Results 1 to 6 of 6

Math Help - Howmany digits in this prime number?

  1. #1
    Newbie
    Joined
    Oct 2009
    Posts
    8

    Howmany digits in this prime number?

    Hey Guys,

    This is my first post and I imagine there will be a few more judging by how many questions I'm stumped on. Here the first question:

    some of you many recognize this value...

    2^6972593 - 1

    A) Without multiplying it out, determine how many digits are needed to write out this number using base-10

    B) Use the factor theorem to show that if 2^p - 1, where p does not equal 3, is a prime number , then p is neither divisible by 4 or divisible by 3. Alternatively , prove that if p is divisible by 4 or 3, then 2^p - 1 is divisible by some number other than +/- itself or +/- .

    Thanks for the help
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by cndman View Post
    Hey Guys,

    This is my first post and I imagine there will be a few more judging by how many questions I'm stumped on. Here the first question:

    some of you many recognize this value...

    2^6972593 - 1

    A) Without multiplying it out, determine how many digits are needed to write out this number using base-10

    2=10^{0.301029996}


    should get you there

    CB
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Jan 2009
    Posts
    591
    Quote Originally Posted by cndman View Post
    Hey Guys,
    This is my first post and I imagine there will be a few more judging by how many questions I'm stumped on. Here the first question:
    some of you many recognize this value...
    2^6972593 - 1

    A) Without multiplying it out, determine how many digits are needed to write out this number using base-10
    Just adding a little explanation to CB's answer.
     2^{6972593} = 10^x

     6972593 \log(2) = x \log(10)

    \dfrac{ 6972593 \log(2)}{\log(10)} = x
    You will need to round x UP to the next integer to get the number of DIGITS in the decimal value.

    .
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by aidan View Post
    Just adding a little explanation to CB's answer.
     2^{6972593} = 10^x

     6972593 \log(2) = x \log(10)

    \dfrac{ 6972593 \log(2)}{\log(10)} = x
    You will need to round x UP to the next integer to get the number of DIGITS in the decimal value.

    .
    You will note that in my post I gave a hint on how to approach this, you should not add explanation to the hint untill there has been some response from the OP or at least something like 48 hours has ellapsed.

    CB
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Oct 2009
    Posts
    8
    Hey Guys,

    This is what I originally figured out:

    log(2)^1000000*6.972593, know that low log(2) ~ 0.3010

    therefore 1000000*.3010 ~ 300000 * 6.97 = 2.091*10^6

    However I think that would be considered multiplying it out, I just couldn't figure out any other way.

    Aidan I appreciate the explanation, just one question log(10) = 1 correct? assuming its base 10 and logb(b) = 1.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member
    Joined
    Oct 2009
    Posts
    82
    Quote Originally Posted by cndman View Post
    Hey Guys,

    This is what I originally figured out:

    log(2)^1000000*6.972593, know that low log(2) ~ 0.3010

    therefore 1000000*.3010 ~ 300000 * 6.97 = 2.091*10^6

    However I think that would be considered multiplying it out, I just couldn't figure out any other way.

    Aidan I appreciate the explanation, just one question log(10) = 1 correct? assuming its base 10 and logb(b) = 1.
    It doesn't matter what base you use, as long as you use the same base for log(2) and log(10). You could choose base 2 or base 10, or base e -- the ratio will remain constant.

    In fact, unless a base is specifically given, you should always assume the base is e in a mathematical context.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: May 3rd 2011, 03:22 PM
  2. Replies: 1
    Last Post: February 11th 2011, 03:52 AM
  3. Replies: 7
    Last Post: November 28th 2010, 09:22 PM
  4. number of combination of 8 digits number
    Posted in the Discrete Math Forum
    Replies: 4
    Last Post: April 7th 2008, 03:37 AM
  5. Finding digits of a prime
    Posted in the Number Theory Forum
    Replies: 4
    Last Post: October 2nd 2007, 11:48 PM

Search Tags


/mathhelpforum @mathhelpforum