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Math Help - Find the 155th digit of 2^17365

  1. #1
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    Find the 155th digit of 2^17365

    So, my bonus question on my test was "Find the 1551th digit of 2^17365". Anyone know how?
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  2. #2
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    Quote Originally Posted by ISeriouslyNeedHelp View Post
    So, my bonus question on my test was "Find the 1551th digit of 2^17365". Anyone know how?
    The 155^{\text{th }} digit (going left from the 1's digit position) occurs when the exponent(a) as in 2^a, exceeds 511.576926.

     17365_{\text{decimal}} is  100001111010101_{\text{binary}}
    or
     2^{16384} + 2^{512} + 2^{469} = 2^{17365}

     2^{469} will NOT affect the value of the 155^{th} digit.

    (16384+512) in binary is 100001000000000
    dividing that by 512
    \dfrac{(16384+512)}{512} = 33

    The 155th digit of 2^{17365} is the same as the least significant digit of 2^{33}

    2^{33} = 8589934592

    The 155^{\text{th}} \text{digit of } 2^{17365} is 2

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  3. #3
    Super Member malaygoel's Avatar
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    Quote Originally Posted by aidan View Post
     2^{16384} + 2^{512} + 2^{469} = 2^{17365}
    THis is not correct.
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  4. #4
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    http://www.wolframalpha.com/input/?i=1551th+digit+of+2^17365

    cheat!
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