The First 96 Powers of Two
| 20 | = | 1 | 212 | = | 4,096 | 224 | = | 16,777,216 | 236 | = | 68,719,476,736 | 248 | = | 281,474,976,710,656 | 260 | = | 1,152,921,504,606,846,976 | 272 | = | 4,722,366,482,869,645,213,696 | 284 | = | 19,342,813,113,834,066,795,298,816 | |||||||
| 21 | = | 2 | 213 | = | 8,192 | 225 | = | 33,554,432 | 237 | = | 137,438,953,472 | 249 | = | 562,949,953,421,312 | 261 | = | 2,305,843,009,213,693,952 | 273 | = | 9,444,732,965,739,290,427,392 | 285 | = | 38,685,626,227,668,133,590,597,632 | |||||||
| 22 | = | 4 | 214 | = | 16,384 | 226 | = | 67,108,864 | 238 | = | 274,877,906,944 | 250 | = | 1,125,899,906,842,624 | 262 | = | 4,611,686,018,427,387,904 | 274 | = | 18,889,465,931,478,580,854,784 | 286 | = | 77,371,252,475,336,267,181,195,264 | |||||||
| 23 | = | 8 | 215 | = | 32,768 | 227 | = | 134,217,728 | 239 | = | 549,755,813,888 | 251 | = | 2,251,799,813,685,248 | 263 | = | 9,223,372,036,854,775,808 | 275 | = | 37,778,931,862,957,161,709,568 | 287 | = | 154,742,504,950,672,534,362,390,528 | |||||||
| 24 | = | 16 | 216 | = | 65,536 | 228 | = | 268,435,456 | 240 | = | 1,099,511,627,776 | 252 | = | 4,503,599,627,370,496 | 264 | = | 18,446,744,073,709,551,616 | 276 | = | 75,557,863,725,914,323,419,136 | 288 | = | 309,485,009,903,345,068,724,783,156 | |||||||
| 25 | = | 32 | 217 | = | 131,072 | 229 | = | 536,870,912 | 241 | = | 2,199,023,255,552 | 253 | = | 9,007,199,254,740,992 | 265 | = | 36,893,488,147,419,103,232 | 277 | = | 151,115,727,451,828,646,838,272 | 289 | = | 618,970,019,806,690,137,449,566,312 | |||||||
| 26 | = | 64 | 218 | = | 262,144 | 230 | = | 1,073,741,824 | 242 | = | 4,398,046,511,104 | 254 | = | 18,014,398,509,481,984 | 266 | = | 73,786,976,294,838,206,464 | 278 | = | 302,231,454,903,657,293,676,544 | 290 | = | 1,237,940,039,613,380,274,899,132,624 | |||||||
| 27 | = | 128 | 219 | = | 524,288 | 231 | = | 2,147,483,648 | 243 | = | 8,796,093,022,208 | 255 | = | 36,028,797,018,963,968 | 267 | = | 147,573,952,589,676,412,928 | 279 | = | 604,462,909,807,314,587,353,088 | 291 | = | 2,475,880,079,226,760,549,798,265,248 | |||||||
| 28 | = | 256 | 220 | = | 1,048,576 | 232 | = | 4,294,967,296 | 244 | = | 17,592,186,044,416 | 256 | = | 72,057,594,037,927,936 | 268 | = | 295,147,905,179,352,825,856 | 280 | = | 1,208,925,819,614,629,174,706,176 | 292 | = | 4,951,760,158,453,521,099,596,530,496 | |||||||
| 29 | = | 512 | 221 | = | 2,097,152 | 233 | = | 8,589,934,592 | 245 | = | 35,184,372,088,832 | 257 | = | 144,115,188,075,855,872 | 269 | = | 590,295,810,358,705,651,712 | 281 | = | 2,417,851,639,229,258,349,412,352 | 293 | = | 9,903,520,316,907,042,199,193,060,992 | |||||||
| 210 | = | 1,024 | 222 | = | 4,194,304 | 234 | = | 17,179,869,184 | 246 | = | 70,368,744,177,664 | 258 | = | 288,230,376,151,711,744 | 270 | = | 1,180,591,620,717,411,303,424 | 282 | = | 4,835,703,278,458,516,698,824,704 | 294 | = | 19,807,040,633,814,084,398,386,121,984 | |||||||
| 211 | = | 2,048 | 223 | = | 8,388,608 | 235 | = | 34,359,738,368 | 247 | = | 140,737,488,355,328 | 259 | = | 576,460,752,303,423,488 | 271 | = | 2,361,183,241,434,822,606,848 | 283 | = | 9,671,406,556,917,033,397,649,408 | 295 | = | 39,614,081,267,628,168,796,772,243,968 |
One can see that starting with 2 the last digit is periodic with period 4, with the cycle 2–4–8–6–, and starting with 4 the last two digits are periodic with period 20. These patterns are generally true of any power, with respect to any base. The pattern continues, of course, where each pattern has starting point 2k length the multiplicative order of 2 modulo 5k.
Read more about this topic: Power Of Two
Famous quotes containing the word powers:
“For human nature, being more highly pitched, selved, and distinctive than anything in the world, can have been developed, evolved, condensed, from the vastness of the world not anyhow or by the working of common powers but only by one of finer or higher pitch and determination than itself.”
—Gerard Manley Hopkins (1844–1889)