a table of integers and their factors
Just a brief one again. The main take-away point is to demonstrate how we can compose new operators out of existing operators.
-- define some operators:
sa: factors |*> #=> factor |_self>
sa: count-factors |*> #=> count-sum factor |_self>
sa: prime |*> #=> if(is-equal[1] count-factors |_self>,|prime>,count-factors|_self>)
-- now show the table:
sa: table[number,factors,prime] range(|number: 1>,|number: 250>)
+--------+-------------+-------+
| number | factors | prime |
+--------+-------------+-------+
| 1 | | 0 |
| 2 | 2 | prime |
| 3 | 3 | prime |
| 4 | 2 2 | 2 |
| 5 | 5 | prime |
| 6 | 2, 3 | 2 |
| 7 | 7 | prime |
| 8 | 3 2 | 3 |
| 9 | 2 3 | 2 |
| 10 | 2, 5 | 2 |
| 11 | 11 | prime |
| 12 | 2 2, 3 | 3 |
| 13 | 13 | prime |
| 14 | 2, 7 | 2 |
| 15 | 3, 5 | 2 |
| 16 | 4 2 | 4 |
| 17 | 17 | prime |
| 18 | 2, 2 3 | 3 |
| 19 | 19 | prime |
| 20 | 2 2, 5 | 3 |
| 21 | 3, 7 | 2 |
| 22 | 2, 11 | 2 |
| 23 | 23 | prime |
| 24 | 3 2, 3 | 4 |
| 25 | 2 5 | 2 |
| 26 | 2, 13 | 2 |
| 27 | 3 3 | 3 |
| 28 | 2 2, 7 | 3 |
| 29 | 29 | prime |
| 30 | 2, 3, 5 | 3 |
| 31 | 31 | prime |
| 32 | 5 2 | 5 |
| 33 | 3, 11 | 2 |
| 34 | 2, 17 | 2 |
| 35 | 5, 7 | 2 |
| 36 | 2 2, 2 3 | 4 |
| 37 | 37 | prime |
| 38 | 2, 19 | 2 |
| 39 | 3, 13 | 2 |
| 40 | 3 2, 5 | 4 |
| 41 | 41 | prime |
| 42 | 2, 3, 7 | 3 |
| 43 | 43 | prime |
| 44 | 2 2, 11 | 3 |
| 45 | 2 3, 5 | 3 |
| 46 | 2, 23 | 2 |
| 47 | 47 | prime |
| 48 | 4 2, 3 | 5 |
| 49 | 2 7 | 2 |
| 50 | 2, 2 5 | 3 |
| 51 | 3, 17 | 2 |
| 52 | 2 2, 13 | 3 |
| 53 | 53 | prime |
| 54 | 2, 3 3 | 4 |
| 55 | 5, 11 | 2 |
| 56 | 3 2, 7 | 4 |
| 57 | 3, 19 | 2 |
| 58 | 2, 29 | 2 |
| 59 | 59 | prime |
| 60 | 2 2, 3, 5 | 4 |
| 61 | 61 | prime |
| 62 | 2, 31 | 2 |
| 63 | 2 3, 7 | 3 |
| 64 | 6 2 | 6 |
| 65 | 5, 13 | 2 |
| 66 | 2, 3, 11 | 3 |
| 67 | 67 | prime |
| 68 | 2 2, 17 | 3 |
| 69 | 3, 23 | 2 |
| 70 | 2, 5, 7 | 3 |
| 71 | 71 | prime |
| 72 | 3 2, 2 3 | 5 |
| 73 | 73 | prime |
| 74 | 2, 37 | 2 |
| 75 | 3, 2 5 | 3 |
| 76 | 2 2, 19 | 3 |
| 77 | 7, 11 | 2 |
| 78 | 2, 3, 13 | 3 |
| 79 | 79 | prime |
| 80 | 4 2, 5 | 5 |
| 81 | 4 3 | 4 |
| 82 | 2, 41 | 2 |
| 83 | 83 | prime |
| 84 | 2 2, 3, 7 | 4 |
| 85 | 5, 17 | 2 |
| 86 | 2, 43 | 2 |
| 87 | 3, 29 | 2 |
| 88 | 3 2, 11 | 4 |
| 89 | 89 | prime |
| 90 | 2, 2 3, 5 | 4 |
| 91 | 7, 13 | 2 |
| 92 | 2 2, 23 | 3 |
| 93 | 3, 31 | 2 |
| 94 | 2, 47 | 2 |
| 95 | 5, 19 | 2 |
| 96 | 5 2, 3 | 6 |
| 97 | 97 | prime |
| 98 | 2, 2 7 | 3 |
| 99 | 2 3, 11 | 3 |
| 100 | 2 2, 2 5 | 4 |
| 101 | 101 | prime |
| 102 | 2, 3, 17 | 3 |
| 103 | 103 | prime |
| 104 | 3 2, 13 | 4 |
| 105 | 3, 5, 7 | 3 |
| 106 | 2, 53 | 2 |
| 107 | 107 | prime |
| 108 | 2 2, 3 3 | 5 |
| 109 | 109 | prime |
| 110 | 2, 5, 11 | 3 |
| 111 | 3, 37 | 2 |
| 112 | 4 2, 7 | 5 |
| 113 | 113 | prime |
| 114 | 2, 3, 19 | 3 |
| 115 | 5, 23 | 2 |
| 116 | 2 2, 29 | 3 |
| 117 | 2 3, 13 | 3 |
| 118 | 2, 59 | 2 |
| 119 | 7, 17 | 2 |
| 120 | 3 2, 3, 5 | 5 |
| 121 | 2 11 | 2 |
| 122 | 2, 61 | 2 |
| 123 | 3, 41 | 2 |
| 124 | 2 2, 31 | 3 |
| 125 | 3 5 | 3 |
| 126 | 2, 2 3, 7 | 4 |
| 127 | 127 | prime |
| 128 | 7 2 | 7 |
| 129 | 3, 43 | 2 |
| 130 | 2, 5, 13 | 3 |
| 131 | 131 | prime |
| 132 | 2 2, 3, 11 | 4 |
| 133 | 7, 19 | 2 |
| 134 | 2, 67 | 2 |
| 135 | 3 3, 5 | 4 |
| 136 | 3 2, 17 | 4 |
| 137 | 137 | prime |
| 138 | 2, 3, 23 | 3 |
| 139 | 139 | prime |
| 140 | 2 2, 5, 7 | 4 |
| 141 | 3, 47 | 2 |
| 142 | 2, 71 | 2 |
| 143 | 11, 13 | 2 |
| 144 | 4 2, 2 3 | 6 |
| 145 | 5, 29 | 2 |
| 146 | 2, 73 | 2 |
| 147 | 3, 2 7 | 3 |
| 148 | 2 2, 37 | 3 |
| 149 | 149 | prime |
| 150 | 2, 3, 2 5 | 4 |
| 151 | 151 | prime |
| 152 | 3 2, 19 | 4 |
| 153 | 2 3, 17 | 3 |
| 154 | 2, 7, 11 | 3 |
| 155 | 5, 31 | 2 |
| 156 | 2 2, 3, 13 | 4 |
| 157 | 157 | prime |
| 158 | 2, 79 | 2 |
| 159 | 3, 53 | 2 |
| 160 | 5 2, 5 | 6 |
| 161 | 7, 23 | 2 |
| 162 | 2, 4 3 | 5 |
| 163 | 163 | prime |
| 164 | 2 2, 41 | 3 |
| 165 | 3, 5, 11 | 3 |
| 166 | 2, 83 | 2 |
| 167 | 167 | prime |
| 168 | 3 2, 3, 7 | 5 |
| 169 | 2 13 | 2 |
| 170 | 2, 5, 17 | 3 |
| 171 | 2 3, 19 | 3 |
| 172 | 2 2, 43 | 3 |
| 173 | 173 | prime |
| 174 | 2, 3, 29 | 3 |
| 175 | 2 5, 7 | 3 |
| 176 | 4 2, 11 | 5 |
| 177 | 3, 59 | 2 |
| 178 | 2, 89 | 2 |
| 179 | 179 | prime |
| 180 | 2 2, 2 3, 5 | 5 |
| 181 | 181 | prime |
| 182 | 2, 7, 13 | 3 |
| 183 | 3, 61 | 2 |
| 184 | 3 2, 23 | 4 |
| 185 | 5, 37 | 2 |
| 186 | 2, 3, 31 | 3 |
| 187 | 11, 17 | 2 |
| 188 | 2 2, 47 | 3 |
| 189 | 3 3, 7 | 4 |
| 190 | 2, 5, 19 | 3 |
| 191 | 191 | prime |
| 192 | 6 2, 3 | 7 |
| 193 | 193 | prime |
| 194 | 2, 97 | 2 |
| 195 | 3, 5, 13 | 3 |
| 196 | 2 2, 2 7 | 4 |
| 197 | 197 | prime |
| 198 | 2, 2 3, 11 | 4 |
| 199 | 199 | prime |
| 200 | 3 2, 2 5 | 5 |
| 201 | 3, 67 | 2 |
| 202 | 2, 101 | 2 |
| 203 | 7, 29 | 2 |
| 204 | 2 2, 3, 17 | 4 |
| 205 | 5, 41 | 2 |
| 206 | 2, 103 | 2 |
| 207 | 2 3, 23 | 3 |
| 208 | 4 2, 13 | 5 |
| 209 | 11, 19 | 2 |
| 210 | 2, 3, 5, 7 | 4 |
| 211 | 211 | prime |
| 212 | 2 2, 53 | 3 |
| 213 | 3, 71 | 2 |
| 214 | 2, 107 | 2 |
| 215 | 5, 43 | 2 |
| 216 | 3 2, 3 3 | 6 |
| 217 | 7, 31 | 2 |
| 218 | 2, 109 | 2 |
| 219 | 3, 73 | 2 |
| 220 | 2 2, 5, 11 | 4 |
| 221 | 13, 17 | 2 |
| 222 | 2, 3, 37 | 3 |
| 223 | 223 | prime |
| 224 | 5 2, 7 | 6 |
| 225 | 2 3, 2 5 | 4 |
| 226 | 2, 113 | 2 |
| 227 | 227 | prime |
| 228 | 2 2, 3, 19 | 4 |
| 229 | 229 | prime |
| 230 | 2, 5, 23 | 3 |
| 231 | 3, 7, 11 | 3 |
| 232 | 3 2, 29 | 4 |
| 233 | 233 | prime |
| 234 | 2, 2 3, 13 | 4 |
| 235 | 5, 47 | 2 |
| 236 | 2 2, 59 | 3 |
| 237 | 3, 79 | 2 |
| 238 | 2, 7, 17 | 3 |
| 239 | 239 | prime |
| 240 | 4 2, 3, 5 | 6 |
| 241 | 241 | prime |
| 242 | 2, 2 11 | 3 |
| 243 | 5 3 | 5 |
| 244 | 2 2, 61 | 3 |
| 245 | 5, 2 7 | 3 |
| 246 | 2, 3, 41 | 3 |
| 247 | 13, 19 | 2 |
| 248 | 3 2, 31 | 4 |
| 249 | 3, 83 | 2 |
| 250 | 2, 3 5 | 4 |
+--------+-------------+-------+
I guess that is it for this post. I hope it is clear what I was trying to show!
Maybe I should also mention it really highlights the location of twin primes.
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updated: 19/12/2016
by Garry Morrison
email: garry -at- semantic-db.org