0:00:04.420,0:00:07.221 Tasavvur qiling, milodan avvalgi yillar. 0:00:07.221,0:00:09.468 Endi o'ylab ko'ring: 0:00:09.468,0:00:12.721 Qanday qilib soatsiz vaqtni aniqlashgan? 0:00:12.721,0:00:15.315 Barcha soatlar vaqt oqimini [br]teng bo'laklarga bo'luvchi 0:00:15.315,0:00:18.890 qandaydir takroriy shaklga asoslangan. 0:00:18.890,0:00:20.688 Bunday takroriy shakillarni topish uchun 0:00:20.688,0:00:22.918 samolarga yuzlanamiz. 0:00:22.918,0:00:24.902 Har kuni, quyoshning chiqishi va botishi 0:00:24.902,0:00:26.184 bunday shakllarning eng oddiysidir. 0:00:26.184,0:00:28.760 Lekin uzoqroq vaqt bo'lagini kuzatish uchun 0:00:28.760,0:00:30.811 uzoqroq takrorlanishlarga e'tibor beramiz. 0:00:30.811,0:00:32.512 Buning uchun esa oyga yuzlanamiz. 0:00:32.512,0:00:33.853 E'tibor bergan bo'lsangiz, 0:00:33.853,0:00:36.578 oy kunlar osha to'lishadi va kichrayadi. 0:00:36.578,0:00:37.894 To'lin oylar orasidagi kunlar sonini 0:00:37.894,0:00:38.978 sanaydigan bo'lsak, 0:00:38.978,0:00:40.910 u 29 kunga teng. 0:00:40.910,0:00:42.833 Bir oydagi kunlar soni shundan [br]kelib chiqqan bo'lsa kerak. 0:00:42.833,0:00:45.873 Ammo 29 ni teng bo'laklarga [br]bo'lishga harakat qilsak, 0:00:45.873,0:00:49.227 bir muammoga duch kelamiz: [br]buning iloji yo'q. 0:00:49.227,0:00:51.676 29 ni teng bo'laklarga bo'lishning [br]yagona yo'li 0:00:51.676,0:00:54.819 uni 29 ta teng bo'lakka bo'lishdan iborat. 0:00:54.819,0:00:57.102 29 soni tub son hisoblanadi. 0:00:57.102,0:00:59.061 Uni bo'linmas deb tasavvur qiling. 0:00:59.061,0:01:00.879 Agar son birdan boshqa 0:01:00.879,0:01:02.814 teng bo'laklarga bo'linsa, 0:01:02.814,0:01:04.621 biz uni 'murakkab son' deb ataymiz. 0:01:04.621,0:01:06.608 Endi biz qiziqishimiz mumkin, 0:01:06.608,0:01:08.450 "Dunyoda nechta tub son bo'lishi mumkin? 0:01:08.450,0:01:10.398 Va ularning eng kattasi [br]nechaga teng ekan?" 0:01:10.398,0:01:13.744 Keling, barcha sonlarni [br]ikkita guruhga bo'lamiz. 0:01:13.744,0:01:15.611 Tub sonlar chap tomonda 0:01:15.611,0:01:17.648 va murakkab sonlar o'ng tomonda. 0:01:17.648,0:01:20.379 Boshida, u tomondan bu tomonga raqs [br]tushayotganga o'xshaydilar. 0:01:20.379,0:01:23.017 Ammo ularning joylashuvida [br]aniq bir shakl mavjud emas. 0:01:23.017,0:01:24.439 Keling, bunday shaklni ko'rish uchun 0:01:24.439,0:01:26.077 zamonaviy usuldan foydalanamiz. 0:01:26.077,0:01:29.047 Bu usul "Ulam spirali" deb nomlanadi. 0:01:29.047,0:01:32.011 Boshida, barcha raqamlarni tartib bilan[br]o'sayotgan spiral 0:01:32.011,0:01:34.043 ichiga joylab chiqamiz. 0:01:34.043,0:01:37.164 Keyin, barcha tub sonlarni [br]ko'k ranga bo'yab chiqamiz. 0:01:37.164,0:01:41.290 Nihoyat, biz millionlab raqamlarni[br]ko'rish uchun uzoqlashamiz. 0:01:41.290,0:01:42.860 Mana bu tugalmas tub sonlarning 0:01:42.860,0:01:45.365 shakli hisoblanadi. 0:01:45.365,0:01:47.967 Hayratlanarlisi shuki, bu shaklning [br]tuliq strukturasi 0:01:47.967,0:01:50.314 haligacha topilmagan. 0:01:50.314,0:01:51.843 Nimanidir kashf etish arafasida[br]turganga o'xshaymiz... 0:01:51.843,0:01:52.987 Keling, m.a. 300 yillarga, 0:01:52.987,0:01:55.526 Qadimgi Gretsiyaga sayr qilamiz. 0:01:55.526,0:01:58.183 Buyuk faylasuf, Aleksandryalik Evklid, 0:01:58.183,0:01:59.411 barcha sonlarni 0:01:59.411,0:02:02.607 bu ikki guruhga ajralishini anglab yetadi. 0:02:02.607,0:02:04.896 Dastlab, u istalgan sonni 0:02:04.896,0:02:07.078 kichik bo'linmas teng [br]sonlar guruhlarigacha 0:02:07.078,0:02:10.599 bo'lish mumkinligini anglab yetadi. 0:02:10.599,0:02:12.921 Va bu eng kichik sonlar esa, har doim 0:02:12.921,0:02:15.760 tub sonlardir. 0:02:15.760,0:02:17.148 Shunday qilib, u barcha sonlar 0:02:17.148,0:02:20.542 tub sonlardan qurilganini tushunib yetadi. 0:02:20.542,0:02:23.317 Aniqrog'i, barcha sonlar olamini [br]tasavvur qiling, 0:02:23.317,0:02:25.674 tub sonlar haqida unuting. 0:02:25.674,0:02:28.037 Endi istalgan murakkab sonni olamiz 0:02:28.037,0:02:30.518 va bo'laklarga ajratamiz 0:02:30.518,0:02:33.354 va bu bo'laklar, har doim [br]tub sonlardir. 0:02:33.354,0:02:34.774 Demak, Evklid istalgan raqam 0:02:34.774,0:02:37.415 kichikroq tub sonlar guruhi orqali ifodalanishi [br]mumkinligin tushunib yetgan. 0:02:37.675,0:02:39.145 Ularni g'ishtlar deb tasavvur qiling. 0:02:40.221,0:02:41.969 Qaysi son bo'lishidan qat'iy nazar, 0:02:41.999,0:02:43.937 uni kichiroq tub sonlarni qo'shish [br]bilan yasash mumkin. 0:02:46.157,0:02:47.972 Mana shu Evklid kashfiyotining [br]asosi bo'lib, 0:02:48.042,0:02:50.759 "Arifmetikaning asosiy nazariyasi" [br]deb nomlanadi. 0:02:50.759,0:02:52.013 Unga ko'ra, 0:02:52.013,0:02:53.934 istalgan raqamni, aytaylik, 30 ni olamiz 0:02:53.934,0:02:55.501 va uning tub ko'paytuvchilarini topamiz. 0:02:55.501,0:02:57.233 30 teng bo'linadi. 0:02:57.233,0:02:59.763 Buni biz "ko'paytuvchilarga ajratish" [br]deb ataymiz. 0:02:59.763,0:03:01.624 Bu bizga tub ko'paytuvchilarni [br]topish imkonini beradi. 0:03:01.624,0:03:05.811 Bizning holatda 2,3 va 5[br]30 ning tub kupaytuvchilaridir. 0:03:05.811,0:03:07.906 Evklid yana shuni tushunib yetdiki, [br]sonning tub ko'paytuvchilarini 0:03:07.906,0:03:10.714 bir necha bor ko'paytirish orqali 0:03:10.714,0:03:12.739 dastlabki sonni keltirib chiqarish [br]mumkin ekan. 0:03:12.739,0:03:13.780 30 sonini yasash uchun esa [br]uning tub ko'paytuvchilarini 0:03:13.780,0:03:16.178 bir martadan ko'paytirish kifoya. 0:03:16.178,0:03:20.158 2 x 3 x 5[br]30 soning tub kupaytuvchilaridir. 0:03:20.158,0:03:23.153 Bularni o'ziga hos kalit yoki [br]kombinatsiya deyish mumkin. 0:03:23.153,0:03:24.887 30 sonini boshqa tub son guruhlari 0:03:24.887,0:03:27.110 ko'paytmasi orqali yasashning 0:03:27.110,0:03:28.792 imkoni yo'q. 0:03:28.792,0:03:31.276 Shunday qilib, istalgan son [br]faqat va faqat 0:03:31.276,0:03:34.046 bitta yo'l bilan [br]tub ko'paytuvchilarga ajraladi. 0:03:34.046,0:03:36.299 Misol uchun, har bir sonni 0:03:36.299,0:03:38.017 alohida qulf deb tasavvur qiling. 0:03:38.033,0:03:39.722 Har bir qulfning (sonning) kaliti 0:03:39.722,0:03:40.722 uning tub ko'paytuvchilari bo'ladi. 0:03:42.045,0:03:43.117 Hech bir qulf bir hil kalitga ega emas. 0:03:43.937,0:03:47.937 Hech bir son bir hil tub ko'paytuvchilardan [br]tashkil topmaydi.