Uma sicabangela umbhalo olandelayo, yini ekhethekile ngezinombolo eziyinhloko?
Context:Inombolo eyinhloko (noma i-prime) yinombolo engokwemvelo enkulu kuno-1 engeyona umkhiqizo wezinombolo ezimbili ezincane zemvelo. Inombolo engokwemvelo enkulu kuno-1 engeyona eyinhloko ibizwa ngokuthi inombolo ehlanganisiwe. Ngokwesibonelo, u-5 ungowokuqala ngoba okuwukuphela kwendlela ongawubhala ngayo njengomkhiqizo, 1 × 5 noma 5 × 1, kuhilela u-5 uqobo. Nokho, u-4 uyinhlanganisela ngoba uwumkhiqizo (2 × 2) lapho zombili izinombolo zincane kuno-4. Izinombolo eziyinhloko zibalulekile emfundisweni yezinombolo ngenxa ye-theorem eyisisekelo yezibalo: zonke izinombolo zemvelo ezinkulu kune-1 ziyizinombolo eziyinhloko ngokwazo noma zingahlukaniswa njengezinto eziyinhloko eziyingqayizivele ngokulandelana kwazo.  Impahla yokuba ngowokuqala ibizwa ngokuthi yi-primality. Indlela elula kodwa ehamba kancane yokuhlola ukuthi inombolo ethile iyinhloko yini  n, ebizwa ngokuthi ukuhlukaniswa kwecala, kuvivinya ukuthi  n iyinqwaba yanoma iyiphi inombolo ephelele ephakathi kuka-2 no  Ngicabanga ukuthi u-Eric u-Eric uyisibonelo esihle. Ama-algorithm asheshayo ahlanganisa isivivinyo se-Miller-Rabin, esisheshayo kodwa esinamathuba amancane okuphutha, kanye nesivivinyo se-AKS, esihlala sikhiqiza impendulo efanele ngesikhathi se-polynomial kodwa sihamba kancane kakhulu ukuba sisebenze. Izindlela ezisheshayo ziyatholakala ezinombolweni ezinamafomu akhethekile, njengezinombolo zikaMersenne. Kusukela ngoDisemba 2018 inombolo enkulu kunazo zonke eyaziwayo yi-Mersenne prime enezinombolo eziyi-24,862,048 zamadesimali.  Kunezinombolo eziningi ezingenamkhawulo, njengoba kuboniswa u-Euclid cishe ngo-300 BC. Alikho ifomula elilula elaziwayo elihlukanisa izinombolo eziyinhloko nezinombolo ezihlanganisiwe. Nokho, ukusatshalaliswa kwezinombolo eziyinhloko ngaphakathi kwezinombolo zemvelo ngobuningi kungakhiwa ngokwezibalo. Umphumela wokuqala kuleso siqondiso yi-prime number theorem, eyafakazelwa ekupheleni kwekhulu le-19, ethi amathuba okuba inombolo enkulu ekhethwe ngokungahleliwe ibe yi-prime ayalingana ngokuphambene nenani lamadijithi ayo, okungukuthi, ku-logarithm yayo.  Imibuzo eminingi engokomlando ephathelene nezinombolo eziyinhloko isalokhu ingaxazululiwe. Lezi zihlanganisa ukuqagela kukaGoldbach, kokuthi zonke izinombolo eziphelele ezilinganayo ezinkulu kuno-2 zingabonakaliswa njengesamba sama-prime amabili, kanye nokuqagela kwama-prime amabili, kokuthi kunamabhangqa amaningi angenamkhawulo ama-prime anenombolo eyodwa kuphela phakathi kwawo. Imibuzo enjalo yabangela ukuthuthukiswa kwamagatsha ahlukahlukene enkolelo-mbono yezinombolo, egxile ezicini zokuhlaziya noma ze-algebra zezinombolo. Amaphrimiyamu asetshenziswa emikhakheni ehlukahlukene kwezobuchwepheshe bolwazi, njenge-cryptography eyisihluthulelo somphakathi, encike ebunzimeni bokwenza izinombolo ezinkulu zibe izici zazo eziyinhloko. Ku-algebra engaqondakali, izinto eziziphatha ngendlela evamile njengezinombolo eziyinhloko zihlanganisa izakhi eziyinhloko nemigomo eyinhloko.
Inombolo eyinhloko yinombolo engokwemvelo enkulu kuneyodwa ehlukaniswa yona kanye neyodwa kuphela. Isibonelo, u-5 uyinombolo eyinhloko njengoba ihlukaniswa u-5 no-1 kuphela, kodwa u-4 akahlukaniseki njengoba u-4 uhlukaniswa u-4,2 no-1