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Prime number chart

The primes up to 100 or 200, marked. Print it, or print a blank to sieve.

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A prime has only itself

Show the steps
71391
  1. 91 = 7 × 13
  2. The circled numbers at the ends are prime, so the tree stops there: 7 × 13.
  3. Grouped as powers: 91 = 7 × 13.
  4. 91 has 4 factors in all (add 1 to each power and multiply).
Printable chart
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Prime numbers from 1 to 100

  1. 1
  2. 2 (prime)
  3. 3 (prime)
  4. 4
  5. 5 (prime)
  6. 6
  7. 7 (prime)
  8. 8
  9. 9
  10. 10
  11. 11 (prime)
  12. 12
  13. 13 (prime)
  14. 14
  15. 15
  16. 16
  17. 17 (prime)
  18. 18
  19. 19 (prime)
  20. 20
  21. 21
  22. 22
  23. 23 (prime)
  24. 24
  25. 25
  26. 26
  27. 27
  28. 28
  29. 29 (prime)
  30. 30
  31. 31 (prime)
  32. 32
  33. 33
  34. 34
  35. 35
  36. 36
  37. 37 (prime)
  38. 38
  39. 39
  40. 40
  41. 41 (prime)
  42. 42
  43. 43 (prime)
  44. 44
  45. 45
  46. 46
  47. 47 (prime)
  48. 48
  49. 49
  50. 50
  51. 51
  52. 52
  53. 53 (prime)
  54. 54
  55. 55
  56. 56
  57. 57
  58. 58
  59. 59 (prime)
  60. 60
  61. 61 (prime)
  62. 62
  63. 63
  64. 64
  65. 65
  66. 66
  67. 67 (prime)
  68. 68
  69. 69
  70. 70
  71. 71 (prime)
  72. 72
  73. 73 (prime)
  74. 74
  75. 75
  76. 76
  77. 77
  78. 78
  79. 79 (prime)
  80. 80
  81. 81
  82. 82
  83. 83 (prime)
  84. 84
  85. 85
  86. 86
  87. 87
  88. 88
  89. 89 (prime)
  90. 90
  91. 91
  92. 92
  93. 93
  94. 94
  95. 95
  96. 96
  97. 97 (prime)
  98. 98
  99. 99
  100. 100
  101. 101 (prime)
  102. 102
  103. 103 (prime)
  104. 104
  105. 105
  106. 106
  107. 107 (prime)
  108. 108
  109. 109 (prime)
  110. 110
  111. 111
  112. 112
  113. 113 (prime)
  114. 114
  115. 115
  116. 116
  117. 117
  118. 118
  119. 119
  120. 120
  121. 121
  122. 122
  123. 123
  124. 124
  125. 125
  126. 126
  127. 127 (prime)
  128. 128
  129. 129
  130. 130
  131. 131 (prime)
  132. 132
  133. 133
  134. 134
  135. 135
  136. 136
  137. 137 (prime)
  138. 138
  139. 139 (prime)
  140. 140
  141. 141
  142. 142
  143. 143
  144. 144
  145. 145
  146. 146
  147. 147
  148. 148
  149. 149 (prime)
  150. 150
  151. 151 (prime)
  152. 152
  153. 153
  154. 154
  155. 155
  156. 156
  157. 157 (prime)
  158. 158
  159. 159
  160. 160
  161. 161
  162. 162
  163. 163 (prime)
  164. 164
  165. 165
  166. 166
  167. 167 (prime)
  168. 168
  169. 169
  170. 170
  171. 171
  172. 172
  173. 173 (prime)
  174. 174
  175. 175
  176. 176
  177. 177
  178. 178
  179. 179 (prime)
  180. 180
  181. 181 (prime)
  182. 182
  183. 183
  184. 184
  185. 185
  186. 186
  187. 187
  188. 188
  189. 189
  190. 190
  191. 191 (prime)
  192. 192
  193. 193 (prime)
  194. 194
  195. 195
  196. 196
  197. 197 (prime)
  198. 198
  199. 199 (prime)
  200. 200

Reading the chart

The marked numbers are prime. A prime has exactly two factors, 1 and itself. Every other number above 1 is composite, a product of smaller primes.

There are 25 primes up to 100 and 46 up to 200. 1 is neither prime nor composite. It has only one factor.

To test a number that isn't on the chart, type it into the box above. You get its prime factors, and a prime comes back as just itself.

List of primes up to 200

The primes up to 100 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

Between 101 and 200 they are 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199.

The Sieve of Eratosthenes

Tick the blank box above the chart and print it. Cross out 1. Circle 2, then cross out every multiple of 2. Move on to the next number that isn't crossed out, circle it and cross out its multiples. Repeat.

For a 1 to 100 grid you can stop after 7. The next prime is 11, and 11 × 11 = 121 is already off the chart, so any composite left would have a factor you have already used. Everything still standing is prime.

Patterns worth spotting

Apart from 2, every prime is odd. Apart from 2 and 5, every prime ends in 1, 3, 7 or 9.

On a ten-wide grid the primes line up in four columns: 1, 3, 7 and 9. Twin primes, pairs two apart such as 11 and 13 or 71 and 73, sit next to each other in those columns.

Questions

Is 1 a prime number?

No. A prime needs exactly two different factors, and 1 has only one. Leaving it out also keeps every number's prime factorisation unique.

Is 2 the only even prime?

Yes. Every other even number has 2 as a factor, so it has at least three factors.

Why is 91 not prime?

91 is 7 × 13. It looks prime because it is odd and doesn't end in 5, which makes it a favourite trick question.

Sources

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