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Completamente magnanimi (numeri)

Rappresentazione dei numeri 

Propongo di chiamare “completamente magnanimi” i numeri naturali tali che che inserendo un qualsiasi numero di segni “+” tra le cifre in qualsiasi posizione si ottengano sempre numeri primi. Per esempio, 4463 è competamente magnanimo, perché 446 + 3 = 449, 44 + 63 = 107, 44 + 6 + 3 = 53, 4 + 463 = 467, 4 + 46 + 3 = 53, 4 + 4 + 63 = 71 e 4 + 4 + 6 + 3 = 17 sono primi.

Il termine si giustifica col fatto che in letteratura questi numeri non hanno ancora un nome, mentre i numeri naturali tali che inserendo un segno “+” tra le cifre in qualsiasi posizione si ottengano sempre numeri primi si chiamano “magnanimi”.

 

La definizione si estende naturalmente a qualsiasi base, considerando le somme sempre nella stessa base; per esempio, 12537 è magnanimo, perché la somma 127 + 57 + 37 in base 7 fa 237 = 17, che è primo, e non 20.

 

Tutti i numeri completamente magnanimi in una base sono magnanimi nella stessa base; come questi ultimi, sono probabilmente in numero finito in ogni base.

 

In una base b pari un numero completamente magnanimo pari non può avere più di 2 cifre, perché tutte le cifre tranne l’ultima devono essere dispari e quindi almeno una somma terminerebbe con una cifra pari; l’unica eventuale eccezione è 110b, se 11b è primo, ossia se b è un primo meno 1.

 

Dato che in base 2 i numeri magnanimi hanno forme particolari, è facile dimostrare che nella stessa base i numeri completamente magnanimi sono solo 112 = 3, 1012 = 5, 1102 = 6, 10012 = 9, 11102 = 14.

 

In base 10 i numeri completamente magnanimi noti sono: 2, 3, 5, 7, 11, 12, 14, 16, 20, 21, 23, 25, 29, 30, 32, 34, 38, 41, 43, 47, 49, 50, 52, 56, 58, 61, 65, 67, 70, 74, 76, 83, 85, 89, 92, 94, 98, 101, 110, 203, 209, 221, 227, 229, 245, 265, 281, 401, 403, 407, 425, 443, 449, 467, 485, 601, 607, 625, 647, 661, 665, 667, 683, 803, 809, 821, 845, 863, 881, 1001, 2209, 2225, 4001, 4445, 4463, 4643, 6001, 6007, 6067, 6265, 6443, 6601, 6803, 8009, 8801, 40001, 60007, 68003, 80009.

Dal lavoro di Giovanni Resta (v. numeri magnanimi) si deduce che se ne esistono altri, sono maggiori di 1016.

 

La tabella seguente mostra i numeri completamente magnanimi fino a 1000 nelle basi fino a 20.

Base

Numeri completamente magnanimi

2

112 = 3, 1012 = 5, 1102 = 6, 10012 = 9

3

23 = 2, 113 = 4, 123 = 5, 203 = 6, 213 = 7, 1023 = 11, 1113 = 13, 1203 = 15, 2013 = 19, 2103 = 21, 10023 = 29, 10113 = 31, 11013 = 37, 11103 = 39, 20013 = 55, 100023 = 83, 100113 = 85, 101013 = 91, 110013 = 109, 1000023 = 245, 1000113 = 247, 1100013 = 325

4

24 = 2, 34 = 3, 114 = 5, 124 = 6, 204 = 8, 214 = 9, 234 = 11, 304 = 12, 324 = 14, 1014 = 17, 1104 = 20, 2034 = 35, 2214 = 41, 2234 = 43, 10014 = 65, 20234 = 139, 22034 = 163, 22214 = 169, 202034 = 547, 222234 = 683

5

25 = 2, 35 = 3, 115 = 6, 125 = 7, 145 = 9, 205 = 10, 215 = 11, 235 = 13, 305 = 15, 325 = 17, 345 = 19, 415 = 21, 435 = 23, 1025 = 27, 1115 = 31, 1205 = 35, 1335 = 43, 1425 = 47, 2015 = 51, 2035 = 53, 2105 = 55, 2215 = 61, 2305 = 65, 3025 = 77, 3045 = 79, 3135 = 83, 3205 = 85, 3315 = 91, 3405 = 95, 4035 = 103, 4125 = 107, 4305 = 115, 10335 = 143, 11105 = 155, 13035 = 203, 14025 = 227, 20035 = 253, 22015 = 301, 22345 = 319, 30045 = 379, 30135 = 383, 30315 = 391, 31035 = 403, 31305 = 415, 40035 = 503, 41025 = 527, 100335 = 643

6

26 = 2, 36 = 3, 56 = 5, 116 = 7, 126 = 8, 146 = 10, 206 = 12, 216 = 13, 236 = 15, 256 = 17, 306 = 18, 326 = 20, 346 = 22, 416 = 25, 436 = 27, 506 = 30, 526 = 32, 1016 = 37, 1106 = 42, 2016 = 73, 2056 = 77, 2236 = 87, 4436 = 171, 10016 = 217, 20016 = 433

7

27 = 2, 37 = 3, 57 = 5, 117 = 8, 127 = 9, 147 = 11, 167 = 13, 207 = 14, 217 = 15, 237 = 17, 257 = 19, 307 = 21, 327 = 23, 347 = 25, 417 = 29, 437 = 31, 507 = 35, 527 = 37, 567 = 41, 617 = 43, 657 = 47, 1047 = 53, 1067 = 55, 1137 = 59, 1157 = 61, 1227 = 65, 1247 = 67, 1317 = 71, 1407 = 77, 1427 = 79, 1517 = 85, 1557 = 89, 1607 = 91, 1647 = 95, 2037 = 101, 2057 = 103, 2127 = 107, 2147 = 109, 2217 = 113, 2237 = 115, 2307 = 119, 2367 = 125, 2417 = 127, 2507 = 133, 2547 = 137, 2637 = 143, 3027 = 149, 3117 = 155, 3207 = 161, 3267 = 167, 3357 = 173, 3467 = 181, 3537 = 185, 3557 = 187, 3627 = 191, 4017 = 197, 4037 = 199, 4107 = 203, 4127 = 205, 4217 = 211, 4367 = 223, 4457 = 229, 4547 = 235, 5027 = 247, 5067 = 251, 5117 = 253, 5157 = 257, 5207 = 259, 5247 = 263, 5337 = 269, 5357 = 271, 5447 = 277, 5517 = 281, 5537 = 283, 5607 = 287, 5667 = 293, 6017 = 295, 6057 = 299, 6107 = 301, 6147 = 305, 6237 = 311, 6327 = 317, 6507 = 329, 6567 = 335, 6657 = 341, 10047 = 347, 10137 = 353, 10227 = 359, 10317 = 365, 10557 = 383, 10647 = 389, 11037 = 395, 11127 = 401, 11147 = 403, 11307 = 413, 11417 = 421, 12047 = 445, 12137 = 451, 12407 = 469, 12537 = 479, 13017 = 491, 13457 = 523, 14027 = 541, 15057 = 593, 15147 = 599, 15237 = 605, 15507 = 623, 20037 = 689, 20057 = 691, 20127 = 695, 20217 = 701, 20237 = 703, 20367 = 713, 20417 = 715, 20547 = 725, 20637 = 731, 21027 = 737, 21117 = 743, 21227 = 751, 21407 = 763, 21537 = 773, 22017 = 785, 22107 = 791, 24017 = 883, 24567 = 923, 25047 = 935, 25137 = 941, 25317 = 953

8

28 = 2, 38 = 3, 58 = 5, 78 = 7, 118 = 9, 128 = 10, 148 = 12, 168 = 14, 208 = 16, 218 = 17, 238 = 19, 258 = 21, 308 = 24, 328 = 26, 348 = 28, 418 = 33, 438 = 35, 478 = 39, 508 = 40, 528 = 42, 568 = 46, 618 = 49, 658 = 53, 678 = 55, 708 = 56, 748 = 60, 768 = 62, 2018 = 129, 2038 = 131, 2218 = 145, 4458 = 293, 6058 = 389, 6658 = 437, 6678 = 439

9

29 = 2, 39 = 3, 59 = 5, 79 = 7, 119 = 10, 129 = 11, 149 = 13, 169 = 15, 209 = 18, 219 = 19, 239 = 21, 259 = 23, 309 = 27, 329 = 29, 349 = 31, 389 = 35, 419 = 37, 439 = 39, 479 = 43, 509 = 45, 529 = 47, 569 = 51, 589 = 53, 619 = 55, 659 = 59, 679 = 61, 709 = 63, 749 = 67, 769 = 69, 839 = 75, 859 = 77, 1029 = 83, 1049 = 85, 1119 = 91, 1139 = 93, 1209 = 99, 1319 = 109, 1409 = 117, 1469 = 123, 1649 = 139, 1739 = 147, 2019 = 163, 2059 = 167, 2109 = 171, 2239 = 183, 2329 = 191, 2389 = 197, 2509 = 207, 2569 = 213, 2659 = 221, 3029 = 245, 3049 = 247, 3119 = 253, 3229 = 263, 3289 = 269, 3319 = 271, 3379 = 277, 3559 = 293, 3649 = 301, 3779 = 313, 3889 = 323, 4019 = 325, 4079 = 331, 4109 = 333, 4169 = 339, 4439 = 363, 4619 = 379, 4709 = 387, 5029 = 407, 5089 = 413, 5209 = 423, 5269 = 429, 5359 = 437, 5539 = 453, 5629 = 461, 5689 = 467, 5869 = 483, 6059 = 491, 6079 = 493, 6149 = 499, 6259 = 509, 6349 = 517, 6419 = 523, 6529 = 533, 6589 = 539, 6619 = 541, 6679 = 547, 6859 = 563, 7049 = 571, 7139 = 579, 7379 = 601, 7409 = 603, 7739 = 633, 8389 = 683, 8569 = 699, 8659 = 707, 8839 = 723, 10029 = 731, 10119 = 739

10

2, 3, 5, 7, 11, 12, 14, 16, 20, 21, 23, 25, 29, 30, 32, 34, 38, 41, 43, 47, 49, 50, 52, 56, 58, 61, 65, 67, 70, 74, 76, 83, 85, 89, 92, 94, 98, 101, 110, 203, 209, 221, 227, 229, 245, 265, 281, 401, 403, 407, 425, 443, 449, 467, 485, 601, 607, 625, 647, 661, 665, 667, 683, 803, 809, 821, 845, 863, 881

11

211 = 2, 311 = 3, 511 = 5, 711 = 7, 1111 = 12, 1211 = 13, 1411 = 15, 1611 = 17, 1A11 = 21, 2011 = 22, 2111 = 23, 2311 = 25, 2511 = 27, 2911 = 31, 3011 = 33, 3211 = 35, 3411 = 37, 3811 = 41, 3A11 = 43, 4111 = 45, 4311 = 47, 4711 = 51, 4911 = 53, 5011 = 55, 5211 = 57, 5611 = 61, 5811 = 63, 6111 = 67, 6511 = 71, 6711 = 73, 7011 = 77, 7411 = 81, 7611 = 83, 7A11 = 87, 8311 = 91, 8511 = 93, 8911 = 97, 9211 = 101, 9411 = 103, 9811 = 107, 9A11 = 109, A111 = 111, A311 = 113, A711 = 117, A911 = 119, 10211 = 123, 10611 = 127, 11111 = 133, 11511 = 137, 12011 = 143, 13311 = 157, 13911 = 163, 14211 = 167, 14811 = 173, 16011 = 187, 16611 = 193, 17511 = 203, 19311 = 223, 19911 = 229, 1A211 = 233, 20111 = 243, 20911 = 251, 21011 = 253, 22711 = 271, 23611 = 281, 25411 = 301, 25A11 = 307, 26311 = 311, 28711 = 337, 29011 = 341, 29611 = 347, 30411 = 367, 30811 = 371, 30A11 = 373, 31311 = 377, 31911 = 383, 32611 = 391, 33111 = 397, 33511 = 401, 33711 = 403, 34011 = 407, 34611 = 413, 35311 = 421, 35911 = 427, 36211 = 431, 36411 = 433, 37311 = 443, 38611 = 457, 39111 = 463, 39511 = 467, 3A011 = 473, 40311 = 487, 40911 = 493, 41211 = 497, 41811 = 503, 43011 = 517, 43611 = 523, 44511 = 533, 46311 = 553, 46911 = 559, 47211 = 563, 47811 = 569, 49011 = 583, 49611 = 589, 50611 = 611, 52411 = 631, 52A11 = 637, 53311 = 641, 53911 = 647, 55111 = 661, 55711 = 667, 56011 = 671, 58411 = 697, 58A11 = 703, 59311 = 707, 59911 = 713, 60111 = 727, 60511 = 731, 60711 = 733, 61011 = 737, 61611 = 743, 62311 = 751, 63211 = 761, 63411 = 763, 64311 = 773, 64911 = 779, 65011 = 781, 66111 = 793, 66711 = 799, 67011 = 803, 67611 = 809, 68911 = 823, 69411 = 829, 69811 = 833, 70611 = 853, 71511 = 863, 73311 = 883, 74211 = 893, 74811 = 899, 76011 = 913, 76611 = 919, 77511 = 929, 79311 = 949, 80911 = 977, 82711 = 997

12

212 = 2, 312 = 3, 512 = 5, 712 = 7, B12 = 11, 1112 = 13, 1212 = 14, 1412 = 16, 1612 = 18, 1A12 = 22, 2012 = 24, 2112 = 25, 2312 = 27, 2512 = 29, 2912 = 33, 2B12 = 35, 3012 = 36, 3212 = 38, 3412 = 40, 3812 = 44, 3A12 = 46, 4112 = 49, 4312 = 51, 4712 = 55, 4912 = 57, 5012 = 60, 5212 = 62, 5612 = 66, 5812 = 68, 6112 = 73, 6512 = 77, 6712 = 79, 6B12 = 83, 7012 = 84, 7412 = 88, 7612 = 90, 7A12 = 94, 8312 = 99, 8512 = 101, 8912 = 105, 8B12 = 107, 9212 = 110, 9412 = 112, 9812 = 116, 9A12 = 118, A112 = 121, A312 = 123, A712 = 127, A912 = 129, B012 = 132, B212 = 134, B612 = 138, B812 = 140, 10112 = 145, 11012 = 156, 20512 = 293, 22312 = 315, 28912 = 393, 44912 = 633, 46712 = 655, 4A312 = 699, 60112 = 865, 60712 = 871, 60B12 = 875, 64712 = 919, 66112 = 937, 66512 = 941, 66B12 = 947, 6A112 = 985

13

213 = 2, 313 = 3, 513 = 5, 713 = 7, B13 = 11, 1113 = 14, 1213 = 15, 1413 = 17, 1613 = 19, 1A13 = 23, 1C13 = 25, 2013 = 26, 2113 = 27, 2313 = 29, 2513 = 31, 2913 = 35, 2B13 = 37, 3013 = 39, 3213 = 41, 3413 = 43, 3813 = 47, 3A13 = 49, 4113 = 53, 4313 = 55, 4713 = 59, 4913 = 61, 5013 = 65, 5213 = 67, 5613 = 71, 5813 = 73, 5C13 = 77, 6113 = 79, 6513 = 83, 6713 = 85, 6B13 = 89, 7013 = 91, 7413 = 95, 7613 = 97, 7A13 = 101, 7C13 = 103, 8313 = 107, 8513 = 109, 8913 = 113, 8B13 = 115, 9213 = 119, 9413 = 121, 9813 = 125, 9A13 = 127, A113 = 131, A313 = 133, A713 = 137, A913 = 139, B013 = 143, B213 = 145, B613 = 149, B813 = 151, BC13 = 155, C113 = 157, C513 = 161, C713 = 163, CB13 = 167, 10413 = 173, 10613 = 175, 10A13 = 179, 11313 = 185, 11513 = 187, 11913 = 191, 12213 = 197, 12413 = 199, 13113 = 209, 13313 = 211, 13713 = 215, 14013 = 221, 14613 = 227, 15113 = 235, 15513 = 239, 16013 = 247, 16413 = 251, 16A13 = 257, 17913 = 269, 17B13 = 271, 18213 = 275, 18813 = 281, 19913 = 295, 1A013 = 299, 1A613 = 305, 1A813 = 307, 1B513 = 317, 1B713 = 319, 1C613 = 331, 20313 = 341, 20513 = 343, 20B13 = 349, 21213 = 353, 21413 = 355, 22113 = 365, 22313 = 367, 22913 = 373, 23013 = 377, 23213 = 379, 23C13 = 389, 24713 = 397, 25013 = 403, 25613 = 409, 25C13 = 415, 26913 = 425, 27413 = 433, 27813 = 437, 27A13 = 439, 28313 = 445, 28713 = 449, 29813 = 463, 29C13 = 467, 2A513 = 473, 2A713 = 475, 2B413 = 485, 2B613 = 487, 2C513 = 499, 2C913 = 503, 30213 = 509, 30413 = 511, 30813 = 515, 31113 = 521, 31313 = 523, 31713 = 527, 32013 = 533, 32213 = 535, 32C13 = 545, 33113 = 547, 33513 = 551, 33B13 = 557, 34413 = 563, 35313 = 575, 36213 = 587, 36813 = 593, 37713 = 605, 38013 = 611, 38613 = 617, 39B13 = 635, 3A413 = 641, 3B313 = 653, 3C813 = 671, 40113 = 677, 40713 = 683, 40913 = 685, 41013 = 689, 41613 = 695, 42713 = 709, 43413 = 719, 44313 = 731, 44513 = 733, 44B13 = 739, 45213 = 743, 45413 = 745, 45A13 = 751, 46113 = 755, 47213 = 769, 47813 = 775, 47C13 = 779, 48113 = 781, 49613 = 799, 49A13 = 803, 4A513 = 811, 4B413 = 823, 4C313 = 835, 4C713 = 839, 50213 = 847, 50613 = 851, 50813 = 853, 51113 = 859, 51513 = 863, 52013 = 871, 52613 = 877, 52C13 = 883, 53313 = 887, 54213 = 899, 54413 = 901, 54A13 = 907, 55113 = 911, 55313 = 913, 55913 = 919, 56013 = 923, 57113 = 937, 57713 = 943, 57B13 = 947, 58013 = 949, 59513 = 967, 59913 = 971, 5A413 = 979, 5B313 = 991

14

214 = 2, 314 = 3, 514 = 5, 714 = 7, B14 = 11, D14 = 13, 1114 = 15, 1214 = 16, 1414 = 18, 1614 = 20, 1A14 = 24, 1C14 = 26, 2014 = 28, 2114 = 29, 2314 = 31, 2514 = 33, 2914 = 37, 2B14 = 39, 3014 = 42, 3214 = 44, 3414 = 46, 3814 = 50, 3A14 = 52, 4114 = 57, 4314 = 59, 4714 = 63, 4914 = 65, 4D14 = 69, 5014 = 70, 5214 = 72, 5614 = 76, 5814 = 78, 5C14 = 82, 6114 = 85, 6514 = 89, 6714 = 91, 6B14 = 95, 6D14 = 97, 7014 = 98, 7414 = 102, 7614 = 104, 7A14 = 108, 7C14 = 110, 8314 = 115, 8514 = 117, 8914 = 121, 8B14 = 123, 9214 = 128, 9414 = 130, 9814 = 134, 9A14 = 136, A114 = 141, A314 = 143, A714 = 147, A914 = 149, AD14 = 153, B014 = 154, B214 = 156, B614 = 160, B814 = 162, BC14 = 166, C114 = 169, C514 = 173, C714 = 175, CB14 = 179, D014 = 182, D414 = 186, D614 = 188, DA14 = 192, 20114 = 393, 20314 = 395, 20914 = 401, 22114 = 421, 22714 = 427, 22D14 = 433, 26314 = 479, 2C314 = 563, 40314 = 787, 44B14 = 851, 46914 = 877, 4A514 = 929

15

215 = 2, 315 = 3, 515 = 5, 715 = 7, B15 = 11, D15 = 13, 1115 = 16, 1215 = 17, 1415 = 19, 1615 = 21, 1A15 = 25, 1C15 = 27, 2015 = 30, 2115 = 31, 2315 = 33, 2515 = 35, 2915 = 39, 2B15 = 41, 3015 = 45, 3215 = 47, 3415 = 49, 3815 = 53, 3A15 = 55, 3E15 = 59, 4115 = 61, 4315 = 63, 4715 = 67, 4915 = 69, 4D15 = 73, 5015 = 75, 5215 = 77, 5615 = 81, 5815 = 83, 5C15 = 87, 5E15 = 89, 6115 = 91, 6515 = 95, 6715 = 97, 6B15 = 101, 6D15 = 103, 7015 = 105, 7415 = 109, 7615 = 111, 7A15 = 115, 7C15 = 117, 8315 = 123, 8515 = 125, 8915 = 129, 8B15 = 131, 9215 = 137, 9415 = 139, 9815 = 143, 9A15 = 145, 9E15 = 149, A115 = 151, A315 = 153, A715 = 157, A915 = 159, AD15 = 163, B015 = 165, B215 = 167, B615 = 171, B815 = 173, BC15 = 177, C115 = 181, C515 = 185, C715 = 187, CB15 = 191, D015 = 195, D415 = 199, D615 = 201, DA15 = 205, E315 = 213, E515 = 215, E915 = 219, 10215 = 227, 10415 = 229, 11115 = 241, 11315 = 243, 12015 = 255, 13115 = 271, 13D15 = 283, 14015 = 285, 14C15 = 297, 16A15 = 325, 19D15 = 373, 1A615 = 381, 1AC15 = 387, 1CA15 = 415, 1D315 = 423, 20115 = 451, 20B15 = 461, 21015 = 465, 22915 = 489, 23E15 = 509, 25615 = 531, 25C15 = 537, 26515 = 545, 26B15 = 551, 28915 = 579, 29215 = 587, 2B015 = 615, 2B615 = 621, 30215 = 677, 30815 = 683, 30E15 = 689, 31115 = 691, 31D15 = 703, 32E15 = 719, 33515 = 725, 33B15 = 731, 33D15 = 733, 34415 = 739, 34A15 = 745, 35B15 = 761, 36815 = 773, 36A15 = 775, 37115 = 781, 38815 = 803, 3A415 = 829, 3B515 = 845, 3CE15 = 869, 3D115 = 871, 3DD15 = 883, 3EE15 = 899, 40115 = 901, 40715 = 907, 40D15 = 913, 41015 = 915, 41C15 = 927, 43415 = 949, 43A15 = 955, 44315 = 963, 44915 = 969, 46715 = 997

16

216 = 2, 316 = 3, 516 = 5, 716 = 7, B16 = 11, D16 = 13, 1116 = 17, 1216 = 18, 1416 = 20, 1616 = 22, 1A16 = 26, 1C16 = 28, 2016 = 32, 2116 = 33, 2316 = 35, 2516 = 37, 2916 = 41, 2B16 = 43, 2F16 = 47, 3016 = 48, 3216 = 50, 3416 = 52, 3816 = 56, 3A16 = 58, 3E16 = 62, 4116 = 65, 4316 = 67, 4716 = 71, 4916 = 73, 4D16 = 77, 4F16 = 79, 5016 = 80, 5216 = 82, 5616 = 86, 5816 = 88, 5C16 = 92, 5E16 = 94, 6116 = 97, 6516 = 101, 6716 = 103, 6B16 = 107, 6D16 = 109, 7016 = 112, 7416 = 116, 7616 = 118, 7A16 = 122, 7C16 = 124, 8316 = 131, 8516 = 133, 8916 = 137, 8B16 = 139, 8F16 = 143, 9216 = 146, 9416 = 148, 9816 = 152, 9A16 = 154, 9E16 = 158, A116 = 161, A316 = 163, A716 = 167, A916 = 169, AD16 = 173, B016 = 176, B216 = 178, B616 = 182, B816 = 184, BC16 = 188, C116 = 193, C516 = 197, C716 = 199, CB16 = 203, D016 = 208, D416 = 212, D616 = 214, DA16 = 218, E316 = 227, E516 = 229, E916 = 233, EF16 = 239, F216 = 242, F416 = 244, F816 = 248, FE16 = 254, 10116 = 257, 11016 = 272, 20516 = 517, 20916 = 521, 20B16 = 523, 20F16 = 527, 22316 = 547, 22716 = 551, 22916 = 553, 22D16 = 557, 24116 = 577, 24516 = 581, 24716 = 583, 26316 = 611, 26516 = 613, 26916 = 617, 26F16 = 623, 28116 = 641, 28716 = 647, 2A116 = 673, 2A516 = 677, 2AB16 = 683, 2C316 = 707, 2E116 = 737, 2E716 = 743, 2ED16 = 749, 2EF16 = 751

17

217 = 2, 317 = 3, 517 = 5, 717 = 7, B17 = 11, D17 = 13, 1117 = 18, 1217 = 19, 1417 = 21, 1617 = 23, 1A17 = 27, 1C17 = 29, 1G17 = 33, 2017 = 34, 2117 = 35, 2317 = 37, 2517 = 39, 2917 = 43, 2B17 = 45, 2F17 = 49, 3017 = 51, 3217 = 53, 3417 = 55, 3817 = 59, 3A17 = 61, 3E17 = 65, 3G17 = 67, 4117 = 69, 4317 = 71, 4717 = 75, 4917 = 77, 4D17 = 81, 4F17 = 83, 5017 = 85, 5217 = 87, 5617 = 91, 5817 = 93, 5C17 = 97, 5E17 = 99, 6117 = 103, 6517 = 107, 6717 = 109, 6B17 = 113, 6D17 = 115, 7017 = 119, 7417 = 123, 7617 = 125, 7A17 = 129, 7C17 = 131, 7G17 = 135, 8317 = 139, 8517 = 141, 8917 = 145, 8B17 = 147, 8F17 = 151, 9217 = 155, 9417 = 157, 9817 = 161, 9A17 = 163, 9E17 = 167, A117 = 171, A317 = 173, A717 = 177, A917 = 179, AD17 = 183, B017 = 187, B217 = 189, B617 = 193, B817 = 195, BC17 = 199, C117 = 205, C517 = 209, C717 = 211, CB17 = 215, D017 = 221, D417 = 225, D617 = 227, DA17 = 231, DG17 = 237, E317 = 241, E517 = 243, E917 = 247, EF17 = 253, F217 = 257, F417 = 259, F817 = 263, FE17 = 269, FG17 = 271, G117 = 273, G317 = 275, G717 = 279, GD17 = 285, GF17 = 287, 10217 = 291, 10617 = 295, 10C17 = 301, 11117 = 307, 11517 = 311, 11B17 = 317, 13917 = 349, 14217 = 359, 16017 = 391, 16617 = 397, 19317 = 445, 1A217 = 461, 1FF17 = 559, 20317 = 581, 20917 = 587, 22117 = 613, 22717 = 619, 23017 = 629, 23617 = 635, 26317 = 683, 28117 = 715, 2FC17 = 845, 30217 = 869, 30817 = 875, 30A17 = 877, 30G17 = 883, 31917 = 893, 32017 = 901, 32617 = 907, 33517 = 923, 33717 = 925, 33D17 = 931, 34C17 = 947, 35F17 = 967, 36217 = 971, 36417 = 973, 37917 = 995

18

218 = 2, 318 = 3, 518 = 5, 718 = 7, B18 = 11, D18 = 13, H18 = 17, 1118 = 19, 1218 = 20, 1418 = 22, 1618 = 24, 1A18 = 28, 1C18 = 30, 1G18 = 34, 2018 = 36, 2118 = 37, 2318 = 39, 2518 = 41, 2918 = 45, 2B18 = 47, 2F18 = 51, 2H18 = 53, 3018 = 54, 3218 = 56, 3418 = 58, 3818 = 62, 3A18 = 64, 3E18 = 68, 3G18 = 70, 4118 = 73, 4318 = 75, 4718 = 79, 4918 = 81, 4D18 = 85, 4F18 = 87, 5018 = 90, 5218 = 92, 5618 = 96, 5818 = 98, 5C18 = 102, 5E18 = 104, 6118 = 109, 6518 = 113, 6718 = 115, 6B18 = 119, 6D18 = 121, 6H18 = 125, 7018 = 126, 7418 = 130, 7618 = 132, 7A18 = 136, 7C18 = 138, 7G18 = 142, 8318 = 147, 8518 = 149, 8918 = 153, 8B18 = 155, 8F18 = 159, 9218 = 164, 9418 = 166, 9818 = 170, 9A18 = 172, 9E18 = 176, A118 = 181, A318 = 183, A718 = 187, A918 = 189, AD18 = 193, B018 = 198, B218 = 200, B618 = 204, B818 = 206, BC18 = 210, C118 = 217, C518 = 221, C718 = 223, CB18 = 227, CH18 = 233, D018 = 234, D418 = 238, D618 = 240, DA18 = 244, DG18 = 250, E318 = 255, E518 = 257, E918 = 261, EF18 = 267, EH18 = 269, F218 = 272, F418 = 274, F818 = 278, FE18 = 284, FG18 = 286, G118 = 289, G318 = 291, G718 = 295, GD18 = 301, GF18 = 303, H018 = 306, H218 = 308, H618 = 312, HC18 = 318, HE18 = 320, 10118 = 325, 11018 = 342, 20118 = 649, 20518 = 653, 20B18 = 659, 20H18 = 665, 22318 = 687, 22918 = 693, 22F18 = 699, 28318 = 795, 2C518 = 869, 2E318 = 903

19

219 = 2, 319 = 3, 519 = 5, 719 = 7, B19 = 11, D19 = 13, H19 = 17, 1119 = 20, 1219 = 21, 1419 = 23, 1619 = 25, 1A19 = 29, 1C19 = 31, 1G19 = 35, 1I19 = 37, 2019 = 38, 2119 = 39, 2319 = 41, 2519 = 43, 2919 = 47, 2B19 = 49, 2F19 = 53, 2H19 = 55, 3019 = 57, 3219 = 59, 3419 = 61, 3819 = 65, 3A19 = 67, 3E19 = 71, 3G19 = 73, 4119 = 77, 4319 = 79, 4719 = 83, 4919 = 85, 4D19 = 89, 4F19 = 91, 5019 = 95, 5219 = 97, 5619 = 101, 5819 = 103, 5C19 = 107, 5E19 = 109, 5I19 = 113, 6119 = 115, 6519 = 119, 6719 = 121, 6B19 = 125, 6D19 = 127, 6H19 = 131, 7019 = 133, 7419 = 137, 7619 = 139, 7A19 = 143, 7C19 = 145, 7G19 = 149, 8319 = 155, 8519 = 157, 8919 = 161, 8B19 = 163, 8F19 = 167, 9219 = 173, 9419 = 175, 9819 = 179, 9A19 = 181, 9E19 = 185, A119 = 191, A319 = 193, A719 = 197, A919 = 199, AD19 = 203, B019 = 209, B219 = 211, B619 = 215, B819 = 217, BC19 = 221, BI19 = 227, C119 = 229, C519 = 233, C719 = 235, CB19 = 239, CH19 = 245, D019 = 247, D419 = 251, D619 = 253, DA19 = 257, DG19 = 263, DI19 = 265, E319 = 269, E519 = 271, E919 = 275, EF19 = 281, EH19 = 283, F219 = 287, F419 = 289, F819 = 293, FE19 = 299, FG19 = 301, G119 = 305, G319 = 307, G719 = 311, GD19 = 317, GF19 = 319, H019 = 323, H219 = 325, H619 = 329, HC19 = 335, HE19 = 337, I119 = 343, I519 = 347, IB19 = 353, ID19 = 355, 10419 = 365, 10A19 = 371, 10C19 = 373, 10I19 = 379, 11319 = 383, 11919 = 389, 11B19 = 391, 11H19 = 397, 12219 = 401, 12819 = 407, 13119 = 419, 13919 = 427, 13F19 = 433, 14619 = 443, 15519 = 461, 15719 = 463, 15D19 = 469, 15H19 = 473, 16C19 = 487, 16G19 = 491, 17319 = 497, 17519 = 499, 17F19 = 509, 18419 = 517, 18A19 = 523, 18E19 = 527, 19119 = 533, 19919 = 541, 1A019 = 551, 1A219 = 553, 1A819 = 559, 1B119 = 571, 1BH19 = 587, 1C019 = 589, 1CA19 = 599, 1D919 = 617, 1DF19 = 623, 1E419 = 631, 1EE19 = 641, 1F719 = 653, 1G219 = 667, 1G619 = 671, 1GC19 = 677, 1I419 = 707, 1IA19 = 713, 20319 = 725, 20519 = 727, 20919 = 731, 20F19 = 737, 21219 = 743, 21819 = 749, 22119 = 761, 22319 = 763, 22719 = 767, 22D19 = 773, 23019 = 779, 23219 = 781, 23C19 = 791, 24119 = 799, 24519 = 803, 24B19 = 809, 25019 = 817, 25419 = 821, 25A19 = 827, 25G19 = 833, 26F19 = 851, 27219 = 857, 27E19 = 869, 28D19 = 887, 29019 = 893, 29619 = 899, 2A519 = 917, 2BI19 = 949, 2C319 = 953, 2C919 = 959, 2D219 = 971, 2D819 = 977, 2E119 = 989

20

220 = 2, 320 = 3, 520 = 5, 720 = 7, B20 = 11, D20 = 13, H20 = 17, J20 = 19, 1120 = 21, 1220 = 22, 1420 = 24, 1620 = 26, 1A20 = 30, 1C20 = 32, 1G20 = 36, 1I20 = 38, 2020 = 40, 2120 = 41, 2320 = 43, 2520 = 45, 2920 = 49, 2B20 = 51, 2F20 = 55, 2H20 = 57, 3020 = 60, 3220 = 62, 3420 = 64, 3820 = 68, 3A20 = 70, 3E20 = 74, 3G20 = 76, 4120 = 81, 4320 = 83, 4720 = 87, 4920 = 89, 4D20 = 93, 4F20 = 95, 4J20 = 99, 5020 = 100, 5220 = 102, 5620 = 106, 5820 = 108, 5C20 = 112, 5E20 = 114, 5I20 = 118, 6120 = 121, 6520 = 125, 6720 = 127, 6B20 = 131, 6D20 = 133, 6H20 = 137, 7020 = 140, 7420 = 144, 7620 = 146, 7A20 = 150, 7C20 = 152, 7G20 = 156, 8320 = 163, 8520 = 165, 8920 = 169, 8B20 = 171, 8F20 = 175, 9220 = 182, 9420 = 184, 9820 = 188, 9A20 = 190, 9E20 = 194, A120 = 201, A320 = 203, A720 = 207, A920 = 209, AD20 = 213, AJ20 = 219, B020 = 220, B220 = 222, B620 = 226, B820 = 228, BC20 = 232, BI20 = 238, C120 = 241, C520 = 245, C720 = 247, CB20 = 251, CH20 = 257, CJ20 = 259, D020 = 260, D420 = 264, D620 = 266, DA20 = 270, DG20 = 276, DI20 = 278, E320 = 283, E520 = 285, E920 = 289, EF20 = 295, EH20 = 297, F220 = 302, F420 = 304, F820 = 308, FE20 = 314, FG20 = 316, G120 = 321, G320 = 323, G720 = 327, GD20 = 333, GF20 = 335, H020 = 340, H220 = 342, H620 = 346, HC20 = 352, HE20 = 354, I120 = 361, I520 = 365, IB20 = 371, ID20 = 373, IJ20 = 379, J020 = 380, J420 = 384, JA20 = 390, JC20 = 392, JI20 = 398, 20120 = 801, 20320 = 803, 22120 = 841, 22J20 = 859, 26F20 = 935, 28J20 = 979

 

Alcuni Autori considerano tra i possibili modi di inserire il segno “+” anche quello di non inserirne alcuno, limitando di fatto la definizione ai soli numeri primi, che potremmo quindi chiamare “primi completamente magnanimi”.

 

La tabella seguente mostra i primi completamente magnanimi fino a 109 nelle basi fino a 20 (M. Fiorentini, 2017).

Base

Primi completamente magnanimi

2

112 = 3, 1012 = 5

3

23 = 2, 123 = 5, 213 = 7, 1023 = 11, 1113 = 13, 2013 = 19, 10023 = 29, 10113 = 31, 11013 = 37, 100023 = 83, 110013 = 109

4

24 = 2, 34 = 3, 114 = 5, 234 = 11, 1014 = 17, 2214 = 41, 2234 = 43, 20234 = 139, 22034 = 163, 202034 = 547, 222234 = 683, 2222214 = 2729

5

25 = 2, 35 = 3, 125 = 7, 215 = 11, 235 = 13, 325 = 17, 345 = 19, 435 = 23, 1115 = 31, 1335 = 43, 1425 = 47, 2035 = 53, 2215 = 61, 3045 = 79, 3135 = 83, 4035 = 103, 4125 = 107, 14025 = 227, 30045 = 379, 30135 = 383, 40035 = 503, 100335 = 643, 300045 = 1879, 400035 = 2503, 1003035 = 3203, 4000035 = 12503

6

26 = 2, 36 = 3, 56 = 5, 116 = 7, 216 = 13, 256 = 17, 1016 = 37, 2016 = 73, 20016 = 433, 200016 = 2593

7

27 = 2, 37 = 3, 57 = 5, 147 = 11, 167 = 13, 237 = 17, 257 = 19, 327 = 23, 417 = 29, 437 = 31, 527 = 37, 567 = 41, 617 = 43, 657 = 47, 1047 = 53, 1137 = 59, 1157 = 61, 1247 = 67, 1317 = 71, 1427 = 79, 1557 = 89, 2037 = 101, 2057 = 103, 2127 = 107, 2147 = 109, 2217 = 113, 2417 = 127, 2547 = 137, 3027 = 149, 3267 = 167, 3357 = 173, 3467 = 181, 3627 = 191, 4017 = 197, 4037 = 199, 4217 = 211, 4367 = 223, 4457 = 229, 5067 = 251, 5157 = 257, 5247 = 263, 5337 = 269, 5357 = 271, 5447 = 277, 5517 = 281, 5537 = 283, 5667 = 293, 6237 = 311, 6327 = 317, 10047 = 347, 10137 = 353, 10227 = 359, 10557 = 383, 10647 = 389, 11127 = 401, 11417 = 421, 12537 = 479, 13017 = 491, 13457 = 523, 14027 = 541, 15057 = 593, 15147 = 599, 20057 = 691, 20217 = 701, 21117 = 743, 21227 = 751, 21537 = 773, 24017 = 883, 25137 = 941, 25317 = 953, 30027 = 1031, 30557 = 1069, 32517 = 1163, 33237 = 1193, 34157 = 1237, 40017 = 1373, 40127 = 1381, 42017 = 1471, 43157 = 1531, 43427 = 1549, 44147 = 1579, 44417 = 1597, 44547 = 1607, 45267 = 1637, 50067 = 1721, 50247 = 1733, 51657 = 1811, 52137 = 1823, 52467 = 1847, 53057 = 1867, 53217 = 1877, 54317 = 1933, 56247 = 2027, 61647 = 2153, 100137 = 2411, 100317 = 2423, 100557 = 2441, 105237 = 2663, 106227 = 2711, 150237 = 4133, 200417 = 4831, 201537 = 4889, 210627 = 5189, 215037 = 5393, 341057 = 8629, 355557 = 9203, 452067 = 11423, 500067 = 12011, 500517 = 12041, 501657 = 12101, 502047 = 12107, 521037 = 12743, 616137 = 15053, 5000247 = 84053

8

28 = 2, 38 = 3, 58 = 5, 78 = 7, 218 = 17, 238 = 19, 658 = 53, 2038 = 131, 4458 = 293, 6058 = 389, 6678 = 439, 66078 = 3463

9

29 = 2, 39 = 3, 59 = 5, 79 = 7, 129 = 11, 149 = 13, 219 = 19, 259 = 23, 329 = 29, 349 = 31, 419 = 37, 479 = 43, 529 = 47, 589 = 53, 659 = 59, 679 = 61, 749 = 67, 1029 = 83, 1319 = 109, 1649 = 139, 2019 = 163, 2059 = 167, 2329 = 191, 2389 = 197, 3229 = 263, 3289 = 269, 3319 = 271, 3379 = 277, 3559 = 293, 3779 = 313, 4079 = 331, 4619 = 379, 5629 = 461, 5689 = 467, 6059 = 491, 6149 = 499, 6259 = 509, 6419 = 523, 6619 = 541, 6679 = 547, 6859 = 563, 7049 = 571, 7379 = 601, 8389 = 683, 10119 = 739, 20019 = 1459, 20329 = 1487, 20389 = 1493, 23359 = 1733, 32029 = 2351, 32089 = 2357, 32359 = 2381, 36379 = 2707, 53389 = 3923, 53659 = 3947, 56089 = 4139, 60859 = 4451, 70049 = 5107, 73679 = 5407, 80389 = 5867, 83629 = 6131, 203359 = 13397, 333379 = 22147, 536329 = 35507, 836029 = 55163

10

2, 3, 5, 7, 11, 23, 29, 41, 43, 47, 61, 67, 83, 89, 101, 227, 229, 281, 401, 443, 449, 467, 601, 607, 647, 661, 683, 809, 821, 863, 881, 4001, 4463, 4643, 6007, 6067, 6803, 8009

11

211 = 2, 311 = 3, 511 = 5, 711 = 7, 1211 = 13, 1611 = 17, 2111 = 23, 2911 = 31, 3411 = 37, 3811 = 41, 3A11 = 43, 4311 = 47, 4911 = 53, 5611 = 61, 6111 = 67, 6511 = 71, 6711 = 73, 7611 = 83, 8911 = 97, 9211 = 101, 9411 = 103, 9811 = 107, 9A11 = 109, A311 = 113, 10611 = 127, 11511 = 137, 13311 = 157, 13911 = 163, 14211 = 167, 14811 = 173, 16611 = 193, 19311 = 223, 19911 = 229, 1A211 = 233, 20911 = 251, 22711 = 271, 23611 = 281, 25A11 = 307, 26311 = 311, 28711 = 337, 29611 = 347, 30411 = 367, 30A11 = 373, 31911 = 383, 33111 = 397, 33511 = 401, 35311 = 421, 36211 = 431, 36411 = 433, 37311 = 443, 38611 = 457, 39111 = 463, 39511 = 467, 40311 = 487, 41811 = 503, 43611 = 523, 47211 = 563, 47811 = 569, 52411 = 631, 53311 = 641, 53911 = 647, 55111 = 661, 60111 = 727, 60711 = 733, 61611 = 743, 62311 = 751, 63211 = 761, 64311 = 773, 67611 = 809, 68911 = 823, 69411 = 829, 70611 = 853, 71511 = 863, 73311 = 883, 76611 = 919, 77511 = 929, 80911 = 977, 82711 = 997, 85A11 = 1033, 88711 = 1063, 90211 = 1091, 90411 = 1093, 90811 = 1097, 91311 = 1103, 91911 = 1109, 92611 = 1117, 93111 = 1123, 95911 = 1153, 96811 = 1163, 99511 = 1193, A0311 = 1213, A1211 = 1223, 103311 = 1367, 113211 = 1487, 130311 = 1697, 160611 = 2063, 190311 = 2423, 1A0211 = 2543, 200911 = 2671, 209611 = 2767, 233311 = 3061, 253711 = 3307, 256A11 = 3343, 280711 = 3637, 296611 = 3823, 300A11 = 4003, 301311 = 4007, 301911 = 4013, 303111 = 4027, 307311 = 4073, 313611 = 4153, 325711 = 4297, 328411 = 4327, 329311 = 4337, 330111 = 4357, 333211 = 4391, 352111 = 4621, 355A11 = 4663, 356911 = 4673, 360411 = 4723, 361311 = 4733, 380611 = 4967, 382411 = 4987, 383911 = 5003, 385711 = 5023, 390511 = 5087, 392311 = 5107, 413511 = 5483, 430611 = 5693, 470211 = 6173, 586A11 = 7699, 600711 = 7993, 606711 = 8059, 607611 = 8069, 609811 = 8093, 620311 = 8231, 638611 = 8443, 670611 = 8839, 680911 = 8963, 686911 = 9029, 688111 = 9043, 700611 = 9323, 709311 = 9419, 713211 = 9473, 770511 = 10169, 800911 = 10657, 803611 = 10687, 806911 = 10723, 809611 = 10753, 836611 = 11083, 900211 = 11981, 900811 = 11987, 902611 = 12007, 905311 = 12037, 905911 = 12043, 908611 = 12073, 910911 = 12109, 914511 = 12149, 920611 = 12227, 925111 = 12277, 930111 = 12343, 956311 = 12653, 960811 = 12713, A00311 = 13313, 1A00211 = 27953, 2009611 = 29387, 2800711 = 39937, 3000A11 = 43933, 3001911 = 43943, 3070311 = 44773, 3600411 = 51913, 3800611 = 54577, 3902311 = 55927, 4300611 = 62563, 4700211 = 67883, 5609311 = 81293, 6000711 = 87853, 6200311 = 90511, 7003311 = 102523, 8360611 = 121853, 9000211 = 131771, 9000811 = 131777, 9002611 = 131797, 9200611 = 134437, 30000A11 = 483163, 30007311 = 483233, 43000611 = 688133, 60000711 = 966313

12

212 = 2, 312 = 3, 512 = 5, 712 = 7, B12 = 11, 1112 = 13, 2512 = 29, 6112 = 73, 6712 = 79, 6B12 = 83, 8512 = 101, 8B12 = 107, A712 = 127, 20512 = 293, 64712 = 919, 66112 = 937, 66512 = 941, 66B12 = 947, 80B12 = 1163, A0712 = 1447, 200512 = 3461, 660B12 = 11243

13

213 = 2, 313 = 3, 513 = 5, 713 = 7, B13 = 11, 1413 = 17, 1613 = 19, 1A13 = 23, 2313 = 29, 2513 = 31, 2B13 = 37, 3213 = 41, 3413 = 43, 3813 = 47, 4113 = 53, 4713 = 59, 4913 = 61, 5213 = 67, 5613 = 71, 5813 = 73, 6113 = 79, 6513 = 83, 6B13 = 89, 7613 = 97, 7A13 = 101, 7C13 = 103, 8313 = 107, 8513 = 109, 8913 = 113, 9A13 = 127, A113 = 131, A713 = 137, A913 = 139, B613 = 149, B813 = 151, C113 = 157, C713 = 163, CB13 = 167, 10413 = 173, 10A13 = 179, 11913 = 191, 12213 = 197, 12413 = 199, 13313 = 211, 14613 = 227, 15513 = 239, 16413 = 251, 16A13 = 257, 17913 = 269, 17B13 = 271, 18813 = 281, 1A813 = 307, 1B513 = 317, 1C613 = 331, 20B13 = 349, 21213 = 353, 22313 = 367, 22913 = 373, 23213 = 379, 23C13 = 389, 24713 = 397, 25613 = 409, 27413 = 433, 27A13 = 439, 28713 = 449, 29813 = 463, 29C13 = 467, 2B613 = 487, 2C513 = 499, 2C913 = 503, 30213 = 509, 31113 = 521, 31313 = 523, 33113 = 547, 33B13 = 557, 34413 = 563, 36213 = 587, 36813 = 593, 38613 = 617, 3A413 = 641, 3B313 = 653, 40113 = 677, 40713 = 683, 42713 = 709, 43413 = 719, 44513 = 733, 44B13 = 739, 45213 = 743, 45A13 = 751, 47213 = 769, 4A513 = 811, 4B413 = 823, 4C713 = 839, 50813 = 853, 51113 = 859, 51513 = 863, 52613 = 877, 52C13 = 883, 53313 = 887, 54A13 = 907, 55113 = 911, 55913 = 919, 57113 = 937, 57B13 = 947, 59513 = 967, 59913 = 971, 5B313 = 991, 5CC13 = 1013, 60513 = 1019, 61413 = 1031, 62913 = 1049, 63813 = 1061, 66513 = 1097, 67413 = 1109, 6CB13 = 1181, 70A13 = 1193, 72413 = 1213, 72813 = 1217, 73713 = 1229, 74213 = 1237, 75113 = 1249, 75B13 = 1259, 77313 = 1277, 77513 = 1279, 77913 = 1283, 78213 = 1289, 79313 = 1303, 79713 = 1307, 7B113 = 1327, 80913 = 1361, 81213 = 1367, 81813 = 1373, 82313 = 1381, 86313 = 1433, 90A13 = 1531, 91913 = 1543, 92C13 = 1559, 93B13 = 1571, 94613 = 1579, 94A13 = 1583, 97713 = 1619, 9AC13 = 1663, A0713 = 1697, A0913 = 1699, A1613 = 1709, A2513 = 1721, A2713 = 1723, A3413 = 1733, A4513 = 1747, A5413 = 1759, A7213 = 1783, AAB13 = 1831, B0813 = 1867, B1513 = 1877, B1713 = 1879, B2413 = 1889, B3313 = 1901, B7113 = 1951, B9B13 = 1987, BAA13 = 1999, BB913 = 2011, C0113 = 2029, C0B13 = 2039, C2913 = 2063, C4313 = 2083, C4713 = 2087, C5613 = 2099, C7A13 = 2129, C9813 = 2153, 100A13 = 2207, 101313 = 2213, 103113 = 2237, 103713 = 2243, 105513 = 2267, 114513 = 2423, 11A713 = 2503, 121113 = 2549, 129713 = 2659, 12B513 = 2683, 131213 = 2719, 140613 = 2879, 145113 = 2939, 153213 = 3083, 170913 = 3389, 172713 = 3413, 179213 = 3499, 180813 = 3557, 1A4413 = 3943, 1B1413 = 4073, 206913 = 4481, 217913 = 4663, 225413 = 4801, 227813 = 4831, 238413 = 5009, 242513 = 5101, 275913 = 5651, 290813 = 5923, 297513 = 6011, 2C5413 = 6491, 2C7813 = 6521, 307713 = 6689, 308613 = 6701, 310113 = 6761, 330B13 = 7109, 33A113 = 7229, 343113 = 7307, 354B13 = 7499, 359613 = 7559, 360213 = 7607, 363513 = 7649, 36BB13 = 7759, 380613 = 7949, 388C13 = 8059, 401613 = 8807, 405A13 = 8863, 406113 = 8867, 407813 = 8887, 420713 = 9133, 424313 = 9181, 425C13 = 9203, 450A13 = 9643, 4A6B13 = 10567, 4B0413 = 10651, 4B1313 = 10663, 4C5213 = 10883, 500813 = 10993, 504A13 = 11047, 505913 = 11059, 507713 = 11083, 507B13 = 11087, 50A413 = 11119, 50B313 = 11131, 510513 = 11159, 511413 = 11171, 520613 = 11329, 522413 = 11353, 527913 = 11423, 529713 = 11447, 52B113 = 11467, 52C413 = 11483, 542C13 = 11699, 544613 = 11719, 545513 = 11731, 550913 = 11839, 552713 = 11863, 554513 = 11887, 557C13 = 11933, 56C613 = 12161, 572913 = 12203, 577413 = 12263, 577A13 = 12269, 590513 = 12511, 592713 = 12539, 5ACA13 = 12841, 5C2A13 = 13049, 5C7513 = 13109, 600513 = 13187, 630813 = 13697, 64AB13 = 13999, 670413 = 14369, 701913 = 15401, 706413 = 15461, 723513 = 15761, 725913 = 15791, 72C813 = 15881, 757413 = 16319, 76C413 = 16553, 775413 = 16631, 777813 = 16661, 790313 = 16903, 792513 = 16931, 7B0113 = 17239, 802713 = 17609, 807213 = 17669, 810213 = 17747, 817113 = 17837, 862113 = 18617, 907313 = 19867, 90BB13 = 19927, 911813 = 19963, 920C13 = 20123, 925713 = 20183, 929313 = 20231, 933813 = 20327, 944613 = 20507, 955A13 = 20693, 975213 = 21023, 9A1B13 = 21487, A00713 = 21977, A01813 = 21991, A02713 = 22003, A03413 = 22013, A05413 = 22039, A07213 = 22063, A07C13 = 22073, A0A913 = 22109, A0C713 = 22133, A11513 = 22157, A1A813 = 22277, A1B913 = 22291, A23213 = 22349, A27A13 = 22409, A2C513 = 22469, A30413 = 22481, A36C13 = 22567, A40513 = 22651, A4A713 = 22783, A6B413 = 23131, AA4713 = 23719, AA6513 = 23743, AC3C13 = 24049, B04413 = 24223, B20413 = 24509, B30313 = 24677, B64A13 = 25243, B9A113 = 25819, BA3713 = 25903, C02913 = 26399, C07413 = 26459, C20913 = 26711, C27813 = 26801, C2C313 = 26861, C40313 = 27043, C52413 = 27239, C72813 = 27581, C95313 = 27953, 1000A13 = 28571, 1004613 = 28619, 1005513 = 28631, 1290713 = 34483, 1701813 = 43961, 2527713 = 68543, 3307413 = 92369, 3308313 = 92381, 3600213 = 98867, 3630513 = 99377, 4005A13 = 114319, 4010613 = 114419, 4050A13 = 115099, 4505513 = 125299, 5002613 = 142837, 5007113 = 142897, 5007B13 = 142907, 5027913 = 143243, 5045513 = 143551, 5100513 = 145007, 5450513 = 152443, 5557713 = 154733, 5715B13 = 158429, 7572213 = 212123, 90B0B13 = 258919, A001613 = 285629, A022513 = 285979, A400513 = 294403, B040413 = 314851, B200413 = 318569, C072213 = 343943, 10000A13 = 371303

14

214 = 2, 314 = 3, 514 = 5, 714 = 7, B14 = 11, D14 = 13, 2114 = 29, 2314 = 31, 2914 = 37, 4314 = 59, 6514 = 89, 6D14 = 97, A914 = 149, C514 = 173, CB14 = 179, 20914 = 401, 22114 = 421, 22D14 = 433, 26314 = 479, 2C314 = 563, 40314 = 787, 46914 = 877, 4A514 = 929, 60514 = 1181, 68914 = 1297, 6A314 = 1319, C0514 = 2357, C2314 = 2383, C6514 = 2441, C8314 = 2467, 400314 = 10979, 680914 = 18041, 80C314 = 22123, C00514 = 32933, C22114 = 33349, C80314 = 34499,

15

215 = 2, 315 = 3, 515 = 5, 715 = 7, B15 = 11, D15 = 13, 1215 = 17, 1415 = 19, 2115 = 31, 2B15 = 41, 3215 = 47, 3815 = 53, 3E15 = 59, 4115 = 61, 4715 = 67, 4D15 = 73, 5815 = 83, 5E15 = 89, 6715 = 97, 6B15 = 101, 6D15 = 103, 7415 = 109, 8B15 = 131, 9215 = 137, 9415 = 139, 9E15 = 149, A115 = 151, A715 = 157, AD15 = 163, B215 = 167, B815 = 173, C115 = 181, CB15 = 191, D415 = 199, 10215 = 227, 10415 = 229, 11115 = 241, 13115 = 271, 13D15 = 283, 19D15 = 373, 20B15 = 461, 23E15 = 509, 29215 = 587, 30215 = 677, 30815 = 683, 31115 = 691, 32E15 = 719, 33D15 = 733, 34415 = 739, 35B15 = 761, 36815 = 773, 3A415 = 829, 3DD15 = 883, 40715 = 907, 46715 = 997, 4C715 = 1087, 53B15 = 1181, 56215 = 1217, 56815 = 1223, 5CE15 = 1319, 60B15 = 1361, 64D15 = 1423, 65215 = 1427, 65815 = 1433, 66715 = 1447, 66B15 = 1451, 69815 = 1493, 70415 = 1579, 73115 = 1621, 80B15 = 1811, 90215 = 2027, 90415 = 2029, 90E15 = 2039, 91D15 = 2053, 9A415 = 2179, 9C215 = 2207, 9E815 = 2243, A0115 = 2251, A6115 = 2341, A6715 = 2347, A9415 = 2389, B0215 = 2477, C0B15 = 2711, C4715 = 2767, C5E15 = 2789, C6B15 = 2801, C9215 = 2837, CA115 = 2851, CC715 = 2887, D3115 = 2971, DC415 = 3109, E3E15 = 3209, E9E15 = 3299, 101115 = 3391, 103D15 = 3433, 130115 = 4051, 190D15 = 5413, 200B15 = 6761, 233B15 = 7481, 300815 = 10133, 301115 = 10141, 302E15 = 10169, 305B15 = 10211, 308815 = 10253, 320E15 = 10589, 323B15 = 10631, 335815 = 10883, 359E15 = 11399, 360815 = 11483, 600B15 = 20261, 604D15 = 20323, 609815 = 20393, 60CB15 = 20441, 640D15 = 21163, 660B15 = 21611, 669215 = 21737, 690815 = 22283, 700415 = 23629, 703115 = 23671, 800B15 = 27011, 900E15 = 30389, 901D15 = 30403, 90C215 = 30557, 916715 = 30697, 935E15 = 31139, 99B815 = 32573, 9E0815 = 33533, A00115 = 33751, A60715 = 35107, C09215 = 40637, C53B15 = 41681, CC0715 = 43207, E03E15 = 47309, 1003D15 = 50683, 1900D15 = 81013, 3000815 = 151883, 3004415 = 151939, 6900815 = 334133, 7003115 = 354421, 8000B15 = 405011, 90C0215 = 458327, A000115 = 506251, C090215 = 609527, C0C5E15 = 610289, CC00715 = 648007

16

216 = 2, 316 = 3, 516 = 5, 716 = 7, B16 = 11, D16 = 13, 1116 = 17, 2516 = 37, 2916 = 41, 2B16 = 43, 2F16 = 47, 4316 = 67, 4716 = 71, 4916 = 73, 4F16 = 79, 6116 = 97, 6516 = 101, 6716 = 103, 6B16 = 107, 6D16 = 109, 8316 = 131, 8916 = 137, 8B16 = 139, A316 = 163, A716 = 167, AD16 = 173, C116 = 193, C516 = 197, C716 = 199, E316 = 227, E516 = 229, E916 = 233, EF16 = 239, 10116 = 257, 20916 = 521, 20B16 = 523, 22316 = 547, 22D16 = 557, 24116 = 577, 26516 = 613, 26916 = 617, 28116 = 641, 28716 = 647, 2A116 = 673, 2A516 = 677, 2AB16 = 683, 2E716 = 743, 2EF16 = 751, 40716 = 1031, 40916 = 1033, 40F16 = 1039, 42516 = 1061, 42716 = 1063, 44316 = 1091, 44516 = 1093, 44F16 = 1103, 46316 = 1123, 46916 = 1129, 4A916 = 1193, 4E116 = 1249, 4EB16 = 1259, 60716 = 1543, 60D16 = 1549, 62316 = 1571, 62F16 = 1583, 64116 = 1601, 64916 = 1609, 64D16 = 1613, 66516 = 1637, 68316 = 1667, 68516 = 1669, 6A116 = 1697, 82116 = 2081, 82716 = 2087, 88316 = 2179, 8AD16 = 2221, 8CB16 = 2251, 8E916 = 2281, A2116 = 2593, A4916 = 2633, A6116 = 2657, A6716 = 2663, A8B16 = 2699, AA916 = 2729, AAB16 = 2731, AE516 = 2789, AE716 = 2791, C0716 = 3079, C6116 = 3169, CC716 = 3271, CE516 = 3301, E0916 = 3593, E2116 = 3617, E2716 = 3623, E2F16 = 3631, E4B16 = 3659, E8716 = 3719, EED16 = 3821, 202716 = 8231, 202916 = 8233, 204716 = 8263, 206316 = 8291, 20A116 = 8353, 20EF16 = 8431, 222116 = 8737, 224F16 = 8783, 226716 = 8807, 228516 = 8837, 22A316 = 8867, 22E516 = 8933, 22ED16 = 8941, 244D16 = 9293, 260516 = 9733, 268116 = 9857, 2E0716 = 11783, 2E2516 = 11813, 2EEB16 = 12011, 402516 = 16421, 404316 = 16451, 408716 = 16519, 420516 = 16901, 420716 = 16903, 426116 = 16993, 442316 = 17443, 44A516 = 17573, 460316 = 17923, 460916 = 17929, 464516 = 17989, 468116 = 18049, 608516 = 24709, 624B16 = 25163, 62A516 = 25253, 640116 = 25601, 640916 = 25609, 644916 = 25673, 64A316 = 25763, 808D16 = 32909, 80E716 = 32999, 822516 = 33317, 826116 = 33377, 84E316 = 34019, 8EAF16 = 36527, A04F16 = 41039, A0E516 = 41189, A24D16 = 41549, A80B16 = 43019, ACAF16 = 44207, AE4D16 = 44621, AE6B16 = 44651, AEE316 = 44771, C22F16 = 49711, C28916 = 49801, C2E316 = 49891, CEED16 = 52973, E02716 = 57383, E04516 = 57413, E22D16 = 57901, E24316 = 57923, E40B16 = 58379, E6AB16 = 59051, E80716 = 59399, EA2F16 = 59951, EE4916 = 61001, EEA316 = 61091, 200EF16 = 131311, 2040716 = 132103, 2282F16 = 141359, 4040316 = 263171, 4202316 = 270371, 4E0EF16 = 319727, 666EF16 = 419567, A04E116 = 656609, A800B16 = 688139, CEE0D16 = 847373, E40E916 = 934121, EA04D16 = 958541, EEA0316 = 977411, 2008E716 = 2099431, A8000B16 = 11010059

17

217 = 2, 317 = 3, 517 = 5, 717 = 7, B17 = 11, D17 = 13, 1217 = 19, 1617 = 23, 1C17 = 29, 2317 = 37, 2917 = 43, 3217 = 53, 3817 = 59, 3A17 = 61, 3G17 = 67, 4317 = 71, 4F17 = 83, 5C17 = 97, 6117 = 103, 6517 = 107, 6717 = 109, 6B17 = 113, 7C17 = 131, 8317 = 139, 8F17 = 151, 9417 = 157, 9A17 = 163, 9E17 = 167, A317 = 173, A917 = 179, B617 = 193, BC17 = 199, C717 = 211, D617 = 227, E317 = 241, F217 = 257, F817 = 263, FE17 = 269, FG17 = 271, 11117 = 307, 11517 = 311, 11B17 = 317, 13917 = 349, 14217 = 359, 16617 = 397, 1A217 = 461, 20917 = 587, 22117 = 613, 22717 = 619, 26317 = 683, 30A17 = 877, 30G17 = 883, 32617 = 907, 34C17 = 947, 35F17 = 967, 36217 = 971, 39117 = 1021, 39B17 = 1031, 3B917 = 1063, 3CG17 = 1087, 3D317 = 1091, 3DF17 = 1103, 40F17 = 1171, 47817 = 1283, 53F17 = 1511, 55D17 = 1543, 56617 = 1553, 58G17 = 1597, 59917 = 1607, 59F17 = 1613, 5F917 = 1709, 60717 = 1741, 63217 = 1787, 63417 = 1789, 6CD17 = 1951, 6FA17 = 1999, 73917 = 2083, 74817 = 2099, 79317 = 2179, 7FF17 = 2293, 7GE17 = 2309, 82117 = 2347, 89C17 = 2477, 8B417 = 2503, 91317 = 2621, 93717 = 2659, 93B17 = 2663, 98C17 = 2749, 9B317 = 2791, 9F517 = 2861, A1217 = 2909, A4517 = 2963, A7217 = 3011, ACF17 = 3109, AD817 = 3119, B0C17 = 3191, B5717 = 3271, B8417 = 3319, C4317 = 3539, C6D17 = 3583, C9G17 = 3637, CF417 = 3727, CFA17 = 3733, D3F17 = 3823, DC617 = 3967, DFF17 = 4027, E0317 = 4049, F0217 = 4337, F0E17 = 4349, F3517 = 4391, F5317 = 4423, F6A17 = 4447, F9517 = 4493, FAC17 = 4517, FCA17 = 4549, FF117 = 4591, FF717 = 4597, FFD17 = 4603, G9C17 = 4789, 160617 = 6653, 206317 = 9931, 303717 = 14797, 307917 = 14867, 308C17 = 14887, 340C17 = 15907, 4FC617 = 24197, 530F17 = 25447, 580G17 = 26893, 5F0917 = 28909, 730917 = 35267, 820117 = 39883, 8B0417 = 42487, 909B17 = 44381, 94CC17 = 45589, 9AC617 = 47317, A40517 = 50291, C60D17 = 60703, C94C17 = 61637, DF0F17 = 68219, F00E17 = 73709, F30517 = 74567, FA0C17 = 76597, FC9117 = 77317, 5300F17 = 432359, 700FF17 = 584917, FA00C17 = 1301957

18

218 = 2, 318 = 3, 518 = 5, 718 = 7, B18 = 11, D18 = 13, H18 = 17, 1118 = 19, 2118 = 37, 2518 = 41, 2B18 = 47, 2H18 = 53, 4118 = 73, 4718 = 79, 6118 = 109, 6518 = 113, 8518 = 149, A118 = 181, AD18 = 193, C718 = 223, CB18 = 227, CH18 = 233, E518 = 257, EH18 = 269, 20518 = 653, 20B18 = 659, 40118 = 1297, 40718 = 1303, 60518 = 1949, 64118 = 2017, 66H18 = 2069, 6AD18 = 2137, A0D18 = 3253, A6D18 = 3361, AC118 = 3457, AC718 = 3463, C2518 = 3929, C6B18 = 4007, C8H18 = 4049, 6C2H18 = 38933, A0C118 = 58537

19

219 = 2, 319 = 3, 519 = 5, 719 = 7, B19 = 11, D19 = 13, H19 = 17, 1419 = 23, 1A19 = 29, 1C19 = 31, 1I19 = 37, 2319 = 41, 2519 = 43, 2919 = 47, 2F19 = 53, 3219 = 59, 3419 = 61, 3A19 = 67, 3E19 = 71, 3G19 = 73, 4319 = 79, 4719 = 83, 4D19 = 89, 5219 = 97, 5619 = 101, 5819 = 103, 5C19 = 107, 5E19 = 109, 5I19 = 113, 6D19 = 127, 6H19 = 131, 7419 = 137, 7619 = 139, 7G19 = 149, 8519 = 157, 8B19 = 163, 8F19 = 167, 9219 = 173, 9819 = 179, 9A19 = 181, A119 = 191, A319 = 193, A719 = 197, A919 = 199, B219 = 211, BI19 = 227, C119 = 229, C519 = 233, CB19 = 239, D419 = 251, DA19 = 257, DG19 = 263, E319 = 269, E519 = 271, EF19 = 281, EH19 = 283, F819 = 293, G319 = 307, G719 = 311, GD19 = 317, HE19 = 337, I519 = 347, IB19 = 353, 10C19 = 373, 10I19 = 379, 11319 = 383, 11919 = 389, 11H19 = 397, 12219 = 401, 13119 = 419, 13F19 = 433, 14619 = 443, 15519 = 461, 15719 = 463, 16C19 = 487, 16G19 = 491, 17519 = 499, 17F19 = 509, 18A19 = 523, 19919 = 541, 1B119 = 571, 1BH19 = 587, 1CA19 = 599, 1D919 = 617, 1E419 = 631, 1EE19 = 641, 1F719 = 653, 1GC19 = 677, 20519 = 727, 21219 = 743, 22119 = 761, 22D19 = 773, 24B19 = 809, 25419 = 821, 25A19 = 827, 27219 = 857, 28D19 = 887, 2C319 = 953, 2D219 = 971, 2D819 = 977, 2F619 = 1013, 2G519 = 1031, 30419 = 1087, 30A19 = 1093, 30E19 = 1097, 31119 = 1103, 31F19 = 1117, 32219 = 1123, 33B19 = 1151, 33D19 = 1153, 35919 = 1187, 38219 = 1237, 39519 = 1259, 3A419 = 1277, 3A619 = 1279, 3BF19 = 1307, 3EC19 = 1361, 3I819 = 1433, 40319 = 1447, 40719 = 1451, 42119 = 1483, 42519 = 1487, 42B19 = 1493, 43A19 = 1511, 44319 = 1523, 48H19 = 1613, 49419 = 1619, 4A319 = 1637, 4BE19 = 1667, 4BG19 = 1669, 4EB19 = 1721, 4ED19 = 1723, 4FI19 = 1747, 4HA19 = 1777, 50619 = 1811, 50I19 = 1823, 51719 = 1831, 52419 = 1847, 53519 = 1867, 53919 = 1871, 53B19 = 1873, 54819 = 1889, 55119 = 1901, 55719 = 1907, 55D19 = 1913, 56C19 = 1931, 57B19 = 1949, 59319 = 1979, 5A219 = 1997, 5A419 = 1999, 5C619 = 2039, 5G219 = 2111, 60D19 = 2179, 65819 = 2269, 65C19 = 2273, 66719 = 2287, 66H19 = 2297, 67A19 = 2309, 68F19 = 2333, 69419 = 2341, 69E19 = 2351, 6AF19 = 2371, 6BE19 = 2389, 6C519 = 2399, 6D419 = 2417, 6DA19 = 2423, 6E919 = 2441, 6G719 = 2477, 70419 = 2531, 70G19 = 2543, 71319 = 2549, 71519 = 2551, 72E19 = 2579, 75B19 = 2633, 76I19 = 2659, 77H19 = 2677, 78819 = 2687, 79F19 = 2713, 7AE19 = 2731, 7BD19 = 2749, 7D319 = 2777, 7DH19 = 2791, 7EA19 = 2803, 7H719 = 2857, 80F19 = 2903, 81A19 = 2917, 82D19 = 2939, 83819 = 2953, 83I19 = 2963, 86919 = 3011, 89219 = 3061, 8A119 = 3079, 8C319 = 3119, 8D219 = 3137, 8FE19 = 3187, 90219 = 3251, 90819 = 3257, 90A19 = 3259, 93719 = 3313, 93H19 = 3323, 94419 = 3329, 94I19 = 3343, 95319 = 3347, 98C19 = 3413, 99D19 = 3433, 9B919 = 3467, 9BB19 = 3469, 9DF19 = 3511, 9FD19 = 3547, 9G419 = 3557, 9I219 = 3593, A0319 = 3613, A0719 = 3617, A1219 = 3631, A1819 = 3637, A3419 = 3671, A3619 = 3673, A5419 = 3709, A6319 = 3727, A6F19 = 3739, A9C19 = 3793, AGH19 = 3931, AIF19 = 3967, B0I19 = 3989, B1H19 = 4007, B2I19 = 4027, B6E19 = 4099, B8A19 = 4133, B9B19 = 4153, BCI19 = 4217, BE419 = 4241, BE619 = 4243, BEG19 = 4253, BFF19 = 4271, BFH19 = 4273, BH319 = 4297, BIE19 = 4327, C0519 = 4337, C2319 = 4373, C3219 = 4391, C4119 = 4409, C6519 = 4451, CHI19 = 4673, D0A19 = 4703, D1919 = 4721, D2219 = 4733, D3119 = 4751, D5519 = 4793, D6A19 = 4817, D8G19 = 4861, D9719 = 4871, DD319 = 4943, DDB19 = 4951, DDH19 = 4957, DF919 = 4987, DFF19 = 4993, DGE19 = 5011, E0519 = 5059, E1419 = 5077, E1E19 = 5087, E2F19 = 5107, E3219 = 5113, E6B19 = 5179, E7A19 = 5197, E9619 = 5231, E9819 = 5233, EBG19 = 5279, ECF19 = 5297, ED219 = 5303, EE319 = 5323, EED19 = 5333, EFC19 = 5351, EHA19 = 5387, F1719 = 5441, F5H19 = 5527, F6219 = 5531, F7F19 = 5563, F8E19 = 5581, FAI19 = 5623, FBF19 = 5639, FBH19 = 5641, FCE19 = 5657, FEC19 = 5693, FFB19 = 5711, FFH19 = 5717, FHB19 = 5749, G0319 = 5779, G0719 = 5783, G1619 = 5801, G1C19 = 5807, G3A19 = 5843, G4919 = 5861, G6719 = 5897, GB219 = 5987, GDE19 = 6037, GFC19 = 6073, GGB19 = 6091, H0E19 = 6151, H6I19 = 6269, H7719 = 6277, H7H19 = 6287, HAG19 = 6343, HBD19 = 6359, HBF19 = 6361, HDD19 = 6397, HGA19 = 6451, HH919 = 6469, HHD19 = 6473, I1419 = 6521, I3819 = 6563, I4719 = 6581, I8319 = 6653, IAF19 = 6703, IFA19 = 6793, IH819 = 6829, 100C19 = 6871, 105D19 = 6967, 105H19 = 6971, 107519 = 6997, 109919 = 7039, 10B119 = 7069, 10DF19 = 7121, 10F719 = 7151, 110H19 = 7237, 111819 = 7247, 116F19 = 7349, 11C919 = 7457, 150519 = 8669, 165719 = 9127, 169319 = 9199, 16C419 = 9257, 175A19 = 9491, 1B0H19 = 10847, 1BFG19 = 11131, 1D1819 = 11579, 1ED119 = 12161, 1HG919 = 13309, 1HH819 = 13327, 1IH719 = 13687, 200519 = 13723, 202319 = 13759, 205G19 = 13829, 216E19 = 14207, 222B19 = 14489, 22C119 = 14669, 243819 = 15227, 247I19 = 15313, 24H819 = 15493, 250419 = 15527, 27H519 = 16573, 280D19 = 16619, 2C2119 = 18089, 2CFI19 = 18353, 2GDC19 = 19753, 2HDB19 = 20113, 2IF819 = 20509, 302C19 = 20627, 308219 = 20731, 308I19 = 20747, 309519 = 20753, 30A419 = 20771, 316919 = 21061, 333A19 = 21727, 33A119 = 21851, 33BC19 = 21881, 363H19 = 22817, 366E19 = 22871, 368C19 = 22907, 390519 = 23831, 3A3319 = 24247, 3BFE19 = 24847, 3IAC19 = 27277, 3IF719 = 27367, 41G819 = 28109, 435519 = 28619, 43E819 = 28793, 44FE19 = 29179, 44H619 = 29209, 46AB19 = 29803, 476E19 = 30091, 477D19 = 30109, 480H19 = 30341, 490419 = 30689, 4B6A19 = 31531, 4E6719 = 32611, 4EF819 = 32783, 4F0I19 = 32869, 4HB919 = 33791, 500619 = 34301, 500I19 = 34313, 502419 = 34337, 507B19 = 34439, 508A19 = 34457, 50F319 = 34583, 531A19 = 35407, 567519 = 36599, 570B19 = 36833, 590319 = 37547, 5A0219 = 37907, 5A3119 = 37963, 5BEB19 = 38543, 5BFA19 = 38561, 5CCI19 = 38873, 5DCH19 = 39233, 5FE719 = 39983, 5HH819 = 40763, 603A19 = 41221, 63E619 = 42509, 663E19 = 43391, 668919 = 43481, 670A19 = 43691, 683C19 = 44111, 6AAH19 = 44971, 6C5I19 = 45599, 6D1319 = 45869, 6DAE19 = 46051, 6DF919 = 46141, 6FAC19 = 46771, 700419 = 48017, 700G19 = 48029, 705B19 = 48119, 707H19 = 48163, 70F119 = 48299, 70FF19 = 48313, 721D19 = 48767, 74EG19 = 49739, 755619 = 49919, 756519 = 49937, 75HI19 = 50159, 76A819 = 50377, 777A19 = 50683, 780819 = 50909, 794B19 = 51349, 79D819 = 51517, 7A0E19 = 51637, 7C5H19 = 52457, 7D0319 = 52709, 7D1219 = 52727, 7DD419 = 52957, 7E2819 = 53113, 7F8H19 = 53597, 806F19 = 55001, 80C319 = 55103, 810A19 = 55243, 816419 = 55351, 81G419 = 55541, 836C19 = 56081, 867219 = 57173, 8D0219 = 59567, 8F7719 = 60427, 901119 = 61751, 90AC19 = 61933, 934D19 = 62903, 93B619 = 63029, 94H119 = 63499, 992B19 = 65029, A00719 = 68597, A01219 = 68611, A02519 = 68633, A04319 = 68669, A04H19 = 68683, A07E19 = 68737, A0E719 = 68863, A0IF19 = 68947, A16219 = 69067, A30419 = 69677, A6B419 = 70969, AAI519 = 72547, ADCC19 = 73523, B03F19 = 75521, B09919 = 75629, B0EG19 = 75731, B0HF19 = 75787, B1E319 = 76079, B1EF19 = 76091, B1HE19 = 76147, B4EC19 = 77171, B5FA19 = 77549, B7HI19 = 78317, B80A19 = 78347, B83719 = 78401, BB6F19 = 79549, BE1F19 = 80537, BE6A19 = 80627, BEF119 = 80789, BF2F19 = 80917, BFE119 = 81131, BIA419 = 82141, C02319 = 82349, C5HD19 = 84449, CC5I19 = 86753, CCAD19 = 86843, CCH619 = 86969, CF3H19 = 87797, CF7D19 = 87869, D02819 = 89213, D07319 = 89303, D0IC19 = 89521, D2FD19 = 90187, D4F519 = 90901, D50519 = 90977, D63719 = 91397, D82E19 = 92107, D89719 = 92233, DCAC19 = 93701, DCH519 = 93827, DD2F19 = 93913, DDA719 = 94057, DF0F19 = 94597, DFA519 = 94777, DG2C19 = 94993, E0CF19 = 96269, E0FC19 = 96323, E10E19 = 96401, E20F19 = 96763, E45I19 = 97583, E55H19 = 97943, E56G19 = 97961, E5F719 = 98123, E66F19 = 98321, E6BA19 = 98411, E6C919 = 98429, E70A19 = 98563, E77319 = 98689, EB5B19 = 100103, EE1C19 = 101111, EE5819 = 101183, EEEH19 = 101363, EEGF19 = 101399, EH7319 = 102299, EHGE19 = 102481, F0D919 = 103141, F0F719 = 103177, F0H919 = 103217, F2DD19 = 103867, F55G19 = 104801, F75A19 = 105517, F77I19 = 105563, FAD519 = 106747, FAG219 = 106801, FB0F19 = 106871, FB5A19 = 106961, FBE119 = 107123, FE0C19 = 107951, FE4819 = 108023, FE5719 = 108041, FF5619 = 108401, FF8919 = 108461, FFF219 = 108587, FGCI19 = 108907, FGFF19 = 108961, FH6519 = 109141, G00719 = 109751, G05219 = 109841, G06119 = 109859, G1GA19 = 110419, G34619 = 110909, G48119 = 111341, GB0219 = 113717, GD0E19 = 114451, GD2C19 = 114487, H04A19 = 116689, H0BF19 = 116827, H0I819 = 116953, H2F919 = 117619, H2I619 = 117673, H3I519 = 118033, H5H819 = 118739, H66E19 = 118897, H7C519 = 119363, H9HI19 = 120193, HA8I19 = 120383, HB0D19 = 120587, HB1E19 = 120607, HD0D19 = 121309, HH2B19 = 122789, I12219 = 123863, IAD219 = 127321, IGDC19 = 129497, IH0819 = 129607, 100B119 = 130531, 1016F19 = 130811, 10EBF19 = 135599, 1500519 = 164621, 1755519 = 180239, 2000519 = 260647, 2222919 = 275129, 2GD0C19 = 375091, 2HD0B19 = 381949, 30A0419 = 394577, 3308F19 = 411707, 4HB0919 = 641867, 5002419 = 651647, 5477I19 = 681719, 5A00219 = 720197, 5CCA819 = 738443, 6700A19 = 829949, 7000419 = 912251, 700D319 = 912497, 7070H19 = 914791, 707A719 = 914971, 7A00E19 = 980851, 8061E19 = 1044767, 8670219 = 1086251, B00EG19 = 1433813, B0H6919 = 1439791, BFE0119 = 1541471, E00HA19 = 1824827, E0F5719 = 1830011, E6C5419 = 1870079, F04E819 = 1956533, F05BA19 = 1956839, G000719 = 2085143, H0BB419 = 2219641, 20000519 = 4952203

20

220 = 2, 320 = 3, 520 = 5, 720 = 7, B20 = 11, D20 = 13, H20 = 17, J20 = 19, 2120 = 41, 2320 = 43, 4320 = 83, 4920 = 89, 6720 = 127, 6B20 = 131, 6H20 = 137, 8320 = 163, C120 = 241, CB20 = 251, CH20 = 257, E320 = 283, ID20 = 373, IJ20 = 379, 22J20 = 859, 2C920 = 1049, 40920 = 1609, 46320 = 1723, 60B20 = 2411, 60H20 = 2417, 66120 = 2521, 66B20 = 2531, 80320 = 3203, 82J20 = 3259, 88D20 = 3373, 8C920 = 3449, 8EJ20 = 3499, AAH20 = 4217, AGH20 = 4337, C0120 = 4801, C0H20 = 4817, C8920 = 4969, CCJ20 = 5059, CIB20 = 5171, E8J20 = 5779, I0D20 = 7213, I0J20 = 7219, I6D20 = 7333, ICB20 = 7451, IE920 = 7489, II120 = 7561, 400920 = 32009, 40I920 = 32369, 600H20 = 48017, 606B20 = 48131, 660B20 = 50411, 880D20 = 67213, A0I920 = 80369, AA0H20 = 84017, ACC920 = 85049, C00120 = 96001, C00H20 = 96017, C0CJ20 = 96259, CCA920 = 101009, I00D20 = 144013, I6A320 = 146603, II0120 = 151201, IIID20 = 151573, 4000920 = 640009, 6000H20 = 960017, 6006B20 = 960131, C000120 = 1920001, 40000920 = 12800009, 60006B20 = 19200131, 400000920 = 256000009

 

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