Culture and Reference

Prime numbers: the first 100

A prime number has exactly two divisors: 1 and itself. The list below has the first 100 — from 2 up to 541 — found with the Sieve of Eratosthenes, not copied from a table, so there is no risk of a transcription error.

  1. 2#1
  2. 3#2
  3. 5#3
  4. 7#4
  5. 11#5
  6. 13#6
  7. 17#7
  8. 19#8
  9. 23#9
  10. 29#10
  11. 31#11
  12. 37#12
  13. 41#13
  14. 43#14
  15. 47#15
  16. 53#16
  17. 59#17
  18. 61#18
  19. 67#19
  20. 71#20
  21. 73#21
  22. 79#22
  23. 83#23
  24. 89#24
  25. 97#25
  26. 101#26
  27. 103#27
  28. 107#28
  29. 109#29
  30. 113#30
  31. 127#31
  32. 131#32
  33. 137#33
  34. 139#34
  35. 149#35
  36. 151#36
  37. 157#37
  38. 163#38
  39. 167#39
  40. 173#40
  41. 179#41
  42. 181#42
  43. 191#43
  44. 193#44
  45. 197#45
  46. 199#46
  47. 211#47
  48. 223#48
  49. 227#49
  50. 229#50
  51. 233#51
  52. 239#52
  53. 241#53
  54. 251#54
  55. 257#55
  56. 263#56
  57. 269#57
  58. 271#58
  59. 277#59
  60. 281#60
  61. 283#61
  62. 293#62
  63. 307#63
  64. 311#64
  65. 313#65
  66. 317#66
  67. 331#67
  68. 337#68
  69. 347#69
  70. 349#70
  71. 353#71
  72. 359#72
  73. 367#73
  74. 373#74
  75. 379#75
  76. 383#76
  77. 389#77
  78. 397#78
  79. 401#79
  80. 409#80
  81. 419#81
  82. 421#82
  83. 431#83
  84. 433#84
  85. 439#85
  86. 443#86
  87. 449#87
  88. 457#88
  89. 461#89
  90. 463#90
  91. 467#91
  92. 479#92
  93. 487#93
  94. 491#94
  95. 499#95
  96. 503#96
  97. 509#97
  98. 521#98
  99. 523#99
  100. 541#100

Como ler este número

How the sieve works

Starting from 2, cross out every multiple of each number found so far. What is never crossed out is prime. It is over 2,000 years old and still the simplest reliable way to find primes by hand or by computer.

Cuidado

Why 1 is not on the list

1 has only one divisor — itself — not two, so it fails the definition of a prime number. Mathematicians also exclude it so that every integer above 1 has exactly one way to be broken into prime factors (a result called the fundamental theorem of arithmetic, which would otherwise fail: 6 would be both 2×3 and 1×2×3).

Why does 2 get to be the only even prime?

Every even number above 2 is divisible by 2 itself, which means it already has a third divisor besides 1 and itself — so it cannot be prime. That leaves 2 as the sole exception: small enough that its only divisors really are 1 and 2.

Do primes run out eventually?

No — Euclid proved around 300 BC that there are infinitely many primes, with an argument that still holds: multiply any finite list of primes together, add 1, and the result must have a prime factor outside that list, which means no finite list can ever be complete.