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:
“And as the sun above the light doth bring,
Though we behold it in the air below,
So from th’ eternal Light the soul doth spring,
Though in the body she her powers do show.”
—Sir John Davies (1569–1626)