Citat:
badzevic:
Evo kako ZAPRAVO izgleda taj famozni niz:
11=2*3+5
17=2*5+7
23=2*5+13
27=2*5+17
29=2*5+19
35=2*11+13
37=2*7+23
...
Nije mi jasno cemu ova komplikacija. Doticni niz, niz svih brojeva koji se ne mogu predstaviti kao zbir dva prosta broja, se dobija tako sto se svi clanovi niza svih slozenih neparnih brojeva uvecaju za dva.
Dakle, niz (izostavili ste nekoliko clanova):
11 17 23 27 29 35 37 41 47 53
57 59 65 67 71 77 79 83
87 89
93 95 97 101.
je ustvari:
9 15 21 25 27 33 35 39 45 51 55 57 ... + 2
Do ove leme se dolazi primenom Goldbahove hipoteze (mislim da je dokazana 90-ih godina, pa vise i nije hipoteza, ali svejedno - proverena je za prvih nekoliko dekalijardi.) Osim nje, znamo da je 2 jedini paran prost broj, i to je to.
Inace, dosao sam pomocu racunara do sledecih parova (granica pretrage mi je bila da Gospodin Zbir nije veci od 10000):
(4,13) (4,61) (16,73) (16,111) (64,73) (32,131) (16,163) (4,181) (64,127) (4,229) (8,239) (13,256) (64,241) (32,311) (8,419) (8,449) (128,419) (256,313) (71,512) (101,512) (128,509) (8,659) (32,641) (128,569) (32,701) (201,556) (256,523) (128,659) (8,809) (64,757) (32,821) (256,673) (128,839) (40,937) (256,733) (421,576) (32,1013) (36,1051) (8,1109) (16,1191) (8,1259) (512,761) (256,1033) (8,1289) (8,1319) (128,1217) (128,1229) (8,1373) (128,1259) (256,1153) (512,911) (4,1447) (16,1483) (8,1499) (128,1409) (211,1408) (32,1601) (16,1641) (512,1151) (128,1553) (128,1559) (512,1181) (8,1709) (128,1619) (32,1721) (3,1756) (16,1753) (512,1289) (128,1709) (32,1811) (256,1601) (128,1733) (4,1867) (8,1949) (64,1909) (376,1609) (8,1979) (512,1481) (128,1889) (256,1783) (8,2039) (5,2048) (64,2017) (4,2161) (128,2039) (32,2141) (4,2209) (512,1721) (256,1993) (128,2129) (239,2048) (512,1811) (8,2339) (256,2203) (32,2441) (449,2048) (64,2437) (1024,1489) (64,2521) (256,2371) (8,2621) (599,2048) (64,2605) (128,2549) (719,2048) (32,2741) (8,2789) (128,2687) (32,2801) (4,2833) (512,2411) (512,2441) (256,2707) (256,2791) (8,3041) (32,3041) (256,2833) (512,2591) (1061,2048) (32,3083) (512,2621) (16,3163) (367,2848) (128,3119) (1223,2048) (1229,2048) (128,3167) (512,2801) (64,3319) (128,3257) (8,3389) (32,3371) (128,3299) (32,3413) (4,3463) (256,3253) (128,3389) (512,3041) (128,3449) (64,3529) (1559,2048) (32,3581) (32,3659) (256,3463) (1709,2048) (8,3767) (32,3761) (421,3424) (512,3389) (128,3779) (256,3673) (32,3911) (512,3461) (1024,2953) (32,4001) (16,4021) (512,3557) (32,4091) (43,4096) (4,4177) (512,3671) (8,4229) (8,4289) (32,4271) (512,3821) (256,4093) (512,3851) (2048,2399) (2048,2459) (128,4409) (463,4096) (512,4049) (2048,2549) (512,4091) (2048,2579) (4,4629) (64,4621) (8,4679) (8,4691) (16,4701) (2048,2699) (619,4192) (2048,2789) (2048,2819) (8,4889) (128,4787) (4,4933) (2048,2909) (2048,2939) (512,4481) (64,4957) (8,5099) (32,5081) (32,5087) (1051,4096) (32,5189) (128,5099) (2048,3209) (8,5279) (32,5261) (79,5224) (256,5059) (256,5101) (2048,3323) (2048,3329) (1303,4096) (8,5483) (2048,3449) (128,5417) (2048,3539) (64,5545) (16,5601) (32,5591) (128,5507) (8,5669) (32,5657) (2048,3659) (64,5647) (12,5743) (256,5521) (128,5669) (2048,3779) (32,5801) (8,5849) (4,5857) (16,5851) (8,5879) (1821,4096) (8,5939) (1192,4759) (512,5441) (128,5879) (128,5897) (32,6047) (2048,4079) (128,6029) (512,5657) (2048,4139) (64,6133) (8,6203) (128,6089) (32,6203) (32,6311) (8,6359) (512,5861) (512,5867) (128,6299) (4,6429) (433,6016) (2048,4421) (128,6359) (64,6427) (2048,4463) (128,6389) (8,6581) (8,6599) (512,6113) (512,6131) (128,6521) (8,6659) (512,6203) (8,6737) (512,6263) (128,6689) (8,6869) (256,6661) (16,6907) (2048,4889) (32,6911) (4,6991) (128,6869) (256,6781) (128,6911) (2048,5009) (512,6551) (512,6581) (8,7109) (512,6653) (32,7151) (1024,6163) (128,7079) (32,7193) (32,7211) (1753,5536) (512,6791) (2048,5279) (32,7331) (3352,4027) (1024,6381) (512,6911) (2048,5399) (512,6959) (128,7349) (256,7243) (8,7499) (2341,5176) (8,7529) (32,7541) (8,7589) (128,7499) (512,7121) (512,7151) (3613,4096) (64,7687) (128,7643) (128,7649) (3711,4096) (8,7829) (2713,5128) (32,7841) (2048,5849) (32,7901) (64,7897) (512,7451) (2048,5939) (512,7481) (512,7487) (3907,4096) (8,8009) (256,7789) (111,7996) (32,8111) (128,8039) (4,8167) (8,8219) (16,8287) (2048,6269) (4096,4243) (512,7841) (191,8192) (3931,4456) (512,7901) (251,8192) (281,8192) (32,8447) (293,8192) (32,8501) (2048,6599) (461,8192) (256,8419) (2048,6719) (32,8741) (128,8669) (512,8291) (1024,7789) (8,8849) (2316,6571) (2048,6869) (256,8713) (32,8951) (8,9029) (512,8573) (128,8969) (911,8192) (512,8597) (256,8859) (941,8192) (4,9133) (256,8923) (128,9059) (2048,7151) (8,9209) (64,9157) (32,9239) (2048,7229) (128,9209) (512,8849) (256,9133) (2048,7349) (32,9371) (8,9419) (2647,6784) (256,9201) (3361,6112) (8,9479) (2473,7048) (2048,7529) (32,9551) (1451,8192) (128,9539) (1511,8192) (64,9643) (32,9677) (8,9719) (512,9221) (1571,8192) (256,9511) (32,9749) (128,9689) (1637,8192) (64,9787) (256,9601) (64,9829) (1721,8192) (8,9929) (512,9479) (2048,7949)
Da li je moguce da ih ima ovoliko?!?