# 2的幂

2的幂是指符合${displaystyle 2^{n}}$型式，而${displaystyle n}$也是整数的数，也就是底数为2，指数为整数 n的幂。

## 表示方法

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

## 与2的幂有关的数字

• 比某一个2的幂小1的素数在数学上被称为梅森素数；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的素数在数学上被称为费马素数；如数字3也是最小的费马素数（${displaystyle 3=2+1=2^{1}+1}$）。
• 一个以2的幂为分母的分数被称为二进有理数。
• 可以表示为连续正整数的和的数被称为礼貌数，这些数则是完全不含2的幂的数。

## 2的幂的列表（部分）

### 2的正指数幂

${displaystyle 2^{n},nin [0,101],nin Z}$

 2 = 1 2 = 4,096 2 = 16,777,216 2 = 68,719,476,736 2 = 281,474,976,710,656 2 = 1,152,921,504,606,846,976 2 = 4,722,366,482,869,645,213,696 2 = 19,342,813,113,834,066,795,298,816 2 = 79,228,162,514,264,337,593,540,590,336 2 = 2 2 = 8,192 2 = 33,554,432 2 = 137,438,953,472 2 = 562,949,953,421,312 2 = 2,305,843,009,213,693,952 2 = 9,444,732,965,739,290,427,392 2 = 38.685,626,227,668,133,590,597,632 2 = 158,456,325,028,528,675,187,087,900,672 2 = 4 2 = 16,384 2 = 67,108,864 2 = 274,877,906,944 2 = 1,125,899,906,842,624 2 = 4,611,686,018,427,387,904 2 = 18,889,465,931,478,580,854,784 2 = 77,371,252,455,336,267,181,195,264 2 = 316,912,650,057,057,350,374,175,081,344 2 = 8 2 = 32,768 2 = 134,217,728 2 = 549,755,813,888 2 = 2,251,799,813,685,248 2 9,223,372,036,854,775,808 2 = 37,778,931,862,957,161,709,568 2 = 154,742,504,910,672,534,362,390,528 2 = 633,825,300,114,114,700,748,351,602,688 2 = 16 2 = 65,536 2 = 268,435,456 2 = 1,099,511,627,776 2 = 4,503,599,627,370,496 2 = 18,446,744,073,709,551,616 2 = 75,557,863,725,914,323,419,136 2 = 309,485,009,821,345,068,724,781,056 2 = 1,267,650,600,228,229,401,496,703,205,376 2 = 32 2 = 131,072 2 = 536,870,912 2 = 2,199,023,255,552 2 = 9,007,199,254,740,992 2 = 36,893,488,147,419,103,232 2 = 151,115,727,451,828,646,838,272 2 = 618,970,019,642,690,137,449,562,112 2 = 2,535,351,200,456,458,802,993,306,410,752 2 = 64 2 = 262,144 2 = 1,073,741,824 2 = 4,398,046,511,104 2 = 18,014,398,509,481,984 2 = 73,786,976,294,838,206,464 2 = 302,231,454,903,657,293,676,544 2 = 1,237,940,039,285,380,274,899,124,224 2 = 128 2 = 524,288 2 = 2,147,483,648 2 = 8,796,093,022,208 2 = 36,028,797,018,963,968 2 = 147,573,952,589,676,412,928 2 = 604,462,909,817,314,587,353,088 2 = 2,475,880,078,570,760,549,798,248,448 2 = 256 2 = 1,048,576 2 = 4,294,967,296 2 = 17,592,186,044,416 2 = 72,057,594,037,927,936 2 = 295,147,905,179,352,825,856 2 = 1,208,925,819,614,629,174,706,176 2 = 4,951,760,157,141,521,099,596,496,896 2 = 512 2 = 2,097,152 2 = 8,589,934,592 2 = 35,184,372,088,832 2 = 144,115,188,075,855,872 2 = 590,295,810,358,705,651,712 2 = 2,417,851,639,229,258,349,412,352 2 = 9,903,520,314,283,042,199192,993,792 2 = 1,024 2 = 4,194,304 2 = 17,179,869,184 2 = 70,368,744,177,664 2 = 288,230,376,151,711,744 2 = 1,180,591,620,717,411,303,424 2 = 4,835,703,278,458,516,698,824,704 2 19,807,040,628,566,084,398,385,987,584 2 = 2,048 2 = 8,388,608 2 = 34,359,738,368 2 = 140,737,488,355,328 2 = 576,460,752,303,423,488 2 = 2,361,183,241,434,822,606,848 2 = 9,671,406,556,917,033,397,649,408 2 39,614,081,257,132,168,796,771,975,168
2 = 2
2 = 4
2 = 16
2 = 256
2 = 65,536
2 = 4,294,967,296
2 = 18,446,744,073,709,551,616
2 = 340,282,366,920,938,463,463,374,607,431,768,211,456
2 = 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

### 2的负指数幂

2的首60个负指数幂

2 = 0.5

2 = 0.25

2 = 0.125

2 = 0.0625

2 = 0.03125

2 = 0.015625

2 = 0.0078125

2 = 0.00390625

2 = 0.001953125

2 = 0.0009765625

2 = 0.00048828125

2 = 0.000244140625

2 = 0.0001220703125

2 = 0.00006103515625

2 = 0.000030517578125

2 = 0.0000152587890625

2 = 0.00000762939453125

2 = 0.000003814697265625

2 = 0.0000019073486328125

2 = 0.00000095367431640625

2 = 0.000000476837158203125

2 = 0.0000002384185791015625

2 = 0.00000011920928955078125

2 = 0.000000059604644775390625

2 = 0.0000000298023223876953125

2 = 0.00000001490116119384765625

2 = 0.000000007450580596923828125

2 = 0.0000000037252902984619140625

2 = 0.00000000186264514923095703125

2 = 0.000000000931322574615478515625

2 = 0.0000000004656612873077392578125

2 = 0.00000000023283064365386962890625

2 = 0.000000000116415321826934814453125

2 = 0.0000000000582076609134674072265625

2 = 0.00000000002910383045673370361328125

2 = 0.000000000014551915228366851806640625

2 = 0.0000000000072759576141834259033203125

2 = 0.00000000000363797880709171295166015625

2 = 0.000000000001818989403545856475830078125

2 = 0.0000000000009094947017729282379150390625

2 = 0.00000000000045474735088646411895751953125

2 = 0.000000000000227373675443232059478759765625

2 = 0.0000000000001136868377216160297393798828125

2 = 0.00000000000005684341886080801486968994140625

2 = 0.000000000000028421709430404007434844970703125

2 = 0.0000000000000142108547152020037174224853515625

2 = 0.00000000000000710542735760100185871124267578125

2 = 0.000000000000003552713678800500929355621337890625

2 = 0.0000000000000017763568394002504646778106689453125

2 = 0.00000000000000088817841970012523233890533447265625

2 = 0.000000000000000444089209850062616169452667236328125

2 = 0.0000000000000002220446049250313080847263336181640625

2 = 0.00000000000000011102230246251565404236316680908203125

2 = 0.000000000000000055511151231257827021181583404541015625

2 = 0.0000000000000000277555756156289135105907917022705078125

2 = 0.00000000000000001387778780781445675529539585113525390625

2 = 0.000000000000000006938893903907228377647697925567626953125

2 = 0.0000000000000000034694469519536141888238489627838134765625

2 = 0.00000000000000000173472347597680709441192448139190673828125

2 = 0.000000000000000000867361737988403547205962240695953369140625