Numere prime de la 2 la 15401, …

Pentru a dovedi că un număr   este prim, se procedează în felul următor:

Exemplu:

Demonstraţi că numărul natural 4441 este prim.

Rezolvare:

4441 nu este divizibil cu 2; cu 3; cu 5;

4441 = 7 ∙ 634 + 3; 634 > 7, r = 3;

4441 = 11 ∙ 403 + 8; 403 >11, r = 8;

4441 = 13 ∙ 341 + 8; 341 > 13, r = 8;

4441 = 17 ∙ 261 + 4; 261 > 17, r = 4;

4441 = 19 ∙ 233 + 14; 233 > 19, r = 14;

4441 = 23 ∙ 193 + 2; 193 > 23, r = 2;

4441 = 29 ∙ 153 + 4; 153 > 29, r = 4;

4441 = 31 ∙ 143 + 8; 143 > 31, r = 8;

4441 = 37 ∙ 120 + 1; 120 > 37, r = 1;

4441 = 41 ∙ 108 + 13; 108 > 41, r = 13;

4441 = 43 ∙ 103 + 12; 103 > 43, r = 12;

4441 = 47 ∙ 94 + 23; 94 > 47, r = 23;

4441 = 53 ∙ 83 + 42; 83 > 53, r = 42;

4441 = 59 ∙ 75 + 16; 75 > 59, r = 16;

4441 = 67 ∙ 66 + 19; 66 < 67, r = 19 => 4441 număr natural prim.

Q.E.D.

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, 1207, 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, 2383, 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, 2641, 2749, 2753, 2761, 2771, 2777, 2789, 2791, 2797, 2801, 2803, 2819, 2833, 2837, 2843, 2851, 2859, 2861, 2879, 2887, 2897, 2903, 2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999,

3001, 3011, 3019, 3023, 3031, 3037, 3041, 3049, 3061, 3067, 3079, 3083, 3089, 3109, 3119, 3121, 3137, 3163, 3167, 3169, 3187, 3191, 3203, 3209, 3217, 3221,  3229, 3251, 3253, 3257, 3259, 3271, 3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331, 3341, 3343, 3359, 3361, 3371, 3373, 3389, 3391, 3401,3407, 3409, 3413, 3421, 3427, 3433, 3437, 3443, 3449, 3457, 3461, 3463, 3467, 3469, 3491,3499, 3511, 3517, 3527, 3529, 3533, 3539, 3541, 3547, 3551, 3557, 3559, 3571, 3581, 3583, 3593, 3601, 3607, 3613, 3617, 3623, 3631, 3637, 3643, 3659, 3671, 3673, 3677, 3679, 3691, 3697, 3701, 3709, 3719, 3721, 3733, 3739, 3761, 3767, 3769, 3779, 3793, 3797, 3799, 3803, 3821, 3823, 3829, 3833, 3847, 3851, 3853, 3863, 3877, 3881, 3899, 3907, 3911, 3917, 3919, 3923, 3929, 3931, 3943, 3947, 3959, 3967, 3989,

4001, 4003, 4007, 4013, 4019, 4021,  4027, 4049, 4051, 4057, 4073, 4079, 4091, 4093, 4099, 4111, 4127, 4121, 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, 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, 5237, 5261, 5273, 7279, 5231, 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, 5785. 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, 6053, 6067, 6073, 6077, 6089, 6091, 6101, 6107, 6113, 6121, 6131, 6133, 6143, 6151, 6161, 6163, 6167, 6173, 6179, 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, 6431, 6449, 6451, 6469, 6473, 6481, 6491, 6497, 6529, 6533, 6547, 6553, 6561, 6563, 6569, 6577, 6599, 6607, ? 6637, 6653, 6659, 6661, 6673, 6679, 6689, 6691, 6701, 6703, 6709, 6719, 6733, 6737, 6751, 6761, 6763, 6779, 6781, 6791, 6793,6823, 6827, 6829, 6833, 6841, 6857, 6871, 6883, 6899, 6907, 6911, 6917, 6947, 6949, 6959, 6961, 6967, 6971, 6977, 6983, 6991, 6997,

 7001, 7013,  7019,  7027, 7039, 7043, 7057, 7067, 7069, 7079, 7103, 7109, 7121, 7127, 7129, 7147, 7151, 7153, 7159, 7177, 7187, 7193, 7207, 7211, 7219, 7229, 7237, 7243, 7253, 7283, 7297, 7307, 7309, 7321, 7331, 7349, 7351, 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, 7669, 7673, 7687, 7691, 7699, 7703, 7717, 7723, 7727, 7741, 7753, 7757, 7759, 7789, 7793,7823, 78290, 7841, 7853, 7867, 7877, 7879, 7883, 7901,79o7, 7919, 7927, 7933, 7937, 7949, 7951, 7963, 7993,

 8009, 8011,8017, 8039, 8053, 8057, 8059, 8069, 8081, 8087, 8089, 8093, 8101, 8111, 8123, 8147,8161, 8167 , 8171, 8191, 8197, 8209, 8213, 8219, 8221, 8231, 8233, 8237, 8243, 8263, 8269, 8273, 8287, 8289, 8291, 8293, 8297, 8299, 8311, 8317, 8329, 8353, 8363, 8369, 8277, 8387, 8389, 8419, 8423, 8429, 8431, 8443, 8447, 8461, 8467, 8501, 8513, 8521, 8527, 8537, 8539, 9543, 8563, 8581, 8597, 8599, 8609, 8623, 8627, 8629, 8641, 8647, 8663, 8669, 8677, 8681, 8689, 8693, 8699, 8707, 8713, 8719, 8731, 8737, 8741, 8747, 8753, 8761, 8779, 8783, 8803, 8807, 8819, 8821, 8831, 8837, 8839, 8849, 8861, 8863, 8867, 8887, 8893, 8899, 8923, 8929, 8933, 8941, 8951, 8963, 8969, 8971, 8989, 8999;

9001, 9007 9011,  9013, 9029, 9041, 9043, 9049, 9059, 9067, 9091, 9103, 9109, 9127, 9133, 9137, 9151, 9157, 9161, 9173, 9181, 9187, 9199, 9203, 9209, 9221, 9227, 9239, 9241, 9257, 9277, 9281, 9283, 9293, 9311, 9319, 9323, 9337, 9341, 9343, 9349, 9371, 9377, 9391, 9397, 9403, 9413, 9419, 9421, 9431, 9433, 9437, 9439, 9461, 9463, 9467, 9473, 9479, 9491, 9497, 9511, 9521, 9533, 9539, 9547, 9551, 9587, 9601, 9613, 9619, 9623, 9629, 9631, 9643, 9649, 9661, 9677, 9679, 9689, 9697, 9719, 9721, 9733, 9739, 9743, 9749, 9767, 9769, 9781, 9787, 9791, 9803, 9811, 9817, 9829, 9833, 9839, 9857, 9859, 9871, 9883, 9887, 9901, 9907, 9923, 9929, 9931, 9941, 9949, 9967, 9973;

 10007, 10009, 10037, 10039, 10061, 10067, 10069, 10079, 10091, 10093, 10103, 10133, 10139, 10141, 10151, 10159, 10163, 10169, 10177, 10181, 10193, 10211, 10223, 10243, 10247, 10253, 10259, 10267, 10271, 10273, 10289, 10301, 10303, 10313, 10321, 10331, 10333, 10337, 10343, 10357, 10391, 10399, 10427, 10429, 10433, 10453, 10457, 10459, 10463, 10477, 10487, 10499, 10501, 10513, 10529, 10531, 10559, 10567, 10589, 10597, 10601, 10607, 10613, 10627, 10631, 10639, 10651, 10657, 10663, 10667, 10687, 10691, 10709, 10711, 10723, 10729, 10733, 10739, 10753, 10771, 10781, 10789, 10799, 10831, 10837, 10847, 10859, 10861, 10867, 10883, 10889, 10891, 10903, 10909, 10937, 10939, 10949, 10957, 10973, 10979, 10987, 10993,

 11003, 11027, 11047, 11057, 11059, 11069, 11071, 11083, 11087, 11093, 11113, 11117, 11119, 11131, 11149, 11159, 11171, 11173, 11177, 11197, 11213, 11239, 11243, 11251, 11257, 11261, 11273, 11279, 11287, 11299, 11311,11317, 11321, 11329, 11351, 11353, 11369, 11383, 11393, 11399, 11411, 11423, 11437, 11443, 11447, 11467, 11471, 11483, 11489, 11491, 11497, 11503, 11519, 11527, 11549, 11551, 11579, 11597, 11593, 11597, 11617, 11621, 11633, 11657, 11677, 11681, 11689, 11699, 11717, 11719, 11731, 11743, 11777, 11779, 11783, 11789, 11801, 11807, 22813, 11821, 11827, 11831, 11833, 11839, 11863, 11867, 11887, 11897, 11903, 11909, 11923, 11927, 11933, 11939, 11941, 11953, 11950, 11969, 11971, 11981, 11987,

 12007, 12011, 12037, 12041, 12043, 12049, 12071, 12073, 12097, 12101, 12107, 12109, 12113, 12119, 12143, 12149, 12157, 12161, 12163, 12197, 12203, 12211, 12227, 12239, 12241, 12251, 12253, 12263, 12269, 12277, 12281, 12289, 12301, 12323, 12329, 12343, 12347, 12373, 12377, 12379, 12391, 12401, 12409, 12413, 12421, 12433, 12437, 12451, 12457, 12473, 12479, 12487, 12491, 12497, 12503, 12511, 12517, 12527, 12539, 12541, 12547, 12553, 12569, 12577, 12583, 12589, 12601, 12611, 12613, 12619, 12611, 12613, 12619, 12637, 12641, 12647, 12653, 12659, 12671, 12689, 12697, 12703,  12713, 12721, 12739, 12743, 12757, 12763, 12781, 12791, 12799, 12809, 12821, 12823, 12829, 12841, 12853, 12889, 12893, 12899, 12907, 12911, 12917, 12919, 12923, 12941, 12953, 12959, 12973, 12977, 12979, 12983,

 13001, 13003, 13007, 13009, 13033, 13043, 13063, 13073, 13093, 13099, 13103, 13109, 13127, 13147, 13151, 13159, 13163, 13177, 13183, 13187, 13219, 13229, 13241, 13249, 13259, 13267, 13291, 13297, 13309, 13313, 13327, 13331, 13337, 13339, 13367, 13381, 13397, 13399, 13411, 13417, 13421, 13441, 13451, 13457, 13463, 13469, 13477, 13487, 13499, 13513, 13523, 13537, 13553, 13567, 13577, 13591, 13597,  13613, 13619, 13627, 13633, 13649, 13669, 13679, 13681, 13687, 13691, 13693, 13697, 13709, 13711, 13721, 13723, 13729, 13751, 13757, 13759, 13763, 13781, 13789, 13799, 13807, 13829, 13831, 13841, 13859, 13873, 13877, 13879, 13901, 13903, 13907, 13913, 13921, 13931, 13933, 13939, 13963, 13967, 13997, 13999,

14009, 14011, 14017, 14029, 14033, 14051, 15057, 14071, 14081, 14083, 14087, 14107, 14143, 14149, 14153, 14159, 14173, 14177, 14197, 14207, 14221, 14243, 14249, 14251, 14281, 14293, 14303, 14321, 14323, 14327, 14341, 14347, 14369, 14387, 14389, 14401, 14407, 14411, 14423, 14431, 14437, 14447, 14449, 14461, 14479, 14489, 14503, 14519, 14533, 14537, 14543, 14549, 14551, 14557, 14561, 14563, 14591, 14593, 14621, 14627, 14629, 14633, 14639, 14653, 14657, 14659, 14669, 14683, 14699, 14713, 14723, 14731, 14737, 14741, 14747, 14753, 14759, 14767, 14771, 14779, 14783, 14797, 14813, 14821, 14827, 14831, 14843, 14851, 14867, 14869, 14873, 14879, 14887, 14891, 14897, 14923, 14929, 14939, 14947, 14951, 14957, 14969, 14983,

 15013, 15017, 15031, 15053, 15073, 15077, 15083, 15091, 15101, 15107, 15121, 15131, 15137, 15139, 15149, 15161, 15173, 15187, 15193, 15199, 15217, 15227, 15233, 15241, 15259, 15263, 15269, 15671, 15277, 15287, 15289, 15299, 15307, 15313, 15319, 15329, 15331, 15349, 15359, 15361, 15373, 15377, 15383, 15391, 15401…

Prof. Natalia Ghiţă, Agnita

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