Nhamba dzekutanga ndidzo idzo vanongova nevaviri vakakamura, nekuti ivo vanongopatsanurana vega uye neiyuniti, ndiko kuti, nhamba 1. Asi chenjera! Izvi zvinorevei? Zviri nyore kwazvo. Iyo yekutanga nhamba, semuenzaniso 2, inogona chete kupatsanurwa ne2, -2, 1, uye -1.
Nhamba dzine vanopfuura vanodarika vaviri vanoshevedzwa nhamba dzakanyorwa. Kana tikatora nhamba yakasanganiswa, semuenzaniso, gumi, tichaona kuti tinogona kuipatsanura pachayo nekubatana, ndiko kuti, pakati pegumi na10, asi zvakare pakati pechipiri na10. Naizvozvo, gumi inhamba inosanganiswa.
Iwo ese manhamba ekutanga kana akaumbika?
Kune maviri nhamba "dzakakosha" izvo hazvisi zvekutanga kana zvakakomberedzwa. iyo 0 uye 1. Sei? Ngatione:
- Iyo nhamba 1 inogona kupatsanurwa pachayo (1/1 = 1) uye nekubatana, ndiko kuti, nhamba 1 (1/1 = 1). Nekudaro, kuti nhamba ifungidzirwe seyakanyanya, inofanirwa kuve iine maviri akasiyana evaparadziri. Iyo nhamba yekutanga chete ine muparadzanisi mumwe, saka haisi prime kana musanganiswa.
- Iyo 0 haigone kupatsanurwa pachayo, nekuti mhedzisiro isingagumi.
Saka kana tikabvisa 0 ne1 kubva pane zvakanyorwa, kunze kwenhamba huru yenhamba dzasara, tinoziva sei kuti ndeapi ekutanga uye asiri iwo?
Ungaziva sei kana nhamba iri yekutanga
Chinhu chakasarudzika kufunga nezvekuzviita nekurasa, ndokuti, kuyedza kutsvaga ivo vaparadzanisi. Iine karukureta inokurumidza, asi kana tichifanira kuzviita takatarisa pasi nepeni nepepa, zvinhu zvinobva zvaoma. Isu tinokudzidzisa iwe nzira mbiri kuti uzive kana nhamba iri yekutanga kana kwete.
Sefa yeEratosthenes
Iyo nesefa yeEratosthenes ndeye hunyanzvi hwekuziva iyo yekutanga nhamba pakati pe2, inova nhamba yekutanga, uye imwe nhamba.
Iyi nzira inosanganisira kugadzira tafura uye kuyambuka kuwanda kwenhamba dzese. Kutanga isu tichabvisa kuwanda kwe2, uyezve 3, zvichingodaro kusvika tasvika panhamba yakakwirwa yakakura kupfuura yekupedzisira tafura.
Kunge zvese mune masvomhu, iyo Eratosthenes sise inonyatsonzwisiswa nemuenzaniso:
- Isu tinogadzira tafura ine nhamba kubva pa2 kusvika makumi matatu.
| 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
| 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
| 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 |
- Isu tinoyambuka kuwanda kwe2 pane iyo runyorwa, ndiko kuti, tinoyambuka kubva 2 kusvika 2: 4, 6, nezvimwe. Chenjerera! Iyo 2, iyo inogona chete kupatsanurwa pakati payo nenhamba 1, hatisi kuyambuka, sezvo iri nhamba yekutanga.
| 2 | 3 | 5 | 7 | 9 | |||||
| 11 | 13 | 15 | 17 | 19 | |||||
| 21 | 23 | 25 | 27 | 29 |
- Isu tinotora iyo inotevera nhamba, 3, uye tarisa kuti squared ishoma pane iyo hombe nhamba iri patafura. Sezvo 32 <30, isu tinoenderera mberi nesefa uye nekuyambuka kuwanda kwayo: 6, 9, 12 ... Semudanho rapfuura, hatibvise iyo nhamba 3, iri zvakare prime.
| 2 | 3 | 5 | 7 | ||||||
| 11 | 13 | 17 | 19 | ||||||
| 23 | 25 | 29 |
- Isu tinodzokorora nhanho yapfuura nenhamba inotevera mutafura: 4 yakabviswa, saka tinotora 5. Sezvo 52 <30, tinodarika kuwanda kwavo.
| 2 | 3 | 5 | 7 | ||||||
| 11 | 13 | 17 | 19 | ||||||
| 23 | 29 |
- Tinoenderera mberi nenhamba inotevera tisina kuyambuka: 7. As 72 = 49, ndiko kuti, mraba wechi7 wakakura kupfuura nhamba yekupedzisira iri patafura, nzira inopera, uye nhamba dzisingabude kunze idzo dziri nhamba dzekutanga.
- Mhedziso. Iwo ekutanga manhamba ari pakati pa2 ne30 ndi: 2, 3, 5, 7, 11, 13, 17, 19, 23 na 29.
Iyo Eratosthenes sieve inzira inokurumidza uye yakapusa yekuziva iyo prime manhamba, asi zvakadii nezveko kana iyo nhamba yatinoda kudzidza yakanyanya kukwirira, semuenzaniso, 54657?
Sezvaunonzwisisa, hazvingaite kuita tafura kubva 2 kusvika 54657, handiti? Chii chatingaite ipapo? Zviri nyore kwazvo: shandisa nzira dzekuparadzanisa.
Kupatsanura maitiro
Maitiro ekupatsanurwa ari inotonga kuti uone kana imwe nhamba ichipatsanurwa neimwe pasina kuita kupatsana.
Nekudaro, kana isu tikashandisa iyi mirau uye tichiona kuti nhamba inopatsanurwa neimwe nhamba isiri iyo pachayo neyuniti, tinozoziva kuti haisi yekutanga.
- Mutsara wekuparadzaniswa kwenhamba 2. Chiverenge chinokamurwa na2 kana chiri kunyange, ndiko kuti, kana ichiguma muna 0, 2, 4, 6 kana 8. Uye, heino hunyengeri: senge chero nhamba inopatsanurwa ne4, 6 kana 8 inoparadzaniswa na2, hatizodi kuziva nzira dzekuparadzanisa dzimwe nhamba.
- Chirevo chekukamurwa kwenhamba 3. Chiverengero chinopatsanurwa na3 kana huwandu hwenhamba dzacho huri kuwanda kwematatu. Ngatione muenzaniso:
267 -> 2 + 6 + 7 = 15
Sezvo gumi nemashanu iri kuwanda kwe15, 3 inopatsanurwa ne267.
Uyezve, sezvo nhamba dzese dzinogovaniswa ne9 dzichipatsanurwa na3, zvichave zvakakwana kuti isu tizive chirevo ichi.
- Chikamu chekukamurwa kwenhamba 5. Chiverengero chinopatsanurwa ne5 kana chikaguma muna 0 kana 5.
- Mutsara wekuparadzaniswa kwenhamba 7. Kuti tione kana nhamba iri kuganhurwa ne7, tinofanirwa kubvisa nhamba isina digit yekupedzisira uye kaviri yekupedzisira digit. Kana nhamba yakawanikwa iri 0 kana kuwanda kwe7, iyo yekutanga nhamba inoparadzaniswa na7. Uchanzwisisa izvi zvirinani nemuenzaniso, ngatitorei pairi!
378 -> 37 − (8 × 2) = 37 − 16 = 21
Sezvo gumi nemashanu iri kuwanda kwe21, 7 inopatsanurwa ne378.
- Musiyano wekuparadzaniswa kwenhamba 11. Kana tikabvisa huwandu hwayo kunyange manhamba uye huwandu hwenhamba dzisinganzwisisike, uye nhamba yakawanikwa iri 0 kana kuwanda kwe11, zvinoreva kuti iyo nhamba yakadzidzwa inoonekwa ne11 Heino muenzaniso:
8591 -> (8 + 9) − (5 + 1) = 17 − 6 = 11
Sezvo gumi nemashanu iri kuwanda kwe11, 11 inopatsanurwa ne8591.
Uye ndizvozvo chete! Ikozvino yave nguva yako: ungadai uchitoziva here kuverenga kana iyo yakakwira nhamba, 54657, iri yekutanga?
Rondedzero yenhamba yepamusoro kubva pa1 kusvika zviuru gumi
Chekupedzisira, kana iwe uchitsvaga runyorwa rwekutanga manhamba kubva pa1 kusvika zviuru gumi, senge 10.000 kusvika 1 kana 100 kusvika 1 1.000, heino yakakwana uye yakagadziridzwa imwe:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997, 1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053, 2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129, 2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213, 2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287, 2293, 2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, 2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423, 2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521, 2531, 2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617, 2621, 2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687, 2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741, 2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819, 2833, 2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903, 2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999, 3001, 3011, 3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079, 3083, 3089, 3109, 3119, 3121, 3137, 3163, 3167, 3169, 3181, 3187, 3191, 3203, 3209, 3217, 3221, 3229, 3251, 3253, 3257, 3259, 3271, 3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331, 3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391, 3407, 3413, 3433, 3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511, 3517, 3527, 3529, 3533, 3539, 3541, 3547, 3557, 3559, 3571, 3581, 3583, 3593, 3607, 3613, 3617, 3623, 3631, 3637, 3643, 3659, 3671, 3673, 3677, 3691, 3697, 3701, 3709, 3719, 3727, 3733, 3739, 3761, 3767, 3769, 3779, 3793, 3797, 3803, 3821, 3823, 3833, 3847, 3851, 3853, 3863, 3877, 3881, 3889, 3907, 3911, 3917, 3919, 3923, 3929, 3931, 3943, 3947, 3967, 3989, 4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049, 4051, 4057, 4073, 4079, 4091, 4093, 4099, 4111, 4127, 4129, 4133, 4139, 4153, 4157, 4159, 4177, 4201, 4211, 4217, 4219, 4229, 4231, 4241, 4243, 4253, 4259, 4261, 4271, 4273, 4283, 4289, 4297, 4327, 4337, 4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409, 4421, 4423, 4441, 4447, 4451, 4457, 4463, 4481, 4483, 4493, 4507, 4513, 4517, 4519, 4523, 4547, 4549, 4561, 4567, 4583, 4591, 4597, 4603, 4621, 4637, 4639, 4643, 4649, 4651, 4657, 4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729, 4733, 4751, 4759, 4783, 4787, 4789, 4793, 4799, 4801, 4813, 4817, 4831, 4861, 4871, 4877, 4889, 4903, 4909, 4919, 4931, 4933, 4937, 4943, 4951, 4957, 4967, 4969, 4973, 4987, 4993, 4999, 5003, 5009, 5011, 5021, 5023, 5039, 5051, 5059, 5077, 5081, 5087, 5099, 5101, 5107, 5113, 5119, 5147, 5153, 5167, 5171, 5179, 5189, 5197, 5209, 5227, 5231, 5233, 5237, 5261, 5273, 5279, 5281, 5297, 5303, 5309, 5323, 5333, 5347, 5351, 5381, 5387, 5393, 5399, 5407, 5413, 5417, 5419, 5431, 5437, 5441, 5443, 5449, 5471, 5477, 5479, 5483, 5501, 5503, 5507, 5519, 5521, 5527, 5531, 5557, 5563, 5569, 5573, 5581, 5591, 5623, 5639, 5641, 5647, 5651, 5653, 5657, 5659, 5669, 5683, 5689, 5693, 5701, 5711, 5717, 5737, 5741, 5743, 5749, 5779, 5783, 5791, 5801, 5807, 5813, 5821, 5827, 5839, 5843, 5849, 5851, 5857, 5861, 5867, 5869, 5879, 5881, 5897, 5903, 5923, 5927, 5939, 5953, 5981, 5987, 6007, 6011, 6029, 6037, 6043, 6047, 6053, 6067, 6073, 6079, 6089, 6091, 6101, 6113, 6121, 6131, 6133, 6143, 6151, 6163, 6173, 6197, 6199, 6203, 6211, 6217, 6221, 6229, 6247, 6257, 6263, 6269, 6271, 6277, 6287, 6299, 6301, 6311, 6317, 6323, 6329, 6337, 6343, 6353, 6359, 6361, 6367, 6373, 6379, 6389, 6397, 6421, 6427, 6449, 6451, 6469, 6473, 6481, 6491, 6521, 6529, 6547, 6551, 6553, 6563, 6569, 6571, 6577, 6581, 6599, 6607, 6619, 6637, 6653, 6659, 6661, 6673, 6679, 6689, 6691, 6701, 6703, 6709, 6719, 6733, 6737, 6761, 6763, 6779, 6781, 6791, 6793, 6803, 6823, 6827, 6829, 6833, 6841, 6857, 6863, 6869, 6871, 6883, 6899, 6907, 6911, 6917, 6947, 6949, 6959, 6961, 6967, 6971, 6977, 6983, 6991, 6997, 7001, 7013, 7019, 7027, 7039, 7043, 7057, 7069, 7079, 7103, 7109, 7121, 7127, 7129, 7151, 7159, 7177, 7187, 7193, 7207, 7211, 7213, 7219, 7229, 7237, 7243, 7247, 7253, 7283, 7297, 7307, 7309, 7321, 7331, 7333, 7349, 7351, 7369, 7393, 7411, 7417, 7433, 7451, 7457, 7459, 7477, 7481, 7487, 7489, 7499, 7507, 7517, 7523, 7529, 7537, 7541, 7547, 7549, 7559, 7561, 7573, 7577, 7583, 7589, 7591, 7603, 7607, 7621, 7639, 7643, 7649, 7669, 7673, 7681, 7687, 7691, 7699, 7703, 7717, 7723, 7727, 7741, 7753, 7757, 7759, 7789, 7793, 7817, 7823, 7829, 7841, 7853, 7867, 7873, 7877, 7879, 7883, 7901, 7907, 7919
