FANDOM


Primes: 2, 3, 5, 7, E, 11, 15, 17, 1E, 25, 27, 31, 35, 37, 3E, 45, 4E, 51, 57, 5E, 61, 67, 6E, 75, 81, 85, 87, 8E, 91, 95, X7, XE, E5, E7, 105, 107, 111, 117, 11E, 125, 12E, 131, 13E, 141, 145, 147, 157, 167, 16E, 171, 175, 17E, 181, 18E, 195, 19E, 1X5, 1X7, 1E1, 1E5, 1E7, 205, 217, 21E, 221, 225, 237, 241, 24E, 251, 255, 25E, 267, 271, 277, 27E, 285, 291, 295, 2X1, 2XE, 2E1, 2EE, 301, 307, 30E, 315, 321, 325, 327, 32E, 33E, 347, 34E, 357, 35E, 365, 375, 377, 391, 397, 3X5, 3XE, 3E5, 3E7, 401, 40E, 415, 41E, 421, 427, 431, 435, 437, 447, 455, 457, 45E, 465, 46E, 471, 481, 485, 48E, 497, 4X5, 4E1, 4EE, 507, 511, 517, 51E, 527, 531, 535, 541, 545, 557, 565, 575, 577, 585, 587, 58E, 591, 59E, 5E1, 5E5, 5E7, 5EE, 611, 615, 617, 61E, 637, 63E, 647, 655, 661, 665, 66E, 675, 687, 68E, 695, 69E, 6X7, 6E1, 701, 705, 70E, 711, 71E, 721, 727, 735, 737, 745, 747, 751, 767, 76E, 771, 775, 77E, 785, 791, 797, 7X1, 7EE, 801, 80E, 817, 825, 82E, 835, 841, 851, 855, 85E, 865, 867, 871, 881, 88E, 8X5, 8X7, 8XE, 8E5, 8E7, 901, 905, 907, 90E, 91E, 921, 927, 955, 95E, 965, 971, 987, 995, 9X7, 9XE, 9E1, 9E5, 9EE, X07, X0E, X11, X17, X27, X35, X37, X3E, X41, X45, X4E, X5E, X6E, X77, X87, X91, X95, X9E, XX7, XXE, XE7, XEE, E11, E15, E1E, E21, E25, E2E, E31, E37, E45, E61, E67, E6E, E71, E91, E95, E97, EX5, EE5, EE7, ... (except 2 and 3, all end with 1, 5, 7 or E (exactly 1 and the primes not divide 10))

Lucky numbers: 1, 3, 7, 9, 11, 13, 19, 21, 27, 29, 31, 37, 41, 43, 53, 57, 59, 61, 63, 67, 73, 79, 83, 89, 93, 97, X7, X9, E1, E3, E9, 107, 113, 117, 121, 123, 139, 141, 143, 149, 151, 157, 163, 167, 173, 177, 179, 181, 197, 199, 1X3, 1X9, 1E7, 1E9, 201, 209, 213, 217, 227, 229, 233, 237, 243, 251, 259, 261, 267, 281, 287, 289, 293, 2X1, 2X7, 2E1, 2E7, 2E9, 301, 317, 327, 337, 339, 343, 347, 349, 353, 367, 371, 373, 381, 387, 389, 391, 3X1, 3X7, 401, 403, 407, 413, 421, 431, 433, 437, 439, 447, 453, 457, 459, 463, 467, 481, 487, 491, 499, 4X3, 4E9, 503, 507, 509, 513, 517, 519, 521, 541, 549, 551, 557, 569, 571, 583, 587, 593, 5X1, 5E3, 603, 609, 617, 619, 627, 629, 633, 651, 653, 657, 659, 661, 679, 681, 693, 697, 699, 6X7, 6X9, 6E1, 701, 703, 711, 713, 719, 727, 729, 739, 741, 767, 771, 773, 779, 781, 783, 791, 797, 7E7, 803, 813, 823, 827, 831, 839, 841, 843, 849, 857, 867, 869, 879, 881, 883, 891, 893, 8X3, 8X9, 8E1, 8E7, 907, 911, 923, 929, 937, 951, 959, 961, 977, 979, 983, 989, 9X1, 9X3, 9E7, X01, X13, X17, X27, X29, X39, X43, X47, X49, X51, X53, X67, X79, X87, X89, XX3, XX7, XE3, XE7, E01, E03, E11, E13, E23, E47, E49, E51, E63, E67, E77, E91, E99, EX1, EX7, EE7, ... (all end with 1, 3, 7 or 9)

Squares: 0, 1, 4, 9, 14, 21, 30, 41, 54, 69, 84, X1, 100, 121, 144, 169, 194, 201, 230, 261, 294, 309, 344, 381, 400, ... (all end with squares (0, 1, 4, 9))

Cubes: 0, 1, 8, 23, 54, X5, 160, 247, 368, 509, 6E4, 92E, 1000, 1331, 1708, 1E53, 2454, 2X15, 3460, 3E77, 4768, 5439, 61E4, 705E, 8000, ... (can end with any digits except 2, 6, X)

Powers of 2: 1, 2, 4, 8, 14, 28, 54, X8, 194, 368, 714, 1228, 2454, 48X8, 9594, 16E68, 31E14, 63X28, 107854, 2134X8, 426994, 851768, 14X3314, 2986628, 5751054, ... (the first number with leading digit 9 is 2^12 = 9594, and the first number with leading digit E is 2^21 = E2X20X8, besides, final digits of these numbers are 1, 2, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, ..., the period is 2 for numbers >= 2^2 (=4))

Powers of 3: 1, 3, 9, 23, 69, 183, 509, 1323, 3969, E483, 2X209, 86623, 217669, 64X783, 1727E09, 497E923, 124EE369, 372E9X83, X98E5809, 2852X5023, 813873069, 203E199183, 60E9553509, 162E443X323, 468X10E6969, ...

Triangular numbers: 0, 1, 3, 6, X, 13, 19, 24, 30, 39, 47, 56, 66, 77, 89, X0, E4, 109, 123, 13X, 156, 173, 191, 1E0, 210, ...

Tetrahedral numbers: 0, 1, 4, X, 18, 2E, 48, 70, X0, 119, 164, 1EX, 264, 31E, 3X8, 488, 580, 689, 7E0, 92X, X84, 1037, 1208, 13E8, 1608, ...

Pronic numbers: 0, 2, 6, 10, 18, 26, 36, 48, 60, 76, 92, E0, 110, 132, 156, 180, 1X8, 216, 246, 278, 2E0, 326, 362, 3X0, 420, ...

Fibonacci numbers: 0, 1, 1, 2, 3, 5, 8, 11, 19, 2X, 47, 75, 100, 175, 275, 42X, 6X3, E11, 15E4, 2505, 3XE9, 6402, X2EE, 14701, 22X00, ... (final digits are 0, 1, 1, 2, 3, 5, 8, 1, 9, X, 7, 5, 0, 5, 5, X, 3, 1, 4, 5, 9, 2, E, 1, 0, 1, 1, 2, 3, 5, 8, 1, 9, X, 7, 5, 0, 5, 5, X, 3, 1, 4, 5, 9, 2, E, 1, ..., the period is 20)

Lucas numbers: 2, 1, 3, 4, 7, E, 16, 25, 3E, 64, X3, 147, 22X, 375, 5X3, 958, 133E, 2097, 3416, 54E1, 8907, 121E8, 1XE03, 310EE, 50002, ...

Pell numbers: 0, 1, 2, 5, 10, 25, 5X, 121, 2X0, 6X1, 1462, 33X5, 8030, 17445, 3X8EX, 94X41, 1X8580, 469981, E04102, 2275E85, 5434050, 10E22065, 2727815X, 63456361, 131E68860, ...

Perfect numbers: 6, 24, 354, 4854, E29E854, 17E8891054, 22777E33854, 1057E377XX9481E854, 65933E8691303X4485432649E134E87854, ... (for even perfect numbers, except 6 and 24, all end with 54, besides, except 6, 24 and 354, all end with 054 or 854) (if any odd perfect number exists, then it must end with 1, 09, 39, 69 or 99)

Narcissistic numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, X, E, 25, X5, 577, 668, X83, 14765, 938X4, 369862, X2394X, ...

Harshad numbers: 1, 2, 3, 4, 5, 6, 7, 8, 9, X, E, 10, 1X, 20, 29, 30, 38, 40, 47, 50, 56, 60, 65, 70, 74, 80, 83, 90, 92, X0, X1, E0, 100, 10X, 110, 115, 119, 120, 122, 128, 130, 134, 137, 146, 150, 153, 155, 164, 172, 173, 182, 191, 1X0, 1E0, 1EX, 200, 209, 20E, 210, 216, 218, 220, 223, 227, 22X, 236, 240, 244, 245, 249, 254, 260, 263, 268, 272, 281, 287, 290, 2X0, 2X6, 2XX, 300, 308, 30X, 310, 311, 314, 316, 317, 326, 330, 331, 335, 338, 344, 353, 360, 362, 366, 371, 380, 390, 394, 39X, 3E8, 3EE, 400, 407, 409, 416, 420, 423, 425, 434, 440, 443, 446, 452, 45X, 461, 470, 480, 483, 488, 48X, 4X8, 4E6, 500, 506, 508, 510, 515, 524, 533, 539, 542, 550, 551, 554, 560, 570, 576, 57X, 598, 5X0, 5XX, 5E3, 5E6, 600, 605, 607, 614, 620, 622, 623, 628, 630, 632, 641, 650, 660, 662, 669, 66X, 674, 688, 6X6, 700, 704, 706, 713, 722, 731, 740, 748, 750, 754, 75X, 770, 778, 794, 796, 799, 7E4, 800, 803, 805, 812, 816, 821, 830, 840, 846, 84X, 868, 880, 886, 8X1, 8X4, 8E4, 900, 902, 904, 911, 920, 926, 930, 933, 938, 93X, 958, 976, 988, 990, 993, 994, 9E2, X00, X01, X03, X10, X20, X2X, X36, X48, X50, X61, X66, X84, X85, XX0, XX2, XX8, E00, E02, E10, E14, E16, E1X, E38, E46, E56, E74, E77, E92, EE0, 1000, ...

Keith numbers: 11, 15, 1E, 22, 2X, 31, 33, 44, 49, 55, 62, 66, 77, 88, 93, 99, XX, EE, 125, 215, 24X, 405, 42X, 654, 80X, 8X3, X59, ...

Nontotient: 12, 22, 2X, 32, 42, 52, 58, 62, 64, 72, 76, 7X, 82, 96, 9X, X2, X4, E2, EX, 102, 108, 10X, 112, 122, 126, 132, 136, 138, 142, 14X, 152, 15X, 162, 172, 176, 178, 182, 184, 186, 188, 192, 196, 1X2, 1XX, 1E2, 1E8, 1EX, 202, 20X, 212, 214, 218, 222, 226, 22X, 232, 23X, 242, 244, 252, 256, 262, 264, 26X, 272, 274, 282, 286, 28X, 292, 296, 298, 29X, 2X2, 2X4, 2X6, 2E2, 2E6, 2E8, 302, 304, 312, 316, 31X, 322, 332, 334, 336, 342, 344, 348, 352, 354, 366, 36X, 370, 372, 37X, 382, 384, 386, 38X, 392, 398, 39X, 3X2, 3X6, 3E2, 3E8, 3EX, 402, 406, 412, 416, 418, 422, 424, 428, 42X, 432, 43X, 442, 444, 44X, 452, 458, 462, 466, 472, 476, 478, 47X, 482, 486, 488, 492, 49X, 4X2, 4X6, 4XX, 4E2, 4E6, 502, 504, 508, 50X, 512, 518, 522, 524, 528, 52X, 532, 536, 53X, 542, 546, 54X, 552, 558, 55X, 562, 566, 56X, 570, 572, 57X, 582, 588, 592, 596, 5X2, 5X4, 5X6, 5XX, 5E2, 602, 604, 606, 608, 60X, 612, 622, 624, 626, 62X, 632, 638, 642, 644, 64X, 652, 65X, 662, 666, 668, 670, 672, 676, 67X, 682, 684, 688, 692, 696, 6X2, 6X4, 6X8, 6XX, 6E2, 6E6, 6EX, 702, 706, 712, 716, 718, 722, 724, 72X, 732, 738, 73X, 742, 748, 74X, 752, 756, 758, 75X, 762, 764, 772, 776, 778, 782, 786, 78X, 792, 79X, 7X2, 7X4, 7X6, 7XX, 7E2, 7E6, 7E8, 802, 804, 806, 810, 812, 81X, 822, 826, 832, 836, 83X, 842, 844, 846, 848, 852, 856, 858, 862, 86X, 872, 876, 878, 87X, 882, 884, 886, 888, 892, 896, 898, 89X, 8X2, 8E2, 8EX, 902, 910, 912, 916, 922, 924, 92X, 932, 934, 936, 938, 93X, 942, 944, 946, 94X, 952, 956, 962, 966, 96X, 972, 976, 978, 97X, 982, 984, 98X, 992, 996, 998, 99X, 9X2, 9X4, 9E2, 9E6, X02, X04, X08, X12, X18, X1X, X22, X24, X2X, X32, X42, X46, X48, X52, X54, X56, X58, X62, X64, X66, X70, X72, X78, X7X, X82, X8X, X92, X96, X98, XX2, XX4, XE2, XE4, XE8, E02, E04, E06, E0X, E12, E16, E18, E22, E26, E32, E38, E3X, E42, E46, E4X, E52, E54, E56, E5X, E62, E72, E76, E7X, E82, E84, E86, E88, E8X, E92, E98, E9X, EX2, EX6, EXX, EE2, EEX, ... (most numbers end with 2 are nontotient)

Fermat primes: 3, 5, 15, 195, 31E15, ... (except 3, all end with 5)

Mersenne primes: 3, 7, 27, X7, 48X7, 63X27, 2134X7, 4EE2308X7, 1057E377E1343360X7, 79524577E0E577476E7X8EX27, 82521X179793278231206852X37X27, 2X695925806818735399X37X20X31E3534X7, ... (except 3, all end with 7)

Palindromic primes: 2, 3, 5, 7, E, 11, 111, 131, 141, 171, 181, 1E1, 535, 545, 565, 575, 585, 5E5, 727, 737, 747, 767, 797, E1E, E2E, E6E, 10301, 10401, 10601, 11111, 11411, 11511, 11811, 11911, 11X11, 11E11, 12421, 12X21, 12E21, 13631, 13831, 13931, 13X31, 13E31, 14041, 14X41, 15051, 15151, 15451, 16061, 16161, 17071, 17371, 17471, 17571, 17971, 17E71, 18381, 18681, 18881, 18X81, 18E81, 19191, 19491, 19591, 19891, 19991, 1X1X1, 1X3X1, 1X4X1, 1E0E1, 1E5E1, 50605, 50705, 50E05, 51715, 51915, 52125, 52225, 52425, 52925, 53135, 53435, 53735, 54245, 54645, 54745, 55855, 55E55, 56165, 56765, 56965, 57175, 57875, 58385, 58885, 58985, 59195, 59295, 59495, 59695, 59995, 59E95, 5X1X5, 5X4X5, 5X6X5, 5E2E5, 5E4E5, 5E7E5, 5E9E5, 70107, 70507, 70607, 70E07, 71317, 71X17, 71E17, 72027, 72127, 72227, 72627, 72827, 72E27, 73037, 73137, 73637, 73837, 74247, 74547, 74847, 75357, 75557, 75657, 75X57, 75E57, 76067, 76267, 76567, 77177, 77277, 77377, 77E77, 78087, 78187, 78587, 78787, 78887, 78E87, 79697, 79897, 7X1X7, 7X2X7, 7X7X7, 7E0E7, 7E1E7, 7E2E7, 7EEE7, E010E, E030E, E090E, E0X0E, E101E, E151E, E181E, E1E1E, E252E, E262E, E303E, E333E, E363E, E414E, E454E, E484E, E4X4E, E505E, E585E, E595E, E5X5E, E606E, E616E, E686E, E696E, E6E6E, E707E, E737E, E7X7E, E818E, E848E, E858E, E919E, E939E, EX6XE, EX9XE, EXXXE, EE1EE, EE9EE, ...

Palindromic squares: 0, 1, 4, 9, 121, 484, 10201, 12321, 14641, 16661, 16Ɛ61, 40804, 41414, 44944, ...

Permutable primes: 2, 3, 5, 7, E, 11, 15, 57, 5E, 111, 117, 11E, 5EEE, 11111, 1111111111111111111, ... (the smallest representative prime of the permutation set)

Circular primes: 2, 3, 5, 7, E, 11, 15, 57, 5E, 111, 117, 11E, 175, 1E7, 157E, 555E, 11111, 115E77, 1111111111111111111, ... (the smallest representative prime of the cycle)

Left-truncatable primes: 2, 3, 5, 7, E, 15, 17, 1E, 25, 27, 35, 37, 3E, 45, 4E, 57, 5E, 67, 6E, 75, 85, 87, 8E, 95, X7, XE, E5, E7, 117, 11E, 125, 13E, 145, 157, 167, 16E, 175, 18E, 195, 1X7, 1E5, 1E7, 217, 21E, 225, 237, 24E, 25E, 267, 285, 295, 2XE, 315, 325, 327, 33E, 34E, 357, 35E, 375, 3XE, 3E5, 3E7, 415, 41E, 427, 435, 437, 457, 45E, 46E, 485, 48E, 517, 51E, 527, 535, 545, 557, 575, 585, 587, 58E, 5E5, 5E7, 615, 617, 61E, 637, 63E, 66E, 675, 687, 68E, 695, 6X7, 71E, 727, 735, 737, 745, 767, 76E, 775, 785, 817, 825, 835, 85E, 867, 88E, 8X7, 8XE, 8E5, 8E7, 91E, 927, 95E, 987, 995, 9X7, 9XE, 9E5, X17, X27, X35, X37, X3E, X45, X4E, X5E, X6E, X87, X95, XX7, XXE, XE7, E15, E1E, E25, E37, E45, E67, E6E, E95, EE5, EE7, ...

Right-truncatable primes: 2, 3, 5, 7, E, 25, 27, 31, 35, 37, 3E, 51, 57, 5E, 75, E5, E7, 251, 255, 25E, 271, 277, 27E, 315, 357, 35E, 375, 377, 3E5, 3E7, 511, 517, 51E, 575, 577, 5E1, 5E5, 5E7, 5EE, 751, E71, 2555, 2557, 2715, 2717, 2771, 27E1, 27E7, 3155, 315E, 35E1, 35E7, 35EE, 3755, 375E, 3771, 377E, 3E51, 3E55, 3E75, 3E7E, 5117, 511E, 51E7, 575E, 5771, 5777, 577E, 5E17, 5E1E, 5E55, 5E75, 5EE1, 7511, E711, 25551, 25577, 27151, 27155, 2715E, 27E17, 27E77, 31551, 315E5, 375E5, 375EE, 37715, 3E515, 3E557, 3E55E, 3E7E5, 511E7, 51E71, 575EE, 57711, 57717, 577E7, 577EE, 5E175, 5E1E7, 5E55E, 5E751, 5EE17, 75111, 75115, E7111, E7115, 255515, 255775, 271555, 2715E1, 27E177, 27E17E, 27E771, 375E55, 375EE5, 377151, 3E5155, 3E5157, 3E515E, 3E5571, 3E557E, 3E55E7, 3E7E5E, 511E77, 51E717, 575EEE, 577117, 577175, 577E75, 5E55E1, 5E55EE, 5EE171, 751115, E71157, ...

Length of repunit primes: 2, 3, 5, 17, 81, 91, 225, 255, 4X5, 5777, 879E, 198Ɛ1, 23175, 311407, ...