11111111111110

2^1000000=(2^4)^250000=16^250000
且任兩個尾數是6的數相乘，結果的尾數也是6
所以2的1000000次方的最後一個數是6

通常，這類題目要用模10計算:
2x2 = 4 mod 10
4x2 = 8 mod 10
8x2 = 6 mod 10
6x2 = 2 mod 10

2^n = 2^(n-4k) mod 10
(n>1, n-4k>1)

1000000 = 4 mod 4

嗯嗯，就像前面一個人說的一樣，用看次方規律的方式，最後1000000/4=250000...0，所以得知最後一位是6。
如果要求末兩位，則要(1000000-1)/20=49999...19，因此可得知末兩位是76。
二的次方末兩位表：
02,04,08,16,32,64,28,56,12,24,48,96,92,84,68,36,72,44,88,76,52,04...
其實本數是192967445229376576

這個數是2的1000000次方ㄝ！
做個簡單的估計...2的10次方比10的3次方稍大，而這個數是2^10的100000次方，絕對大於10的300000次方，即至少有300001位數，你的數字是錯的吧

我想 justpoppingin 有誤解了：
2^1000,000 = 2^(10^6) ≠ (2^10)^6 = 2^60 =1,152,921,504,606,846,976

至於 justpoppingin 的 192967445229376576 怎麼來的，我猜不到。

joey 估得沒錯至少有300001位數：講得更簡單一些：
2^1000,000 = (2^10)^100,000 ≒ (10^3)^100,000 = 10^300,000 (這個數有300,001位)

事實上是 301,030 位數。
9,900,656,229,295,898,250,697,923,616,301,903,250,733,624,241,787,567,332,866,396,114,531,709,483,309,486,103,054,614,551,234,648,391,482,431,507,034,583,723,883,510,658,989,416,314,927,422,565,031,572,905,372,314,869,377,232,871,775,494,713,664,238,970,125,842,914,489,614,716,338,412,188,631,103,792,398,056,007,740,136,270,960,553,070,538,667,179,812,336,061,592,179,279,832,732,236,430,322,862,606,574,309,256,916,278,582,042,834,772,001,794,493,190,056,995,140,975,103,125,269,173,943,089,615,493,140,378,429,176,713,780,793,147,953,357,424,131,614,194,925,264,632,270.................................................388,240,673,741,858,577,571,237,989,895,175,986,725,568,600,702,493,511,694,682,921,171,113,852,563,711,376,533,487,112,022,676,879,462,444,600,041,932,855,783,251,617,241,085,645,011,001,036,578,193,204,466,256,314,580,375,135,866,175,958,334,510,775,841,705,204,022,698,031,471,290,583,891,295,636,747,619,296,417,826,487,441,672,855,818,541,664,120,161,336,264,596,269,328,635,225,914,285,144,229,375,864,163,429,343,101,487,229,024,976,509,832,906,753,689,215,241,457,079,293,625,964,237,491,439,317,020,877,311,008,625,357,775,069,148,569,092,075,651,782,488,478,598,420,407,064,596,334,261,847,462,588,170,731,310,996,021,657,706,771,510,081,099,833,511,546,595,845,746,196,783,679,831,720,727,072,683,207,591,757,100,428,209,192,420,228,872,667,749,052,301,871,236,104,888,403,162,747,109,376
(9/25更正)

原來中間有刪節號

引用：

myfund168 寫道:
281,172,164 ..............................173,053,513

2的1次方個位數是2，
2的2次方個位數是4，
2的3次方個位數是8，
2的4次方個位數是6，
2的5次方個位數是2。
每5個數循環一次。
1000000/5=200000
1000000次方的最後一個數是2

2^10≡24 (mod 100)
2^20≡76 (mod 100)
2^40≡76 (mod 100)
2^1000,000=(2^20)^50,000
2^1000,000≡76 (mod 100)

這樣也可以，我猜！

引用：

joey 寫道:
這個數是2的1000000次方ㄝ！
做個簡單的估計...2的10次方比10的3次方稍大，而這個數是2^10的100000次方，絕對大於10的300000次方，即至少有300001位數，你的數字是錯的吧

對啦！我後來檢查才發現是2的60次方，不過答案還是對的XD！