U Vikipediyi ye statti pro inshi znachennya cogo termina Bliznyuki znachennya Prosti chisla bliznyuki para prostih chisel riznicya mizh yakimi dorivnyuye 2 Najmenshimi chislami bliznyukami ye 3 5 5 7 11 13 17 19 29 31 41 43 59 61 71 73 101 103 107 109 137 139 149 151 179 181 191 193 197 199 227 229 239 241 269 271 281 283 311 313 347 349 419 421 431 433 461 463 521 523 569 571 599 601 617 619 641 643 659 661 809 811 821 823 827 829 857 859 881 883 Zmist 1 Vlastivosti 2 Najbilshi vidomi prosti bliznyuki 3 Gipoteza pro neskinchennist 3 1 Gipoteza Gardi Litlvuda 4 Prosti chisla tripleti 5 PrimitkiVlastivosti RedaguvatiVsi pari prostih bliznyukiv krim 3 5 mayut viglyad 6 n 1 displaystyle 6n pm 1 nbsp Spravdi dlya bud yakoyi pari prostih chisel bliznyukiv chislo sho znahoditsya mizh nimi ochevidno ye parnim Takozh vono dilitsya na 3 oskilki z troh poslidovnih chisel odne maye dilitisya na tri Z cih dvoh tverdzhen viplivaye sho vono takozh bude dilitisya na 6 todi dva susidnih chisla budut mati viglyad 6 n 1 displaystyle 6n pm 1 nbsp Chisla m m 2 ye prostimi chislami bliznyukami todi i tilki todi koli 4 m 1 1 m mod m m 2 displaystyle 4 m 1 1 equiv m pmod m m 2 nbsp Dijsno 4 m 1 1 m 0 mod m m 2 displaystyle 4 m 1 1 m equiv 0 pmod m m 2 nbsp vikonuyetsya v tomu i tilki tomu vipadku koli vikonuyutsya rivnosti 4 m 1 1 m 0 mod m displaystyle 4 m 1 1 m equiv 0 pmod m nbsp 4 m 1 1 m 0 mod m 2 displaystyle 4 m 1 1 m equiv 0 pmod m 2 nbsp Persha z cih rivnostej ekvivalentna m 1 1 0 mod m displaystyle m 1 1 equiv 0 pmod m nbsp sho zgidno z teoremoyu Vilsona vikonuyetsya todi i tilki todi koli m proste chislo U drugij rivnosti domnozhimo obi chastini na m Pislya elementarnih peretvoren oderzhuyemo 4 m 4 m m 2 0 mod m 2 displaystyle 4m 4m m 2 equiv 0 pmod m 2 nbsp Nevazhko pomititi sho ostannya rivnist vikonuyetsya v tomu i lishe tomu vipadku koli m 1 mod m 2 displaystyle m equiv 1 pmod m 2 nbsp sho zgidno z variantom teoremi Vilsona ekvivalentno tverdzhennyu sho chislo m 2 proste Teorema Bruna ryad iz sum chisel obernenih do chisel bliznyukiv zbigayetsya B 2 1 3 1 5 1 5 1 7 1 11 1 13 1 17 1 19 1 902160583104 displaystyle B 2 left frac 1 3 frac 1 5 right left frac 1 5 frac 1 7 right left frac 1 11 frac 1 13 right left frac 1 17 frac 1 19 right ldots approx 1 902160583104 nbsp Chislo sho ye sumoyu ryadu nazivayetsya konstantoyu Bruna Najbilshi vidomi prosti bliznyuki RedaguvatiNa danij chas najbilshoyu vidomoyu paroyu prostih bliznyukiv ye 3756801695685 2666669 1 1 Desyat najbilshih vidomih par 2 3756801695685 2 666669 1 displaystyle 3756801695685 cdot 2 666669 pm 1 nbsp 200700 cifr 65516468355 2 333333 1 displaystyle 65516468355 cdot 2 333333 pm 1 nbsp 100355 cifr 2003663613 2 195000 1 displaystyle 2003663613 cdot 2 195000 pm 1 nbsp 58711 cifr 194772106074315 2 171960 1 displaystyle 194772106074315 cdot 2 171960 pm 1 nbsp 51780 cifr 100314512544015 2 171960 1 displaystyle 100314512544015 cdot 2 171960 pm 1 nbsp 51780 cifr 16869987339975 2 171960 1 displaystyle 16869987339975 cdot 2 171960 pm 1 nbsp 51779 cifr 33218925 2 169690 1 displaystyle 33218925 cdot 2 169690 pm 1 nbsp 51090 cifr 22835841624 7 54321 1 displaystyle 22835841624 cdot 7 54321 pm 1 nbsp 45917 cifr 1679081223 2 151618 1 displaystyle 1679081223 cdot 2 151618 pm 1 nbsp 45651 cifr 84966861 2 140219 1 displaystyle 84966861 cdot 2 140219 pm 1 nbsp 42219 cifr Gipoteza pro neskinchennist RedaguvatiOdniyeyu z znamenitih vidkritih problem teoriyi chisel ye skinchennist chi neskinchennist prostih bliznyukiv Intuyitivno bilshist matematikiv shilyayutsya do dumki pro isnuvannya neskinchennoyi kilkosti takih chisel prote cej fakt zalishayetsya nedovedenim Gipoteza Gardi Litlvuda Redaguvati Za gipotezoyu Gardi Litlvuda kilkist p 2 x displaystyle pi 2 x nbsp par prostih bliznyukiv sho ne perevishuyut x asimptotichno nablizhayetsya do p 2 x 2 C 2 2 x d t ln t 2 displaystyle pi 2 x sim 2C 2 int limits 2 x frac dt ln t 2 nbsp de C 2 displaystyle C 2 nbsp konstanta prostih bliznyukiv C 2 p 3 1 1 p 1 2 0 66016118158468695739278121100145 displaystyle C 2 prod p geq 3 left 1 frac 1 p 1 2 right approx 0 66016118158468695739278121100145 ldots nbsp Prosti chisla tripleti RedaguvatiPoslidovnist prostih chisel p p 2 p 6 abo p p 4 p 6 nazivayetsya tripletom Pershi prosti chisla tripleti 5 7 11 7 11 13 11 13 17 13 17 19 17 19 23 37 41 43 41 43 47 67 71 73 97 101 103 101 103 107 103 107 109 107 109 113 191 193 197 193 197 199 223 227 229 227 229 233 277 281 283 307 311 313 311 313 317 347 349 353 457 461 463 461 463 467 613 617 619 641 643 647 821 823 827 823 827 829 853 857 859 857 859 863 877 881 883 881 883 887 Na danij chas najbilshimi vidomimi prostimi chislami tripletami ye p p 2 p 6 de p 2072644824759 233333 1 10047 cifr listopad 2008 Norman Luhn Francois Morain FastECPP Primitki Redaguvati http www primegrid com download twin 666669 pdf Arhivovano 26 listopada 2013 u Wayback Machine 3756801695685 2666669 1 TPS official announcement http primes utm edu top20 page php id 1 Arhivovano 27 sichnya 2013 u Wayback Machine Twin Primes Otrimano z https uk wikipedia org w index php title Prosti chisla bliznyuki amp oldid 36691484
