It is not possible to list either all composite or all prime numbers as there are an infinite amount of both.
See the related question for a list of primes. Any number over one that's not on the lists linked there are composites.
4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100, 102, 104, 105, 106, 108, 110, 111, 112, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 128, 129, 130, 132, 133, 134, 135, 136, 138, 140, 141, 142, 143, 144, 145, 146, 147, 148, 150, 152, 153, 154, 155, 156, 158, 159, 160, 161, 162, 164, 165, 166, 168, 169, 170, 171, 172, 174, 175, 176, 177, 178, 180, 182, 183, 184, 185, 186, 187, 188, 189, 190, 192, 194, 195, 196, 198, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 224, 225, 226, 228, 230, 231, 232, 234, 235, 236, 237, 238, 240, 242, 243, 244, 245, 246, 247, 248, 249, 250, 252, 253, 254, 255, 256, 258, 259, 260, 261, 262, 264, 265, 266, 267, 268, 270, 272, 273, 274, 275, 276, 278, 279, 280, 282, 284, 285, 286, 287, 288, 289, 290, 291, 292, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 308, 309, 310, 312, 314, 315, 316, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 330, 332, 333, 334, 335, 336, 338, 339, 340, 341, 342, 343, 344, 345, 346, 348, 350, 351, 352, 354, 355, 356, 357, 358, 360, 361, 362, 363, 364, 365, 366, 368, 369, 370, 371, 372, 374, 375, 376, 377, 378, 380, 381, 382, 384, 385, 386, 387, 388, 390, 391, 392, 393, 394, 395, 396, 398, 399, 400, 402, 403, 404, 405, 406, 407, 408, 410, 411, 412, 413, 414, 415, 416, 417, 418, 420, 422, 423, 424, 425, 426, 427, 428, 429, 430, 432, 434, 435, 436, 437, 438, 440, 441, 442, 444, 445, 446, 447, 448, 450, 451, 452, 453, 454, 455, 456, 458, 459, 460, 462, 464, 465, 466, 468, 469, 470, 471, 472, 473, 474, 475, 476, 477, 478, 480, 481, 482, 483, 484, 485, 486, 488, 489, 490, 492, 493, 494, 495, 496, 497, 498, 500, 501, 502, 504, 505, 506, 507, 508, 510, 511, 512, 513, 514, 515, 516, 517, 518, 519, 520, 522, 524, 525, 526, 527, 528, 529, 530, 531, 532, 533, 534, 535, 536, 537, 538, 539, 540, 542, 543, 544, 545, 546, 548, 549, 550, 551, 552, 553, 554, 555, 556, 558, 559, 560, 561, 562, 564, 565, 566, 567, 568, 570, 572, 573, 574, 575, 576, 578, 579, 580, 581, 582, 583, 584, 585, 586, 588, 589, 590, 591, 592, 594, 595, 596, 597, 598, 600, 602, 603, 604, 605, 606, 608, 609, 610, 611, 612, 614, 615, 616, 618, 620, 621, 622, 623, 624, 625, 626, 627, 628, 629, 630, 632, 633, 634, 635, 636, 637, 638, 639, 640, 642, 644, 645, 646, 648, 649, 650, 651, 652, 654, 655, 656, 657, 658, 660, 662, 663, 664, 665, 666, 667, 668, 669, 670, 671, 672, 674, 675, 676, 678, 679, 680, 681, 682, 684, 685, 686, 687, 688, 689, 690, 692, 693, 694, 695, 696, 697, 698, 699, 700, 702, 703, 704, 705, 706, 707, 708, 710, 711, 712, 713, 714, 715, 716, 717, 718, 720, 721, 722, 723, 724, 725, 726, 728, 729, 730, 731, 732, 734, 735, 736, 737, 738, 740, 741, 742, 744, 745, 746, 747, 748, 749, 750, 752, 753, 754, 755, 756, 758, 759, 760, 762, 763, 764, 765, 766, 767, 768, 770, 771, 772, 774, 775, 776, 777, 778, 779, 780, 781, 782, 783, 784, 785, 786, 788, 789, 790, 791, 792, 793, 794, 795, 796, 798, 799, 800, 801, 802, 803, 804, 805, 806, 807, 808, 810, 812, 813, 814, 815, 816, 817, 818, 819, 820, 822, 824, 825, 826, 828, 830, 831, 832, 833, 834, 835, 836, 837, 838, 840, 841, 842, 843, 844, 845, 846, 847, 848, 849, 850, 851, 852, 854, 855, 856, 858, 860, 861, 862, 864, 865, 866, 867, 868, 869, 870, 871, 872, 873, 874, 875, 876, 878, 879, 880, 882, 884, 885, 886, 888, 889, 890, 891, 892, 893, 894, 895, 896, 897, 898, 899, 900, 901, 902, 903, 904, 905, 906, 908, 909, 910, 912, 913, 914, 915, 916, 917, 918, 920, 921, 922, 923, 924, 925, 926, 927, 928, 930, 931, 932, 933, 934, 935, 936, 938, 939, 940, 942, 943, 944, 945, 946, 948, 949, 950, 951, 952, 954, 955, 956, 957, 958, 959, 960, 961, 962, 963, 964, 965, 966, 968, 969, 970, 972, 973, 974, 975, 976, 978, 979, 980, 981, 982, 984, 985, 986, 987, 988, 989, 990, 992, 993, 994, 995, 996, 998, 999 and 1000 are composite.
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First, zero is not applied to the terms prime and composite because the definitions only apply to natural numbers (positive whole numbers, which does not include zero). One is not prime or composite because one is the unit that is used within the definition of prime of composite numbers, and many definitions of prime and composite even exclude one from the definition. If you want to categorize one within a discussion of prime and composite, it is common to simply call one the unit.
289 is a composite number. This is because composite numbers are any number that has more than two factors(one and itself). Therefore, since 17 is a factor of 289 that makes it a composite number.
121 is a composite number because it can be divided evenly by numbers other than 1 and itself. In this case, 121 can be divided by 11 and 1. Prime numbers are only divisible by 1 and themselves, which is not the case for 121.
Composite numbers are numbers composed of 2 or more primes. 2 is a prime number. Any other (positive) even number is a product of 2 and some other number (not 1).