List of Prime and Composite Numbers with Examples

With many hackers posing threats to the data like credit cards, medical information, Whatsapp, etc., numbers, like prime and composite numbers, are playing a vital role in encryption. Let us first know what exactly it means by Prime and Composite numbers and then see how it exactly is used in real-time.

Since the two may be slightly confusing, it is crucial to understand the comparison between Prime vs Composite Numbers.

What is a number?

The number is a mathematical value that can be denoted in a word, symbol or even a figure that speaks about the amount of a particular thing.

How are numbers categorized?

Numbers are categorized into number systems and include the following major types:  

What are Prime and Composite numbers?

Prime numbers: A natural number greater than one and can be divided by one and itself without any remainder (it has only two factors itself and one). It is not a product of any smaller natural number but itself.

Read: Finding the successor and predecessor of numbers

As per Euclid’s theorem, there are infinitely many Prime numbers.

Example: Two is Prime because it can be divided by two or one only without any remainder, and factors of two are one and two

Table with list of Prime numbers from 1-1000

Number rangePrime numbers
1-102, 3, 5, 7
11-2011, 13, 17, 19
21-3023, 29
31-4031, 37
41-5041, 43, 47
51-6053, 59
61-7061, 67
71-8071, 73, 79
81-9083, 89
91-10097
101 – 200101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199
201 – 300211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293
301 – 400307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397
401 – 500401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499
501 – 600503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599
601 – 700601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691
701 – 800701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797
801 – 900809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887
901 – 1000907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997
Total Prime numbers from 1-1000168

 Things to remember about Prime numbers:

  • The smallest Prime number known is 2 (the rest have three factors 1, 2 and themselves).
  • It is the only even prime number as well.
  • The largest Prime number is known to date (November 2021) is 282,589,933 – 1. It has 24,862,048 digits on writing in base 10 form (Great Internet Mersenne Prime Search contribution)
  • 1 has only one factor itself, so it is not a Prime number.
  • A number becomes divisible by three if the sum of that number’s digits is a multiple of three.
  • There is no prime number that is greater than 5 and ends in 5

Method to check if it’s a Prime number

Method 1: Dividing by two if you get the whole number, then it is unlikely to be a Prime number

Example: 5/2 does not give a whole number, so 5 is a prime number

Method 2: Every Prime number greater than three satisfies the condition 6n ± 1 (n=natural number)

Example: 6(3)+1=19

Method 3: If the number is greater than 40, replace that number in the place of n in the formula given below

n2+n+41. This formula claims for any positive integer ‘n’. This formula is Prime.

Example:22+2+41=47

Composite numbers: A natural number greater than one and can be divided by at least one number other than one and itself. It can be formed by multiplying small natural numbers (It has more than two factors).

Example: Four is a Composite number because it can be divided by one, two, as well as four and has factors one, two, four

Table showing list of Composite numbers from 1-1000

Number rangeComposite numbers
1-104, 6, 8, 9, 10
11-2012, 14, 15, 16, 18, 20
21-3021, 22, 24, 25, 26, 27, 28, 30
31-4032, 33, 34, 35, 36, 38, 39, 40
41-5042, 44, 45, 46, 48, 49, 50
51-6051, 52, 54, 55, 56, 57, 58, 60
61-7062, 63, 64, 65, 66, 68, 69, 70
71-8072, 74, 75, 76, 77, 78, 80
81-9081, 82, 84, 85, 86, 87, 88, 90
91-10091, 92, 93, 94, 95, 96, 98, 99, 100
101-200102, 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
201-300201, 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
301-400301, 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
401-500402, 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
501-600501, 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
601-700602, 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
701-800702, 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 
801-900801, 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
901-1000901, 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, 1000

Things to remember about Composite numbers:

v  4 is the smallest of all Composite numbers

v  More than two factors are present for a composite number

v  Every Composite number has two Prime numbers as its factors (Eg. 8= 2 x 4, where 2 and 4 are Prime numbers)

v   They can be divided evenly by smaller integers

v  We can write Composite numbers as the product of Prime numbers

Types of Composite numbers: There are different ways to classify composite numbers. These are some ways

  1. Based on the number of Prime factors:
    1. Semiprime Composite numbers: have two Prime factors (factors need not be distinct)

Example: 4, 6, 9, 10

  1. Squarefree semiprimes are semiprimes with squarefree numbers

Example: 6,10, 14, 15

  1. Sphenic Composite numbers: has three Prime factors and are distinct

Example: 40 (40 = 2 × 4 × 5)

  1. Odd Composite numbers: Integers that are odd numbers and are not Prime numbers.
    1. It has an odd number of distinct Prime factors

Example: 21, 25, 27

  1. Even Composite numbers: Integers that are even and are not Prime numbers
    1. It has an even number of distinct Prime factors

Example: 4, 8, 10, 12

  1. Based on the position of prime factors above or below some Prime number
    1. Smooth number
    2. Rough number

Method to check if it’s a Composite number

  1. By number of factors: More than two factors means it’s a Composite number

Example: 30 (2 × 3 × 5 more than two factors)

  1. By divisibility: Divide the numbers to check if the number gets divided by another number completely with no remainder.

Example: 64 gets completed divided by 2 with no remainder, so it is a Composite number

Differences between Prime and Composite numbers:

Prime numberComposite number
Divisible only by one and itselfDivisible by more numbers than one and itself
They have two factorsThey have more than two factors
Two is the smallest in the groupFour is the smallest in the group
Example:2, 3, 5Example:4, 6, 9

Conclusion

We now know Prime numbers can be divided by themselves, and 1 and Composite numbers are obtained when multiplying two Prime numbers. This is applied in the encryption of credit cards, medical data, and many more data to be kept secure. Encryption codes in the form of Composite numbers are designed using algorithms by engineers. 

Read: Most effective tips to Prepare for Class 10th Maths Olympiad

The computer recognizes these codes. But the factors used are known by users only. Hackers need to identify these by trial and error methods that need a very long period as Composite numbers are very large. This ensures data is safe with organizations that have created it.

Popular Categories

Popular Read

Daniel Johnhttps://firmwarefile.co
An Astrophile, a technophile, and an Android Fan.

Related Articles

LEAVE A REPLY

Please enter your comment!
Please enter your name here