WEBVTT 00:00:01.370 --> 00:00:03.367 kulo mboniso bhanyabhanya ndifuna ukuthetha kancinane malunga 00:00:03.367 --> 00:00:07.500 Nokuba kuthwani xakuthethwa nge Prime Number 00:00:07.500 --> 00:00:10.094 kwa nalento uzokuyi bona kulo mboniso bhanyabhanya 00:00:10.110 --> 00:00:12.608 ngumcimbi nje lo ocacileyo 00:00:12.608 --> 00:00:15.302 kodwa njengokuba uqhubekeka kwi kamva lakho lezobalo 00:00:15.302 --> 00:00:17.601 uzawukubona ukuba kukho eminye imicimbi ezamekayo noko 00:00:17.601 --> 00:00:20.712 enokuthiwa yakhelwe phezulu kwe Prime Number 00:00:20.712 --> 00:00:23.359 eminye yayo ibandakanya icebo le cryptography (ukufihlwa kwamanani okanye amagame aze angakwazi ukufundeka) 00:00:23.359 --> 00:00:25.612 kwakhona umhlawumbi ezinye zee zitshintsho enokuthi ikhompyutha yakho 00:00:25.612 --> 00:00:28.026 izisebenzise ngoku zingakwazi ukwakhelwa phezu kwee Prime Numbers 00:00:28.026 --> 00:00:29.931 kodwa ukuba awumazi ukuba u-encryption uthetha ukuthini 00:00:29.931 --> 00:00:31.718 ungaxhalabi ngayo loonto ngoku 00:00:31.718 --> 00:00:33.785 kumele nje wazi ukuba yintoni nje iPrime Number kuko oko okubalulekileyo. 00:00:33.785 --> 00:00:36.966 Koko, ndizawukunika inkcazelo yayo ukuba yintoni 00:00:36.966 --> 00:00:39.404 kwaye inkcazelo ingafuna ukubhidisa nje kancinane 00:00:39.404 --> 00:00:43.839 kodwa xa siyibona ngemizekeliso inokuba lula kwaye icace 00:00:43.839 --> 00:00:49.946 Inani liyi Prime ukuba linjengokuba linjalo 00:00:49.946 --> 00:00:57.794 umzekelo, Inye, Zimbini, okanye Zintathu (ukubalwa kwamanani kuqalwa kwelo kuqala) 00:00:57.794 --> 00:01:00.488 Okanye ukwanako ukuthi "iPositive intergers" 00:01:00.488 --> 00:01:30.962 Ilinani elinjengokuba linjalo elithi lahlulwahlulwe kanye kanye ngamanani amabini anjengokuba enjalo: Inani kwakunye nelokuqala 00:01:30.962 --> 00:01:39.823 Lawo ngamanani amabini ethi yahlulwehlulwe ngawo. 00:01:39.823 --> 00:01:43.468 Ukuba lento ayenzi mqondo apha kuwe masike senze nje imizekelo 00:01:43.468 --> 00:01:46.115 Masikhe sifunise ukuba ingaba amanyee amanani azi Prime numbers okanye hayi. 00:01:46.115 --> 00:01:48.948 Masikhe siqale ngamanani angawona akhe amancinane. 00:01:48.948 --> 00:01:52.268 Inani lokuqala. Ungathi umhlawumbi inani lokuqala lahluleka kwangelokuqala 00:01:52.268 --> 00:01:59.095 kwaye inani lokuqala likwahluleka kwangelokuqala, andithi, inani lokuqala liyi Prime Number 00:01:59.095 --> 00:02:02.137 Kodwa khumbula, inxalenye yenkcazelo yethu, ibisithi kufuneka ikwazi ukwahluleka 00:02:02.137 --> 00:02:07.803 kanye kanye ngamanani amabini anjengokuba enjalo. Elokuqala likwahluleka ngenani elinjengokuba linjalo elinye, ngenani elilelokuqala. 00:02:07.803 --> 00:02:16.673 Lilonke, inani lokuqala, nokuba umhlawumbi linoku chasana nokufunxa kolwazi kungakhange kucingisiswe, ayisililo inali eliyi Prime 00:02:16.673 --> 00:02:20.504 Masigqithele siye kwi nani lesibini 00:02:20.504 --> 00:02:28.102 lilonke inani lesibini lahluleka ngelokuqalakwakunye kwangalo elesibini, kwaye alahluleki ngelinye inani elingenjengokuba linjalo 00:02:28.102 --> 00:02:30.906 ingathi kengoku iyayo nela imibambela yethu. 00:02:30.906 --> 00:02:33.948 Lahlula hluleka kanye kanye ngawo amanani amabini anjengokuba enjalo. 00:02:33.948 --> 00:02:42.238 Elesibini kwakunye nelokuqala. Ngoko ke inani lesibini liyiyo iPrime 00:02:42.238 --> 00:02:52.849 Ndizakuwa kwelela isangqa amanani azi Prime. 00:02:52.849 --> 00:02:55.334 Inani lesibini lenza umdla kuba 00:02:55.334 --> 00:02:57.818 Lilo lodwa inani eligqagqeneyo elikwayiyo neliyi Prime 00:02:57.818 --> 00:03:00.396 Ukuba ke uyayicigisisa lento, nokuba leliphi na inani eligqagqeneyo 00:03:00.396 --> 00:03:03.620 lizawukwazi ukwahlula hluleka nge nani lesibini, ngoko ke alizukuba yiyo iPrime 00:03:03.620 --> 00:03:06.688 Sizakucinga ngayo loonto kakhulu kwimiboniso bhanyabhanya ezayo. 00:03:06.688 --> 00:03:13.144 Masikhe sizame inani lesithathu. Koko, inani lesithathu liyahlula hluleka ngelo kuqala kwangalo elesiThathu 00:03:13.144 --> 00:03:15.651 kwaye alikwazi ukwahlula hluleka ngenye into engenye. 00:03:15.651 --> 00:03:20.272 alikwazi ukwahlula hluleka ngelesibini. Koko, inani lesithathu likwayiyo iPrime Number 00:03:20.272 --> 00:03:25.264 Masizame inani leSine. 00:03:25.264 --> 00:03:29.676 Inani leSine liyakwazi ukwahlula hluleka ngenani lokuqala kwangalo eleSine, kodwa 00:03:29.676 --> 00:03:36.224 Liyakwazi ukwahlula hluleka kwangalo inani leSibini. Koko, liyahlula hluleka 00:03:36.224 --> 00:03:40.311 ngamanani amaThathu anjengokuba enjalo: Elokuqala, EleSibini kwakunye EleSine. 00:03:40.311 --> 00:03:44.723 Ngoko, alikwazi ukwanele umlinganiselo wethu wokuba yi Prime 00:03:44.723 --> 00:03:48.252 Masizame inani lesiHlanu. 00:03:48.252 --> 00:03:51.015 inani lesiHlanu liya kwazi ukwahlula hluleka ngelo kuqala, 00:03:51.015 --> 00:03:57.842 alikwazi ukwahlula hluleka ngenani leSibini, lesiThathu okanye leSine 00:03:57.842 --> 00:04:01.209 (ungalahlula hlula inani lesiHlanu okanye leSine kodwa uzawukufumana intshiyekela) 00:04:01.209 --> 00:04:05.133 kwaye liyakwazi ukwahlula hluleka kwangalo inani lesiHlanu ngokokucacileyo. 00:04:05.133 --> 00:04:10.265 kwakhona ke ngoko, inani lesiHlanu liyakwazi ukwahlula hluleka kanye kanye ngawo amanani anjengokuba enjalo: elokuqala kwakunye nelesiHlanu 00:04:10.265 --> 00:04:14.235 ngoko kwakhona, inani lesiHlanu liyiyo iPrime. Masiqhubekeke 00:04:14.235 --> 00:04:17.393 khonukuze sikwazi ukubona ukuba ikhona na enye indlela apha 00:04:17.393 --> 00:04:19.924 kwaye umhlawumbi ndizawukuzama enzinyana 00:04:19.924 --> 00:04:26.031 eye ithande ukuwisa abantu. Masizame kengoku inani lesiThandathu 00:04:26.031 --> 00:04:34.622 Liyahlula hluleka ngelokuqala, leSibini, lesiThathu kwakunye elesiThandathu 00:04:34.622 --> 00:04:37.595 Lilonke inamanani amane anjengokuba enjalo "factors" 00:04:37.595 --> 00:04:40.033 Ndicinga ukuba ungakwazi ukutsho nje kanjalo 00:04:40.033 --> 00:04:43.005 ukwenzela ukuba ingabi nawo kanye kanye amanani amabini ethi yahlula hluleke ngalo 00:04:43.005 --> 00:04:46.743 inamanani amane, koko ayisiyiyo iPrime 00:04:46.743 --> 00:04:49.715 Masigqithele kwi nani lesi Xhenxe 00:04:49.715 --> 00:04:55.869 Inani lesiXhenxe lahlula hluleka ngenani lokuqala HAYI eleSibini, lesiThathu, leSine, lesihlanu okanye lesiThandathu, 00:04:55.869 --> 00:05:00.791 kodwa likwakwazi ukwahlula hluleka ngenani lesi Xhenxe 00:05:00.791 --> 00:05:03.624 Lilonke inani lesiXhenxe liyiyo iPrime. Ndicinga ukuba uyayi noko lento 00:05:03.624 --> 00:05:06.689 Mangaphi amanani anjengokuba enjalo, amanani anje ngeLokuqala, leSibini, lesiThathu, leSine, lesiHlanu 00:05:06.689 --> 00:05:09.383 Amanani othi uwafunde xa uneminyaka emibini ubuncinane 00:05:09.383 --> 00:05:11.681 ungalibali inani elingengokho (iqanda) ukwangawadibanisi amanani aziinegative 00:05:11.681 --> 00:05:13.980 ukwangawadibanisi amacala kwakunye nawo amanani kwakunye nawo amanani aziirrational 00:05:13.980 --> 00:05:15.768 kwaye namanani azii Decimal kwakunye nawo onke amanye 00:05:15.768 --> 00:05:18.578 kwakunye nawo nje amanye amanani aziiPositive 00:05:18.578 --> 00:05:21.318 ukuba ke unamanani amabini kuphela, 00:05:21.318 --> 00:05:23.733 ukuba ke wahlula hluleka ngawe kwakunye ngenani lokuqala 00:05:23.733 --> 00:05:25.544 uzakuba yiyo ke iPrime. 00:05:25.544 --> 00:05:27.192 kwangohlobo ke endiyicinga ngayo, 00:05:27.192 --> 00:05:29.607 ukuba ke asicingi ngemeko ekhethekileyo yenani lokuqala 00:05:29.607 --> 00:05:31.604 amanani aziPrime angafaniswa namanani okwakha 00:05:31.604 --> 00:05:33.299 awunokwazi ukuwaphula. 00:05:33.299 --> 00:05:34.809 Ziphantse zafana neeAtoms. 00:05:34.809 --> 00:05:36.285 Ukuba ke uyayicingisisisa ukuba iAtom yintoni 00:05:36.285 --> 00:05:38.111 okanye abantu bacinga ukuba iAtom yintoni ekuqaleni 00:05:38.111 --> 00:05:39.991 babecinga ukuba zizo ezi zinto 00:05:39.991 --> 00:05:41.890 wawungena kwazi ukuzahlula hlula 00:05:41.890 --> 00:05:43.986 ngoku ke siyayazi ukuba siyakwazi ukuzahlula hlula iAtoms kwaye futhi 00:05:43.986 --> 00:05:46.475 ukuba awuzahluli unokwenza into ekuthiwa luqhushumbo lwe nuclear 00:05:46.475 --> 00:05:49.655 kodwa isekwa lelo cebo eli lisemva kwa manani aziiPrime 00:05:49.655 --> 00:05:52.618 awukwazi ukuwaphula 00:05:52.618 --> 00:05:57.402 abezi zinto ezincinane ngokwamanani anjengokuba enjalo 00:05:57.402 --> 00:06:01.256 Amanani anje nge siThandathu uyakwazi ukuthi, inani Isibini uze usi phindaphinde kaThathu, 00:06:01.256 --> 00:06:03.717 uyakwazi ukuwaphula kwaye uqaphele ukuba siyawaphula 00:06:03.717 --> 00:06:06.411 njenge nani eliphuma kwi nani eliyi Prime 00:06:06.411 --> 00:06:08.872 Siye ke saba kuwaphula aba ngamaceba 00:06:08.872 --> 00:06:11.217 awukwazi kengoko ukuphinda uwaphule kwakhona 00:06:11.217 --> 00:06:14.817 Into onokuyithetha yeyokuba isiXhenxe senziwa linani lokuqala okanye UNYE uze umphindaphinde kasiXhenxe. 00:06:14.817 --> 00:06:16.930 kwaye kuleyo ke imeko awukayi phuli kangako 00:06:16.930 --> 00:06:19.066 Use nelo nani lisisiXhenxe kwakhona. 00:06:19.066 --> 00:06:20.877 inani lesiThandathu uyakwazi ukulaphula 00:06:20.877 --> 00:06:23.965 Inani leSine nalo uyakwazi ukulaphula ngokuthi inani leSibini okanye Uzimbini uze umphindaphinde kabini. 00:06:23.965 --> 00:06:25.800 Njengoko ke sesiyi susile ke leyo endleleni yethu masicinge ke 00:06:25.800 --> 00:06:27.425 ngawo amanani amakhulu kwaye sicinge ngokuba 00:06:27.425 --> 00:06:30.072 ingaba loomanani makhulu angamanani aziiPrime 00:06:30.072 --> 00:06:34.902 Masizame ke inani leShumi linesiThandathu 00:06:34.902 --> 00:06:38.872 Kucacile ke ukuba nokuba leliphi inani elinjengokuba linjalo liyakwazi ukwahlula hluleka ngo Nye (Inani lokuqala) kwaye kwanangalo. 00:06:38.872 --> 00:06:42.262 Ngoko ke iShumi elinesiThandathu liyakwazi ukwahlula hluleka ngo Nye kwakunye nangalo iShumi elinesiThadathu. 00:06:42.262 --> 00:06:44.143 Ngoko ke uzawukuqala ngenani uZimbini 00:06:44.143 --> 00:06:46.071 ngoko ke ukuba uyakwazi ukufumana enye into engenye ethi ingene apha 00:06:46.071 --> 00:06:48.207 uzawukwazi ke ukuba ayisiyiyo iPrime 00:06:48.207 --> 00:06:51.109 kwaye ke inani eli Shumi elinesiThandathu ungakwazi ukuthi uZimbini uze umphindaphinde kaSibhozo 00:06:51.109 --> 00:06:53.362 ungamfumana nango Zine umphindaphinde kaNe 00:06:53.362 --> 00:06:55.451 ngoko ke ineton yamanani amancinane 00:06:55.451 --> 00:06:57.588 ngaphezu koko nagaphaya kwenani elingu Nye kwakunye neShumi elinesiThandathu. 00:06:57.588 --> 00:07:02.278 ngoko ke uShumi elinesiThandathu akayiyo iPrime. 00:07:02.278 --> 00:07:06.411 uNye kwakunye neShumi elinesiXhenxe uzakunika ishumi elinesiXhenxe 00:07:06.411 --> 00:07:10.846 uZimbini akayi kuShumi elinesiXhenxe, uZintathu akayi ku Zine, Zinhlanu, zintandathu, ZisiXhenxe, ZisiBhozo... 00:07:10.846 --> 00:07:14.701 alikho inani ke apho eliphakathi koNye kwakunye noShumielinesiXhenxe 00:07:14.701 --> 00:07:21.086 Lilonke ke uShumi elinesiXhenxe uyiyo iPrime 00:07:21.086 --> 00:07:23.803 Ngoku ke ndizawukunika engathi inzima 00:07:23.803 --> 00:07:26.822 Lena ke yona ingaba bhida abantu abaninzi 00:07:26.822 --> 00:07:34.345 Sizakuthini kengoku ngamaShumi Amahlanu anaNye? Ingaba uyi Prime? 00:07:34.345 --> 00:07:37.480 kwaye ukuba ke unomdla ungakwazi ukumisa kancinane lomboniso bhanyabhanya apha 00:07:37.480 --> 00:07:39.500 kwaye uzame ukuzifunela ngokwakho 00:07:39.500 --> 00:07:41.520 ukuba ingaba amaShumi amaHlanu anaNye ayi Prime number 00:07:41.520 --> 00:07:45.142 Ukuba ke uyakwazi ukufumana nokuba yeyiphi enye into ngaphandle koNye okanye Amashumi Amahlanu ananye 00:07:45.142 --> 00:07:48.161 enokuthi yahlula hluleke kumashumi amahlanu ananye. Kuyabonakala ukuba... 00:07:48.161 --> 00:07:50.042 wow linani eli noko elithanda ukunga qheleki 00:07:50.042 --> 00:07:52.340 Ungacinga ukuba iyiyo iPrime, 00:07:52.340 --> 00:07:54.268 Kodwa ngoku ndizawuku ninika impendulo 00:07:54.268 --> 00:07:59.933 Akayiyo iPrime, kuba nayo ayikwazi ukwahlula hluleka ngeSithathu nakwangeShumi elinesiXhenxe 00:07:59.933 --> 00:08:02.998 Isithathu ke usiphindaphinde ngeshumi elinesiXhenxe likunika amashumi amahlanu ananye. 00:08:02.998 --> 00:08:04.779 ngoko ke ngethemba ukuba lento ikunika ukuqonda okulungileyo 00:08:04.779 --> 00:08:06.388 ngokokuba amanani aziiPrime angantoni na 00:08:06.388 --> 00:08:09.407 ngokwe themba ke singakunika ukuzilolonga 00:08:09.407 --> 99:59:59.999 kuyo imiboniso bhanyabhanya kwixa elizayo kwaye umhlawumbi nakuzo ezinye izibalo ezincinane