a 11�

Al-Zumar 13 Al-‘Alaq 19�FuEEilat 11 Al-Qadr 5�

Page 21: Binary Symmetric Book 1 luluya giden · 72 23·3 2 12 215 5·43 48 73 773373 73 216 2 3·3 15 74 2·37 39 217 7·31 38 75 3·5 2 13 218 2·109 111 76 22·19 23 219 3·73 76 77 7·11

�Sum�of�the�Prime�Factors�

217

Al-Shūrā 53 Al-‘Ādiyāt 11�Al-Zukhruf 89 Al-Qāri‘ah 11�Al-Dukhān 59 Al-‘Asr 3�Al-Jāthiyah 37 Al-Fīl 5�

Al-Fat@ 29 Al-Mā‘ūn 7�Qāf 11 Al-Kawthar 3�

Al-Wāqi‘ah 13 Al-Kāfirūn 5�Al-Nadīd 29 Al-NaEr 3�

Al-Mujādalah 13 Tabbat 5�Al-Mumta@inah 13 Al-Falaq 5�

Al-Jumu‘ah 11 Al-Nās 5�List-106�

If�we�count�the�members�of�the�List-106,�we�find�that�the�total�members�of�this�set�are�60606060.�

The�set�of�surahs�with�The�set�of�surahs�with�The�set�of�surahs�with�The�set�of�surahs�with�nonnonnonnon----prime�prime�prime�prime�aaaa0000�(number�of�ayats)�(number�of�ayats)�(number�of�ayats)�(number�of�ayats)����

�� XXX ����

SurahSurahSurahSurah aaaa0000((((AyatAyatAyatAyat))))

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aaaa0000((((AyatAyatAyatAyat))))����

Al-Baqarah 26 Al-Najm 33�Āl�‘Imrān 16 Al-Qamar 16�

Al-Māidah 14 Al-Ra@mān 18�Al-A‘rāf 105 Al-Nashr 9�

Al-Tawbah 46 Al-Saff 9�Hūd 44 Al-Taghābun 8�

Yūsuf 40 Al-Mulk 10�Al-Na@l 14 Al-Ma‘ārij 15�Al-’Isrā 40 Al-Muzzammil 9�Al-Kahf 18 Al-Mursalāt 12�Maryam 16 Al-Nāzi‘āt 25�

Māhā 14 ‘Abasa 12�Al-Anbiyā 15 Al-MuIaffifīn 10�

Al-Najj 18 Al-Inshiqāq 10�Al-Nūr 12 Al-Ghāshiyah 15�

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218

Al-Furqān 18 Al-Fajr 10�Al-Naml 34 Al-Balad 9�

Al-‘Ankabūt 26 Al-Shams 8�Al-Rūm 12 Al-Layl 10�

Al-Sajdah 10 Al-Inshirā@ 6�Al-Saffāt 22 Al-Tīn 6�

Al-Mu’min 22 Al-Bayyinah 6�Al-A@qāf 12 Al-Zilzāl 6�

Mu@ammad 21 Al-Takāthur 6�Al-Nujurāt 8 Al-Humaza 6�Al-Dhāriyāt 12 Quraysh 4�

Al-Mūr 14 Al-IkhlāE 4�List-107�

If�we�count�the�members�of�the�List-107,�we�find�that�the�total�members�of�this�set�are�54545454.�

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Figure-22�The�distribution�of�the�surahs�with�prime�and�non-prime�number�in�a0�(number�of�ayats)�is�seen.�

�EvaluationEvaluationEvaluationEvaluation

As you can remember, the number of ayats of the 114 surahs consists of 60 even and 54 odd numbers. Now, the same sharing occurs as prime and non-prime numbers in the sum of the prime factors of the number of ayats!!!

�Let’s�see�the�results�which�outcome�collectively:

114 � � �

60 54�

The�total�number�of�surahs�

The�number�of�

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a0�(number�of�

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The�number�of�

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�Sum�of�the�Prime�Factors�

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Al-Baqarah 286 Al-Rūm 60�Āl�‘Imrān 200 Luqmān 34�Al-Nisā 176 Al-Sajdah 30�

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Maryam 98 Al-Nujurāt 18�Al-Anbiyā 112 Al-Dhāriyāt 60�

Al-Najj 78 Al-Najm 62�Al-Mu’minūn 118 Al-Ra@mān 78�

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�Sum�of�the�Prime�Factors�

223

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225

The�surahs�which�take�place�in�the�The�surahs�which�take�place�in�the�The�surahs�which�take�place�in�the�The�surahs�which�take�place�in�the�first�half�of�the�first�half�of�the�first�half�of�the�first�half�of�the�Qur’ānQur’ānQur’ānQur’ān�with�a��with�a��with�a��with�a�nonnonnonnon----prime�number�of�prime�number�of�prime�number�of�prime�number�of�aaaa0000�(number�of��(number�of��(number�of��(number�of�ayatsayatsayatsayats))))����

XXXXX SurahSurahSurahSurah���� aaaa0000((((AyatAyatAyatAyat))))����

SurahSurahSurahSurah���� aaaa0000((((AyatAyatAyatAyat))))

Al-Baqarah 26 Al-Furqān 18�Āl�‘Imrān 16 Al-Naml 34�

Al-Māidah 14 Al-‘Ankabūt 26�Al-A‘rāf 105 Al-Rūm 12�

Al-Tawbah 46 Al-Sajdah 10�Hūd 44 Al-Saffāt 22�

Yūsuf 40 Al-Mu’min 22�Al-Na@l 14 Al-A@qāf 12�Al-’Isrā 40 Mu@ammad 21�Al-Kahf 18 Al-Nujurāt 8�Maryam 16 Al-Dhāriyāt 12�

Māhā 14 Al-Mūr 14�Al-Anbiyā 15 Al-Najm 33�

Al-Najj 18 Al-Qamar 16�Al-Nūr 12 Al-Ra@mān 18�

List-112�There�are�30303030�surahs�in�List-112��

The�surahs�which�take�place�in�the�The�surahs�which�take�place�in�the�The�surahs�which�take�place�in�the�The�surahs�which�take�place�in�the�first�half�of�the�first�half�of�the�first�half�of�the�first�half�of�the�Qur’ān�with�Qur’ān�with�Qur’ān�with�Qur’ān�with�an�an�an�an�oddoddoddodd�number�of�ayats�number�of�ayats�number�of�ayats�number�of�ayats����

XXXXXXXXXX SurahSurahSurahSurah���� AyatAyatAyatAyat����

SurahSurahSurahSurah���� AyatAyatAyatAyat

Al-Fāti@a 7 Al-A@zāb 73�Al-En‘ām 165 FāIir 45�Al-Anfāl 75 Yāsīn 83�

Al-Tawbah 129 Al-Zumar 75�

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226

Yūnus 109 Al-Mu’min 85�Hūd 123 Al-Shūrā 53�

Yūsuf 111 Al-Zukhruf 89�Al-Ra‘d 43 Al-Dukhān 59�Al-Nijr 99 Al-Jāthiyah 37�Al-’Isrā 111 Al-A@qāf 35�

Māhā 135 Al-Fat@ 29�Al-Furqān 77 Qāf 45�Al-Shu‘arā 227 Al-Mūr 49�Al-Naml 93 Al-Qamar 55�

Al-‘Ankabūt 69 Al-Nadīd 29�List-113�

There�are�30303030�surahs�in�List-113��

The�surahs�which�take�place�in�the�The�surahs�which�take�place�in�the�The�surahs�which�take�place�in�the�The�surahs�which�take�place�in�the�secondsecondsecondsecond�half�of�the��half�of�the��half�of�the��half�of�the�Qur’ānQur’ānQur’ānQur’ān�with�with�with�with�a��a��a��a�nonnonnonnon----prime�number�of�prime�number�of�prime�number�of�prime�number�of�aaaa0000�(number�of��(number�of��(number�of��(number�of�ayatsayatsayatsayats))))����

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Al-Nashr 9 Al-Fajr 10�Al-Saff 9 Al-Balad 9�

Al-Taghābun 8 Al-Shams 8�Al-Mulk 10 Al-Layl 10�

Al-Ma‘ārij 15 Al-Inshirā@ 6�Al-Muzzammil 9 Al-Tīn 6�

Al-Mursalāt 12 Al-Bayyinah 6�Al-Nāzi‘āt 25 Al-Zilzāl 6�

‘Abasa 12 Al-Takāthur 6�Al-MuIaffifīn 10 Al-Humaza 6�Al-Inshiqāq 10 Quraysh 4�

Al-Ghāshiyah 15 Al-IkhlāE 4�List-114�

There�are�24242424�surahs�in�List-114��

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�Sum�of�the�Prime�Factors�

227

The�surahs�which�take�place�in�the�The�surahs�which�take�place�in�the�The�surahs�which�take�place�in�the�The�surahs�which�take�place�in�the�secondsecondsecondsecond�half�of�the��half�of�the��half�of�the��half�of�the�QurQurQurQur’ān�with�’ān�with�’ān�with�’ān�with�an�an�an�an�oddoddoddodd�number�of�ayats�number�of�ayats�number�of�ayats�number�of�ayats����

XXXXXXXX SurahSurahSurahSurah���� AyatAyatAyatAyat����

SurahSurahSurahSurah���� AyatAyatAyatAyat

Al-Mumta@inah 13 Al-‘Alaq 19�Al-Jumu‘ah 11 Al-Qadr 5�

Al-Munāfiqūn 11 Al-‘Ādiyāt 11�Al-Insān 31 Al-Qāri‘ah 11�

Al-Takwīr 29 Al-‘Asr 3�Al-InfiIār 19 Al-Humaza 9�

Al-Inshiqāq 25 Al-Fīl 5�Al-Māriq 17 Al-Mā‘ūn 7�Al-A‘lā 19 Al-Kawthar 3�

Al-Shams 15 Al-NaEr 3�Al-Layl 21 Tabbat 5�

Al-Qu@a 11 Al-Falaq 5�List-115�

There�are�24242424�surahs�in�List-115��EvaluationEvaluationEvaluationEvaluation

We see above that the number of surahs with a non-prime number of a0(the number of ayats) is equal to the number of surahs with an odd number of ayats. Now we observe that these two surah sets with equal number of members, take place in both the first and the second half of Holy Qur’an in equal numbers!

�Let’s�see�the�results�which�outcome�collectively:���

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228

7 A l - F ā t i ḥ a 7286 A l - B a q a r a h 26200 Ā l ‘ I m r ā n 16176 A l - N i s ā 19120 A l - M ā i d a h 14165 A l - E n ‘ ā m 19206 A l - A ‘ r ā f 10575 A l - A n f ā l 13129 A l - T a w b a h 46109 Y ū n u s 109123 H ū d 44111 Y ū s u f 4043 A l - R a ‘ d 4352 I b r ā h ī m 1799 A l - Ḥ i j r 17128 A l - N a ḥ l 14111 A l - ’ I s r ā 40110 A l - K a h f 1898 M a r y a m 16135 Ṭ ā h ā 14112 A l - A n b i y ā 1578 A l - Ḥ a j j 18118 A l - M u ’ m i n ū n 6164 A l - N ū r 1277 A l - F u r q ā n 18227 A l - S h u ‘ a r ā 22793 A l - N a m l 3488 A l - Q a ṣ a ṣ 1769 A l - ‘ A n k a b ū t 2660 A l - R ū m 1234 L u q m ā n 1930 A l - S a j d a h 1073 A l - A ḥ z ā b 7354 S a b a 1145 F ā ṭ i r 1183 Y ā s ī n 83182 A l - Ṣ a f f ā t 2288 Ṣ ā d 1775 A l - Z u m a r 1385 A l - M u ’ m i n 2254 F u ṣ ṣ i l a t 1153 A l - S h ū r ā 5389 A l - Z u k h r u f 8959 A l - D u k h ā n 5937 A l - J ā t h i y a h 3735 A l - A ḥ q ā f 1238 M u ḥ a m m a d 2129 A l - F a t ḥ 2918 A l - Ḥ u j u r ā t 845 Q ā f 1160 A l - D h ā r i y ā t 1249 A l - Ṭ ū r 1462 A l - N a j m 3355 A l - Q a m a r 1678 A l - R a ḥ m ā n 1896 A l - W ā q i ‘ a h 1329 A l - Ḥ a d ī d 29

22 A l - M u j ā d a l a h 1324 A l - Ḥ a s h r 913 A l - M u m t a ḥ i n a h 1314 A l - Ṣ a f f 911 A l - J u m u ‘ a h 1111 A l - M u n ā f i q ū n 1118 A l - T a g h ā b u n 812 A l - Ṭ a l ā q 712 A l - T a ḥ r ī m 730 A l - M u l k 1052 A l - Q a l a m 1752 A l - Ḥ ā q q a h 1744 A l - M a ‘ ā r i j 1528 N ū ḥ 1128 A l - J i n n 1120 A l - M u z z a m m i l 956 A l - M u d d a t h t h i r 1340 A l - Q i y ā m a h 1131 A l - I n s ā n 3150 A l - M u r s a l ā t 1240 A l - N a b a’ 1146 A l - N ā z i ‘ ā t 2542 ‘A b a s a 1229 A l - T a k w ī r 2919 A l - I n f i ṭ ā r 1936 A l - M u ṭ a f f i f ī n 1025 A l - I n s h i q ā q 1022 A l - B u r ū j 1317 A l - Ṭ ā r i q 1719 A l - A ‘ l ā 1926 A l - G h ā s h i y a h 1530 A l - F a j r 1020 A l - B a l a d 915 A l - S h a m s 821 A l - L a y l 1011 A l - Ḍ u ḥ a 118 A l - I n s h i r ā ḥ 68 A l - T ī n 619 A l - ‘ A l a q 195 A l - Q a d r 58 A l - B a y y i n a h 68 A l - Z i l z ā l 611 A l - ‘ Ā d i y ā t 1111 A l - Q ā r i ‘a h 118 A l - T a k ā t h u r 63 A l - ‘A s r 39 A l - H u m a z a 65 Al-Fīl 54 Q u r a y s h 47 A l - M ā ‘ ū n 73 A l - K a w t h a r 36 A l - K ā f i r ū n 53 A l - N a ṣ r 35 T a b b a t 54 A l - I k h l ā ṣ 45 A l - F a l a q 56 A l - N ā s 5

Ayat SURAH a0(Ayat) Surahs With Odd Number of Ayats Surahs With Non-Prime a0(number of ayats)

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�Sum�of�the�Prime�Factors�

229

� QuestionQuestionQuestionQuestion:�when�we�consider�the�sum�of�the�prime�factors�of�the�sequence�numbers�of�the�surahs,�and�the�sum�of�the�prime�factors� of� the� number� of� ayats,� how� many� of� them� are�homogeneous�and�how�many�of�them�are�non-homogeneous�with�respect�to�being�a�prime�number?�

In�order�to�give�an�answer�to�this�question,�we�should�have�to�constitute�these�two�sets:�

� The set of homogeneous surahs with respect to a0 (sequence number) and a0 (number of ayats) being as prime numbers�� The set of non-homogeneous surahs with respect to a0 (sequence number) and a0 (number of ayats) being as prime numbers��

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aaaa0000((((No.No.No.No.)))) SurahSurahSurahSurah

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Inshiqāq 10�

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�Sum�of�the�Prime�Factors�

231

11 Hūd 44 21 Al-Qalam 17�7 Yūsuf 40 26 Al-Nāqqah 17�

9 Ibrāhīm 17 12 Al-Jinn 11�

8 Al-Nijr 17 73 Al-

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17 Al-’Isrā 40 39 Al-

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37 Al-Saffāt 22 89 Al-Fajr 10�11 Al-Mu’min 22 13 Al-Balad 9�12 Al-Shūrā 53 34 Al-Qu@a 11�15 Al-Dukhān 59 17 Al-Zilzāl 6�

47 Mu@ammad 21 14 Al-‘Ādiyāt 11�12 Qāf 11 19 Al-Humaza 6�17 Al-Mūr 14 15 Al-Fīl 5�53 Al-Najm 33 18 Al-NaEr 3�

11 Al-Qamar 16 40 Tabbat 5�

22 Al-Nadīd 29 24 Al-Nās 5�

59 Al-Nashr 9 �List-117�

If�we�count�the�members�of�the�List-116,�we�find�that�the�total�members�of�this�set�are�61.�

61616161�is�also�a�prime�number!��

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232

1 A l - F ā t i ḥ a 72 A l - B a q a r a h 263 Ā l ‘ I m r ā n 164 A l - N i s ā 195 A l - M ā i d a h 145 A l - E n ‘ ā m 197 A l - A ‘ r ā f 1056 A l - A n f ā l 136 A l - T a w b a h 467 Y ū n u s 10911 H ū d 447 Y ū s u f 4013 A l - R a ‘ d 439 I b r ā h ī m 178 A l - Ḥ i j r 178 A l - N a ḥ l 1417 A l - ’ I s r ā 408 A l - K a h f 1819 M a r y a m 169 Ṭ ā h ā 1410 A l - A n b i y ā 1513 A l - Ḥ a j j 1823 A l - M u ’ m i n ū n 619 A l - N ū r 1210 A l - F u r q ā n 1815 A l - S h u ‘ a r ā 2279 A l - N a m l 3411 A l - Q a ṣ a ṣ 1729 A l - ‘ A n k a b ū t 2610 A l - R ū m 1231 L u q m ā n 1910 A l - S a j d a h 1014 A l - A ḥ z ā b 7319 S a b a 1112 F ā ṭ i r 1110 Y ā s ī n 8337 A l - Ṣ a f f ā t 2221 Ṣ ā d 1716 A l - Z u m a r 1311 A l - M u ’ m i n 2241 F u ṣ ṣ i l a t 1112 A l - S h ū r ā 5343 A l - Z u k h r u f 8915 A l - D u k h ā n 5911 A l - J ā t h i y a h 3725 A l - A ḥ q ā f 1247 M u ḥ a m m a d 2111 A l - F a t ḥ 2914 A l - Ḥ u j u r ā t 812 Q ā f 1120 A l - D h ā r i y ā t 1217 A l - Ṭ ū r 1453 A l - N a j m 3311 A l - Q a m a r 1616 A l - R a ḥ m ā n 1813 A l - W ā q i ‘ a h 1322 A l - Ḥ a d ī d 2931 A l - M u j ā d a l a h 1359 A l - Ḥ a s h r 912 A l - M u m t a ḥ i n a h 1361 A l - Ṣ a f f 933 A l - J u m u ‘ a h 1113 A l - M u n ā f i q ū n 1112 A l - T a g h ā b u n 818 A l - Ṭ a l ā q 716 A l - T a ḥ r ī m 767 A l - M u l k 1021 A l - Q a l a m 1726 A l - Ḥ ā q q a h 1714 A l - M a ‘ ā r i j 1571 N ū ḥ 11

12 A l - J i n n 1173 A l - M u z z a m m i l 939 A l - M u d d a t h t h i r 1313 A l - Q i y ā m a h 1123 A l - I n s ā n 3118 A l - M u r s a l ā t 1218 A l - N a b a’ 1179 A l - N ā z i ‘ ā t 2513 ‘A b a s a 1212 A l - T a k w ī r 2943 A l - I n f i ṭ ā r 1983 A l - M u ṭ a f f i f ī n 1014 A l - I n s h i q ā q 1022 A l - B u r ū j 1345 A l - Ṭ ā r i q 1732 A l - A ‘ l ā 1917 A l - G h ā s h i y a h 1589 A l - F a j r 1013 A l - B a l a d 920 A l - S h a m s 827 A l - L a y l 1034 A l - Ḍ u ḥ a 1149 A l - I n s h i r ā ḥ 6

24 A l - T ī n 613 A l - ‘ A l a q 1997 A l - Q a d r 516 A l - B a y y i n a h 617 A l - Z i l z ā l 614 A l - ‘ Ā d i y ā t 11101 A l - Q ā r i ‘a h 1122 A l - T a k ā t h u r 6103 A l - ‘A s r 319 A l - H u m a z a 615 Al-Fīl 555 Q u r a y s h 4107 A l - M ā ‘ ū n 713 A l - K a w t h a r 3109 A l - K ā f i r ū n 518 A l - N a ṣ r 340 T a b b a t 515 A l - I k h l ā ṣ 4

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NON-HOMOGENOUS SURAHS

In the figure, (prime-prime) distribution of the homogenous and non-homogenous surahs is shown.

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a0(NO.) SURAH a0(Ayat) HOMOGENOUS SURAHS

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�Sum�of�the�Prime�Factors�

233

1 A l - F ā t i ḥ a 72 A l - B a q a r a h 263 Ā l ‘ I m r ā n 164 A l - N i s ā 195 A l - M ā i d a h 145 A l - E n ‘ ā m 197 A l - A ‘ r ā f 1056 A l - A n f ā l 136 A l - T a w b a h 467 Y ū n u s 10911 H ū d 447 Y ū s u f 4013 A l - R a ‘ d 439 I b r ā h ī m 178 A l - Ḥ i j r 178 A l - N a ḥ l 1417 A l - ’ I s r ā 408 A l - K a h f 1819 M a r y a m 169 Ṭ ā h ā 1410 A l - A n b i y ā 1513 A l - Ḥ a j j 1823 A l - M u ’ m i n ū n 619 A l - N ū r 1210 A l - F u r q ā n 1815 A l - S h u ‘ a r ā 2279 A l - N a m l 3411 A l - Q a ṣ a ṣ 1729 A l - ‘ A n k a b ū t 2610 A l - R ū m 1231 L u q m ā n 1910 A l - S a j d a h 1014 A l - A ḥ z ā b 7319 S a b a 1112 F ā ṭ i r 1110 Y ā s ī n 8337 A l - Ṣ a f f ā t 2221 Ṣ ā d 1716 A l - Z u m a r 1311 A l - M u ’ m i n 2241 F u ṣ ṣ i l a t 1112 A l - S h ū r ā 5343 A l - Z u k h r u f 8915 A l - D u k h ā n 5911 A l - J ā t h i y a h 3725 A l - A ḥ q ā f 1247 M u ḥ a m m a d 2111 A l - F a t ḥ 2914 A l - Ḥ u j u r ā t 812 Q ā f 1120 A l - D h ā r i y ā t 1217 A l - Ṭ ū r 1453 A l - N a j m 3311 A l - Q a m a r 1616 A l - R a ḥ m ā n 1813 A l - W ā q i ‘ a h 1322 A l - Ḥ a d ī d 2931 A l - M u j ā d a l a h 1359 A l - Ḥ a s h r 912 A l - M u m t a ḥ i n a h 1361 A l - Ṣ a f f 933 A l - J u m u ‘ a h 1113 A l - M u n ā f i q ū n 1112 A l - T a g h ā b u n 818 A l - Ṭ a l ā q 716 A l - T a ḥ r ī m 767 A l - M u l k 1021 A l - Q a l a m 1726 A l - Ḥ ā q q a h 1714 A l - M a ‘ ā r i j 1571 N ū ḥ 11

12 A l - J i n n 1173 A l - M u z z a m m i l 939 A l - M u d d a t h t h i r 1313 A l - Q i y ā m a h 1123 A l - I n s ā n 3118 A l - M u r s a l ā t 1218 A l - N a b a’ 1179 A l - N ā z i ‘ ā t 2513 ‘A b a s a 1212 A l - T a k w ī r 2943 A l - I n f i ṭ ā r 1983 A l - M u ṭ a f f i f ī n 1014 A l - I n s h i q ā q 1022 A l - B u r ū j 1345 A l - Ṭ ā r i q 1732 A l - A ‘ l ā 1917 A l - G h ā s h i y a h 1589 A l - F a j r 1013 A l - B a l a d 920 A l - S h a m s 827 A l - L a y l 1034 A l - Ḍ u ḥ a 1149 A l - I n s h i r ā ḥ 6

24 A l - T ī n 613 A l - ‘ A l a q 1997 A l - Q a d r 516 A l - B a y y i n a h 617 A l - Z i l z ā l 614 A l - ‘ Ā d i y ā t 11101 A l - Q ā r i ‘a h 1122 A l - T a k ā t h u r 6103 A l - ‘A s r 319 A l - H u m a z a 615 Al-Fīl 555 Q u r a y s h 4107 A l - M ā ‘ ū n 713 A l - K a w t h a r 3109 A l - K ā f i r ū n 518 A l - N a ṣ r 340 T a b b a t 515 A l - I k h l ā ṣ 4

113 A l - F a l a q 524 A l - N ā s 5

a0(NO.) SURAH a0(Ayat) HOMOGENOUS SURAHS NON-HOMOGENOUS SURAHS

In the figure, (prime-prime) distribution of the homogenous and non-homogenous surahs is shown.

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Prime

Prime