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:
“Whenever any form of government shall become destructive of these ends, it is the right of the people to alter or to abolish it, & to institute new government, laying it’s foundation on such principles & organising it’s powers in such form, as to them shall seem most likely to effect their safety & happiness.”
—Thomas Jefferson (1743–1826)