# 2的幂

2的幂是指符合${\displaystyle 2^{n}}$型式，而${\displaystyle n}$也是整數的數，也就是底數2指數為整數 n

## 表示方法

• ${\displaystyle 2^{n}}$
• ${\displaystyle 2\uparrow n}$
• ${\displaystyle 2[3]n}$
• 2 ^ n
• 2 ** n
• power(2, n)
• 2的n次幂
• 2的n次方

## 與2的冪有關的數字

• 比某一个2的幂小1的素数，在数学上称为梅森素数；例如数字3是最小的梅森素数（${\displaystyle 3=4-1=2^{2}-1}$ ）。
• 比某一个2的幂大1的素数，在数学上称为费马素数；如数字3也是最小的费马素数（${\displaystyle 3=2+1=2^{1}+1}$ ）。
• 一个以2的幂为分母的分数称为二进有理数
• 可以表示为连续正整数和的数称为礼貌数，2的幂不會是礼貌数。

## 2的幂列表

${\displaystyle 2^{n},n\in [0,63],n\in Z}$

 20 = 1 216 = 65,536 232 = 4,294,967,296 248 = 281,474,976,710,656 21 = 2 217 = 131,072 233 = 8,589,934,592 249 = 562,949,953,421,312 22 = 4 218 = 262,144 234 = 17,179,869,184 250 = 1,125,899,906,842,624 23 = 8 219 = 524,288 235 = 34,359,738,368 251 = 2,251,799,813,685,248 24 = 16 220 = 1,048,576 236 = 68,719,476,736 252 = 4,503,599,627,370,496 25 = 32 221 = 2,097,152 237 = 137,438,953,472 253 = 9,007,199,254,740,992 26 = 64 222 = 4,194,304 238 = 274,877,906,944 254 = 18,014,398,509,481,984 27 = 128 223 = 8,388,608 239 = 549,755,813,888 255 = 36,028,797,018,963,968 28 = 256 224 = 16,777,216 240 = 1,099,511,627,776 256 = 72,057,594,037,927,936 29 = 512 225 = 33,554,432 241 = 2,199,023,255,552 257 = 144,115,188,075,855,872 210 = 1,024 226 = 67,108,864 242 = 4,398,046,511,104 258 = 288,230,376,151,711,744 211 = 2,048 227 = 134,217,728 243 = 8,796,093,022,208 259 = 576,460,752,303,423,488 212 = 4,096 228 = 268,435,456 244 = 17,592,186,044,416 260 = 1,152,921,504,606,846,976 213 = 8,192 229 = 536,870,912 245 = 35,184,372,088,832 261 = 2,305,843,009,213,693,952 214 = 16,384 230 = 1,073,741,824 246 = 70,368,744,177,664 262 = 4,611,686,018,427,387,904 215 = 32,768 231 = 2,147,483,648 247 = 140,737,488,355,328 263 = 9,223,372,036,854,775,808

## 2的2的幂次方列表

220 = 21 = 2
221 =22 = 4
222 =24 = 16
223 =28 = 256
224 =216 = 65,536
225 =232 = 4,294,967,296
226 =264 = 18,446,744,073,709,551,616
227 =2128 = 340,282,366,920,938,463,463,374,607,431,768,211,456
228 =2256 = 115,792,089,237,316,195,423,570,985,008,687,907,853,269,984,665,640,564,039,457,584,007,913,129,639,936

## 參考資料

1. ^ Lipschutz, Seymour. Schaum's Outline of Theory and Problems of Essential Computer Mathematics. New York: McGraw-Hill. 1982: 3. ISBN 0-07-037990-4.
2. ^ Sewell, Michael J. Mathematics Masterclasses. Oxford: Oxford University Press. 1997: 78. ISBN 0-19-851494-8.