Don't take life too seriously: it's just a temporary situation

Primi circolari

Rappresentazione dei numeri 

Si chiamano “primi circolari” i numeri primi, che rimangono tali per ogni permutazione circolare delle cifre, vale a dire portando ripetutamente la prima cifra all’ultimo posto. Per esempio, 1193 è un primo circolare, perché 1931, 9311 e 3199 sono primi.

 

Gli unici noti in base 10 sono: 2, 3, 5, 7, 13, 17, 37, 79, 113, 197, 199, 337, 1193, 3779, 11939, 19937, 193939, 199933, oltre ovviamente alle permutazioni cicliche di questi e ai primi pluriunitari, come 11 e 1111111111111111111; se ne esistono altri, devono avere almeno 24 cifre (Walter Schneider e N. Pavlos, 2003, 2003).

Da notare che, come quelli banali di una e due cifre, 113, 199, 337, 11939 e 193939 mantengono la loro proprietà circolare anche se letti a rovescio.

 

La definizione può essere estesa ad altre basi.

In qualsiasi base i primi circolari sono formati esclusivamente dalle cifre diverse da zero e prime rispetto alla base; per esempio, in base 10 un primo circolare non può contenere cifre pari o uguali a 5.

 

In base 2 gli unici primi circolari sono i primi di Mersenne.

 

E’ probabile che i primi circolari non pluriunitari siano in numero finito in ogni base.

 

Ogni primo p maggiore di 2 è pluriunitario e quindi circolare in base p – 1.

 

La tabella seguente mostra i primi circolari inferiori a 106 nelle basi da 2 a 20, considerando solo la permutazione delle cifre che dà il numero minimo.

Base

Primi circolari

2

112 = 3, 1112 = 7, 111112 = 31, 11111112 = 127, 11111111111112 = 8191, 111111111111111112 = 131071, 11111111111111111112 = 524287

3

23 = 2, 123 = 5, 1113 = 13, 11111113 = 1093, 11111111111113 = 797161

4

24 = 2, 34 = 3, 114 = 5, 134 = 7, 1134 = 23, 113334 = 383

5

25 = 2, 35 = 3, 235 = 13, 345 = 19, 1115 = 31, 11325 = 167, 14245 = 239, 132345 = 1069, 144445 = 1249, 11111115 = 19531

6

26 = 2, 36 = 3, 56 = 5, 156 = 11, 1116 = 43, 1556 = 71, 11111116 = 55987

7

27 = 2, 37 = 3, 57 = 5, 147 = 11, 167 = 13, 237 = 17, 257 = 19, 567 = 41, 1427 = 79, 1557 = 89, 1667 = 97, 2457 = 131, 11657 = 439, 12537 = 479, 13257 = 509, 14447 = 571, 15437 = 619, 16557 = 677, 23267 = 853, 25647 = 977, 26567 = 1021, 45557 = 1657, 111117 = 2801, 115157 = 3001, 156527 = 4447, 366447 = 9587, 1254527 = 23557, 1415447 = 27031, 12551657 = 165079, 25464557 = 331231

8

28 = 2, 38 = 3, 58 = 5, 78 = 7, 158 = 13, 358 = 29, 378 = 31, 578 = 47, 1118 = 73, 11378 = 607, 13178 = 719, 13578 = 751, 17758 = 1021, 33378 = 1759, 1377178 = 49103, 1557538 = 56299

9

29 = 2, 39 = 3, 59 = 5, 79 = 7, 129 = 11, 149 = 13, 189 = 17, 259 = 23, 479 = 43, 789 = 71, 1229 = 101, 1759 = 149, 2549 = 211, 2789 = 233, 7889 = 647, 12889 = 971, 14779 = 1123, 17729 = 1361, 18579 = 1429, 22859 = 1697, 45559 = 3371, 77789 = 5741, 128159 = 8681, 152729 = 10433, 557779 = 37087, 1212789 = 73133, 1241479 = 75211, 1288449 = 78691, 1445749 = 88681, 1447459 = 88817, 1455829 = 89417, 1818729 = 112979, 2245579 = 134593, 2278249 = 136993, 2477549 = 150061, 2744579 = 167317, 4575779 = 274579

10

2, 3, 5, 7, 11, 13, 17, 37, 79, 113, 197, 199, 337, 1193, 3779, 11939, 19937, 193939, 199933

11

211 = 2, 311 = 3, 511 = 5, 711 = 7, 1211 = 13, 1611 = 16, 1811 = 19, 2711 = 29, 2911 = 31, 3411 = 37, 3A11 = 43, 4911 = 53, 5611 = 61, 6711 = 73, 8911 = 97, 11711 = 139, 13911 = 163, 19311 = 223, 1AA11 = 241, 23611 = 281, 26911 = 317, 33511 = 401, 36411 = 433, 36A11 = 439, 3A611 = 479, 56611 = 677, 58811 = 701, 7AA11 = 967, 124411 = 1621, 124A11 = 1627, 145911 = 1879, 156911 = 2011, 157411 = 2017, 187511 = 2381, 259711 = 3373, 276611 = 3581, 277711 = 3593, 279511 = 3613, 294811 = 3803, 34A411 = 4591, 353811 = 4639, 357411 = 4679, 37A711 = 4957, 3A6A11 = 5279, 44A911 = 5927, 477911 = 6257, 478A11 = 6269, 57A911 = 7621, 698A11 = 9173, 9AAA11 = 13309, 1989A11 = 27697, 1A98911 = 29137, 3677411 = 52837, 7AAAA11 = 117127, 11174311 = 177917, 11215711 = 178537, 11246511 = 178909, 11517411 = 182549, 11533411 = 182747, 11636411 = 184111, 1217A811 = 192629, 12536611 = 197423, 12551511 = 197609, 12AA6411 = 204923, 13226311 = 207947, 13477711 = 211229, 13697711 = 214133, 13716511 = 214483, 13934711 = 217367, 13964411 = 217727, 14142911 = 221461, 14151511 = 221567, 14426A11 = 225257, 14469511 = 225769, 14578211 = 227207, 145A9211 = 227581, 14622811 = 227873, 14767411 = 229739, 14A88211 = 233983, 15337211 = 238691, 15533611 = 241313, 15716911 = 243769, 15798911 = 244759, 157A4A11 = 244837, 15A75511 = 248473, 16295611 = 252709, 16422611 = 254491, 16543A11 = 256079, 16766311 = 259009, 16782911 = 259213, 16886211 = 260581, 17493311 = 269987, 177A7511 = 274147, 18219811 = 281069, 18264A11 = 281621, 18436511 = 283937, 18896511 = 289987, 18A78311 = 292427, 18AA8611 = 292793, 19889211 = 304537, 19947911 = 305369, 19948611 = 305377, 19A97511 = 307301, 1A273611 = 311009, 1A29A711 = 311329, 1A666411 = 316243, 1A788511 = 317839, 1A969211 = 320267, 228AA911 = 363361, 232A5711 = 369959, 23524711 = 372973, 23879411 = 377623, 23967A11 = 378817, 242A9411 = 384641, 24428911 = 386329, 24987711 = 393697, 25347A11 = 399871, 2585A311 = 406673, 26497511 = 416443, 267A7511 = 420557, 27332A11 = 428977, 27977911 = 437501, 27A33611 = 438301, 27A86811 = 438941, 28972911 = 452087, 2945A311 = 459913, 29544511 = 461059, 29553711 = 461171, 2A2A3411 = 472421, 2A99A311 = 481693, 35449811 = 562273, 35A95911 = 570821, 364A9711 = 577639, 36784511 = 581333, 38447711 = 606173, 38A95611 = 614741, 39785511 = 625267, 39A95511 = 629381, 3A3A8711 = 634861, 45577511 = 724993, 4584A811 = 728659, 46789511 = 742439, 46A78811 = 746303, 47954A11 = 759329, 47984911 = 759691, 48497911 = 767831, 48865A11 = 772771, 48A4A511 = 775241, 55698611 = 887629, 5576AA11 = 888623, 575A8811 = 915703, 57769911 = 917893, 5A9AA911 = 964973

12

212 = 2, 312 = 3, 512 = 5, 712 = 7, B12 = 11, 1112 = 13, 1512 = 17, 5712 = 67, 5B12 = 71, 11112 = 157, 11712 = 163, 11B12 = 167, 17512 = 233, 1B712 = 283, 157B12 = 2543, 555B12 = 9431, 1111112 = 22621, 115B7712 = 279883

13

213 = 2, 313 = 3, 513 = 5, 713 = 7, B13 = 11, 1413 = 17, 1613 = 19, 1A13 = 23, 2313 = 29, 2513 = 31, 3813 = 47, 5613 = 71, 5813 = 73, 6B13 = 89, 7A13 = 101, 7C13 = 103, 9A13 = 127, 11B13 = 193, 13313 = 211, 15513 = 239, 15713 = 241, 17B13 = 271, 22913 = 373, 24713 = 397, 24B13 = 401, 27413 = 433, 29613 = 461, 33B13 = 557, 34A13 = 569, 37913 = 607, 38613 = 617, 38813 = 619, 3B913 = 659, 3CA13 = 673, 4A513 = 811, 4BA13 = 829, 5C813 = 1009, 77913 = 1283, 78A13 = 1297, 7A813 = 1321, 117213 = 2459, 12BB13 = 2689, 131C13 = 2729, 134B13 = 2767, 137813 = 2803, 13BA13 = 2857, 142A13 = 2909, 146213 = 2953, 14B313 = 3019, 14CC13 = 3041, 163713 = 3257, 164813 = 3271, 16B513 = 3359, 16C613 = 3373, 176313 = 3461, 181913 = 3571, 183513 = 3593, 185913 = 3623, 18AC13 = 3691, 196713 = 3803, 1A3513 = 3931, 1B5C13 = 4133, 1CB513 = 4373, 223C13 = 4783, 235713 = 4973, 243413 = 5113, 245C13 = 5147, 247A13 = 5171, 26C913 = 5573, 27A413 = 5711, 282B13 = 5783, 284913 = 5807, 29A813 = 6053, 2A9A13 = 6211, 2AC713 = 6247, 2B7913 = 6353, 337413 = 7193, 33BC13 = 7253, 344C13 = 7331, 34CA13 = 7433, 358913 = 7549, 35AB13 = 7577, 369513 = 7727, 36B913 = 7757, 385913 = 8017, 38CC13 = 8111, 3A6413 = 8363, 3AA813 = 8419, 3CA413 = 8753, 3CC413 = 8779, 3CC813 = 8783, 444513 = 9521, 446513 = 9547, 446913 = 9551, 44B613 = 9613, 45A613 = 9769, 49B513 = 10457, 49B713 = 10459, 4AB613 = 10627, 557C13 = 11933, 55AB13 = 11971, 575813 = 12241, 58B713 = 12487, 58BB13 = 12491, 59BA13 = 12659, 5BC913 = 13009, 5CA813 = 13151, 666713 = 14281, 67CC13 = 14533, 69C813 = 14867, 6B6C13 = 15131, 7BBC13 = 17393, 1111113 = 30941, 1257213 = 33893, 125C513 = 33961, 1361813 = 36187, 1363C13 = 36217, 16C1913 = 43793, 1A62A13 = 51581, 1B3CA13 = 53401, 1BC7413 = 54851, 25A8A13 = 69911, 2878613 = 75991, 2978913 = 78191, 29BA513 = 78889, 2B76913 = 82559, 3553913 = 97561, 3B76A13 = 111121, 455BA13 = 126227, 4764A13 = 130699, 55C5813 = 155891, 57BAA13 = 160183, 6AAA713 = 195163, 11785913 = 416659, 11AA3413 = 423557, 11BA8413 = 425819, 12712A13 = 443999, 1285A313 = 446969, 12C46413 = 455537, 12C7B213 = 456107, 15737C13 = 530087, 159A7B13 = 535663, 168B5A13 = 562169, 182A9B13 = 605993, 1A3B2813 = 665387, 1A68CA13 = 671603, 22A63C13 = 822743, 22A7AC13 = 823003, 24434613 = 866183, 27ACB513 = 966659, 28B87513 = 996689

14

214 = 2, 314 = 3, 514 = 5, 714 = 7, B14 = 11, D14 = 13, 1314 = 17, 1514 = 19, 1914 = 23, 3514 = 47, 3B14 = 53, 5914 = 79, 9B14 = 137, 9D14 = 139, BD14 = 167, 11114 = 211, 33D14 = 643, 111914 = 2963, 135514 = 3407, 139514 = 3463, 15D514 = 3911, 15DD14 = 3919, 1BB514 = 5059, 1BD514 = 5087, 59DD14 = 15679, 5DBB14 = 16433, 9DBB14 = 27409, 11BBD514 = 608767, 11BD9314 = 609101, 15151914 = 733651, 15DB9914 = 767867

15

215 = 2, 315 = 3, 515 = 5, 715 = 7, B15 = 11, D15 = 13, 1215 = 17, 1415 = 19, 1E15 = 29, 2715 = 37, 2B15 = 41, 2D15 = 43, 4715 = 67, 4D15 = 73, 7815 = 113, 8B15 = 131, 11115 = 241, 12E15 = 269, 1DD15 = 433, 22715 = 487, 27E15 = 569, 28715 = 577, 2ED15 = 673, 44B15 = 971, 47815 = 1013, 47E15 = 1019, 4D815 = 1103, 77D15 = 1693, 7BD15 = 1753, BEE15 = 2699, 114B15 = 3671, 118715 = 3727, 11B215 = 3767, 11D815 = 3803, 11EB15 = 3821, 141715 = 4297, 144415 = 4339, 148E15 = 4409, 17B415 = 5119, 18B715 = 5347, 1DB415 = 6469, 1DB815 = 6473, 2B7B15 = 9341, 48B815 = 15473, 7DDE15 = 26759, 11B8415 = 56599, 1282415 = 59209, 148BD15 = 66103, 14E8E15 = 67409, 17B1D15 = 76753, 17EB415 = 77569, 1848815 = 78653, 1DD2415 = 97459, 2448715 = 115777, 24E2715 = 117937, 2DB8715 = 147727, 44D7B15 = 219041, 4B4D715 = 240727, 7777D15 = 379693, 77B7B15 = 380591, 7887B15 = 383291, 7DB8E15 = 400859, 7DDE815 = 401393, 88D8E15 = 435059, 111D4715 = 816367, 118D2215 = 839957, 11E14415 = 857539

16

216 = 2, 316 = 3, 516 = 5, 716 = 7, B16 = 11, D16 = 13, 1116 = 17, 1716 = 23, 1F16 = 31, 3516 = 53, 3B16 = 59, 3D16 = 61, 5916 = 89, BF16 = 191, 11516 = 277, 11B16 = 283, 13716 = 311, 13D16 = 317, 17516 = 373, 1FD16 = 509, 35916 = 857, 37716 = 887, 3FB16 = 1019, 3FD16 = 1021, 55D16 = 1373, 59F16 = 1439, 5BF16 = 1471, 7BB16 = 1979, BDD16 = 3037, 179B16 = 6043, 199316 = 6547, 1D5316 = 7507, 1D7D16 = 7549, 1DB316 = 7603, 1F7516 = 8053, 373F16 = 14143, 397916 = 14713, 397D16 = 14717, 399516 = 14741, 55FD16 = 22013, 1117316 = 70003, 1133916 = 70457, 11BD516 = 72661, 11D7716 = 73079, 13D3316 = 81203, 1593B16 = 88379, 1977716 = 104311, 1B7BD16 = 112573, 1BD5D16 = 114013, 1D5B716 = 120247, 1F73F16 = 128831, 1F93D16 = 129341, 1F99F16 = 129439, 355B516 = 218549, 3799F16 = 227743, 395FF16 = 235007, 5B79B16 = 374683, 5F79B16 = 391067, 799DF16 = 498143

17

217 = 2, 317 = 3, 517 = 5, 717 = 7, B17 = 11, D17 = 13, 1617 = 23, 1E17 = 31, 2317 = 37, 2D17 = 47, 3817 = 59, 3A17 = 61, 4517 = 73, 4B17 = 79, 5G17 = 101, 6B17 = 113, 7C17 = 131, 8D17 = 149, 8F17 = 151, 9A17 = 163, AB17 = 181, 11117 = 307, 13917 = 349, 26317 = 683, 28517 = 719, 2E517 = 821, 3EC17 = 1117, 3F717 = 1129, 6A917 = 1913, 6BC17 = 1933, 7AA17 = 2203, 7GG17 = 2311, ACF17 = 3109, 116517 = 5309, 121B17 = 5519, 135417 = 5869, 143B17 = 6131, 14C417 = 6277, 14D917 = 6299, 14E417 = 6311, 15B617 = 6551, 173417 = 6991, 177E17 = 7069, 1A7517 = 7927, 1A8A17 = 7949, 1AC417 = 8011, 1B7A17 = 8221, 1CF517 = 8641, 1D2917 = 8713, 1E5517 = 9049, 1EA817 = 9137, 1F4317 = 9319, 1FEB17 = 9497, 1FF817 = 9511, 1G4817 = 9613, 1G6A17 = 9649, 224F17 = 10487, 227617 = 10529, 23C617 = 10903, 244917 = 11059, 24DA17 = 11213, 258417 = 11411, 273317 = 11903, 27EE17 = 12101, 288317 = 12277, 28AF17 = 12323, 28E317 = 12379, 2AB417 = 12907, 2ABG17 = 12919, 2B9517 = 13163, 2DAA17 = 13763, 2DD317 = 13807, 2DEA17 = 13831, 2F3917 = 14221, 2F7D17 = 14293, 2GA717 = 14627, 35A917 = 16363, 35BA17 = 16381, 36AE17 = 16657, 376F17 = 16879, 379C17 = 16927, 37BE17 = 16963, 388417 = 17191, 399417 = 17497, 39GB17 = 17623, 3A9717 = 17789, 3B3C17 = 17981, 3B7617 = 18043, 3C4E17 = 18289, 3ED717 = 19013, 3EGC17 = 19069, 44B617 = 21001, 44EF17 = 21061, 476A17 = 21787, 486D17 = 22079, 4A9E17 = 22709, 4ADE17 = 22777, 4CC917 = 23333, 4DBD17 = 23609, 4DG817 = 23689, 4EB817 = 23893, 4EG717 = 23977, 4FEE17 = 24239, 559E17 = 26177, 55BC17 = 26209, 567D17 = 26431, 58AE17 = 27061, 5EAC17 = 28793, 5EBF17 = 28813, 5F6717 = 29009, 5F9A17 = 29063, 5G8E17 = 29339, 669E17 = 31379, 686F17 = 31907, 68BE17 = 31991, 6A9C17 = 32533, 6B8A17 = 32803, 6BAC17 = 32839, 6CE717 = 33191, 6DDD17 = 33469, 6EFC17 = 33791, 7AG817 = 37561, 7EBF17 = 38639, 7EGE17 = 38723, 7FB817 = 38921, 7FED17 = 38977, 7GC817 = 39227, 88G917 = 41897, 8B9D17 = 42649, 8BCG17 = 42703, 8DEE17 = 43313, 99DC17 = 47051, 9FCB17 = 48767, ABDD17 = 52543, BBDE17 = 57457, BECG17 = 58309, 1111117 = 88741, 16C4417 = 116539, 1GF8917 = 166609, 35F6617 = 279571, 3776E17 = 287093, 3AD7C17 = 303581, 6FBFC17 = 578267

18

218 = 2, 318 = 3, 518 = 5, 718 = 7, B18 = 11, D18 = 13, H18 = 17, 1118 = 19, 1B18 = 29, 5718 = 97, 5D18 = 103, 5H18 = 107, 7D18 = 139, 11B18 = 353, 11H18 = 359, 1DD18 = 571, 55B18 = 1721, 7BB18 = 2477, 7HH18 = 2591, BBH18 = 3779, 151B18 = 7481, 17HH18 = 8423, 1B1H18 = 9431, 1BB718 = 9601, 1DBH18 = 10259, 5BDB18 = 32969, 5DBH18 = 33587, BDDD18 = 68611, BDHD18 = 68683

19

219 = 2, 319 = 3, 519 = 5, 719 = 7, B19 = 11, D19 = 13, H19 = 17, 1A19 = 29, 1C19 = 31, 2319 = 41, 2519 = 43, 2919 = 47, 3419 = 61, 3A19 = 67, 3E19 = 71, 3G19 = 73, 4719 = 83, 4D19 = 89, 5819 = 103, 5C19 = 107, 5E19 = 109, 5I19 = 113, 7G19 = 149, 7I19 = 151, 8F19 = 167, 9A19 = 181, BE19 = 223, BI19 = 227, DG19 = 263, EH19 = 283, 11319 = 383, 12219 = 401, 18A19 = 523, 1CC19 = 601, 1DB19 = 619, 1FF19 = 661, 1IG19 = 719, 22D19 = 773, 29E19 = 907, 2E919 = 997, 2FE19 = 1021, 2HI19 = 1063, 36G19 = 1213, 37719 = 1223, 39519 = 1259, 3AA19 = 1283, 3AG19 = 1289, 3BF19 = 1307, 3EI19 = 1367, 3I819 = 1433, 44B19 = 1531, 45A19 = 1549, 46919 = 1567, 4FC19 = 1741, 57B19 = 1949, 5AG19 = 2011, 5BF19 = 2029, 5C619 = 2039, 5F919 = 2099, 5HF19 = 2143, 6BE19 = 2389, 77H19 = 2677, 79F19 = 2713, 7GC19 = 2843, 8EF19 = 3169, AIF19 = 3967, BFF19 = 4271, BFH19 = 4273, BGE19 = 4289, CGF19 = 4651, 125B19 = 7687, 127919 = 7723, 137E19 = 8089, 143H19 = 8377, 144819 = 8387, 15I719 = 9013, 169719 = 9203, 16FD19 = 9323, 17G719 = 9697, 18GG19 = 10067, 197I19 = 10259, 1AE419 = 10739, 1B6519 = 10949, 1BA719 = 11027, 1C3919 = 11257, 1C3D19 = 11261, 1CEA19 = 11467, 1EC819 = 12149, 1FD619 = 12527, 1G5919 = 12739, 1GDH19 = 12899, 1GHF19 = 12973, 1IF719 = 13649, 1IGI19 = 13679, 24A919 = 15361, 252819 = 15569, 258819 = 15683, 275919 = 16349, 27AG19 = 16451, 293919 = 17033, 2A7619 = 17467, 2D5B19 = 18517, 2D5H19 = 18523, 2DDD19 = 18671, 2FF319 = 19421, 2GEH19 = 19777, 2HB719 = 20071, 2I4519 = 20297, 2I6319 = 20333, 2IBG19 = 20441, 2IDG19 = 20479, 337A19 = 21803, 343F19 = 22093, 34EG19 = 22303, 354B19 = 22469, 355619 = 22483, 36FD19 = 23041, 36H519 = 23071, 385719 = 23567, 38G419 = 23773, 38I619 = 23813, 3A7H19 = 24337, 3AEG19 = 24469, 3B7G19 = 24697, 3B8919 = 24709, 3BHI19 = 24889, 3C3D19 = 24979, 3D5819 = 25373, 3E8I19 = 25801, 3EI819 = 25981, 44CF19 = 29123, 44DA19 = 29137, 457919 = 29383, 46GB19 = 29917, 476C19 = 30089, 47I819 = 30313, 4A5A19 = 31151, 4ADE19 = 31307, 4B8E19 = 31573, 4BD919 = 31663, 4BF719 = 31699, 4C6919 = 31891, 4D8G19 = 32297, 4E8519 = 32647, 4EBI19 = 32717, 4EG719 = 32801, 4F6I19 = 32983, 4F8A19 = 33013, 4FAC19 = 33053, 4GE919 = 33487, 4GIF19 = 33569, 4IAH19 = 34141, 557819 = 36241, 559619 = 36277, 55BA19 = 36319, 55D619 = 36353, 58DB19 = 37441, 59C919 = 37781, 5AF719 = 38197, 5EII19 = 39709, 5FCF19 = 39953, 5H7C19 = 40577, 69EE19 = 44683, 6A8B19 = 44927, 6BEC19 = 45403, 6DHH19 = 46187, 6FEI19 = 46853, 6GAH19 = 47137, 7A7B19 = 51767, 7CIA19 = 52697, 7E8C19 = 53231, 7EGA19 = 53381, 8EBE19 = 60149, 8EEH19 = 60209, 9EDB19 = 67043, 9FEF19 = 67427, 9GII19 = 67867, 9HHI19 = 68209, 9IFH19 = 68531, AAEF19 = 72481, AAFI19 = 72503, ADCI19 = 73529, AEGD19 = 73961, BEII19 = 80863, CHIE19 = 88801, DEHH19 = 94561, 123I719 = 145471, 15A1I19 = 168263, 15I8519 = 171271, 16AAG19 = 175291, 16F3419 = 176951, 1A84619 = 201881, 1A96F19 = 202289, 1B6FA19 = 208231, 1C6D919 = 215051, 1CE7D19 = 217829, 1CGA419 = 218599, 1DHC619 = 225859, 1F33F19 = 234361, 1HHFF19 = 253361, 1I7F819 = 256603, 22A5619 = 278071, 23F7419 = 286771, 23G7919 = 287137, 2579619 = 297641, 2CBEE19 = 347201, 2FFCB19 = 369181, 33AIF19 = 415507, 33D9D19 = 416417, 33DG619 = 416543, 33I6519 = 418157, 33I8919 = 418199, 35CG519 = 429899, 3648A19 = 433723, 368G819 = 435317, 379I619 = 442573, 37E7A19 = 444173, 38HCD19 = 452213, 3999519 = 456119, 3A7FC19 = 462377, 3BBB519 = 470597, 3BGF419 = 472477, 3E5HA19 = 489127, 3F9AG19 = 497303, 3H5GE19 = 509689, 46CHE19 = 567107, 48FHF19 = 581909, 48IAF19 = 582859, 4976F19 = 585671, 4DH7819 = 616729, 4E6AF19 = 619681, 4EB7519 = 621419, 4GB7F19 = 635147, 4HBBA19 = 642077, 4HH5C19 = 644131, 4HH9619 = 644201, 4I6BA19 = 647131, 55FGC19 = 691631, 55HI819 = 692387, 57B6619 = 703709, 58A9F19 = 710273, 5B6C919 = 729457, 5C5DE19 = 735979, 5H6EH19 = 770657, 5HBHF19 = 772517, 5HEC719 = 773497

20

220 = 2, 320 = 3, 520 = 5, 720 = 7, B20 = 11, D20 = 13, H20 = 17, J20 = 19, 1320 = 23, 1920 = 29, 3B20 = 71, 3D20 = 73, 3J20 = 79, 7B20 = 151, 7H20 = 157, 9B20 = 191, 9D20 = 193, 9H20 = 197, 9J20 = 199, BD20 = 233, DH20 = 277, HJ20 = 359, 11120 = 421, 33H20 = 1277, 3B920 = 1429, 3H920 = 1549, 77D20 = 2953, 111320 = 8423, 111920 = 8429, 119J20 = 8599, 11B720 = 8627, 13J720 = 9587, 177H20 = 10957, 19D320 = 11863, 19HJ20 = 11959, 1B1H20 = 12437, 1D3720 = 13267, 1H9320 = 14983, 339B20 = 25391, 33DB20 = 25471, 39HD20 = 27953, 3B7J20 = 28559, 3BD920 = 28669, 3HHD20 = 31153, 7HBB20 = 63031, BDHJ20 = 93559

 

Bibliografia

  • Gardner, Martin;  "Giochi matematici" in Le Scienze, Milano, n. 149, gennaio 1981, pag. 114 – 117.
  • Wells, David;  Prime Numbers, John Wiley & Sons, 2005 -

    Una miniera di informazioni sui numeri primi.

Contattami

Potete contattarmi al seguente indirizzo bitman[at]bitman.name per suggerimenti o segnalazioni d'errori relativi a questo articolo.