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.
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