Results 1 to 4 of 4

Math Help - What kind is an algorithm that opens large natural number exponents?

  1. #1
    Newbie
    Joined
    Jan 2013
    From
    Europe
    Posts
    20

    What kind is an algorithm that opens large natural number exponents?

    Hello everybody!
    This is my 1st question in this forum.
    I have passed just high-school level mathematics, so I would appreciate an answer that is understandable to such educational level of a person.
    Time to time they say in popular science math books, that a large exponent number is such and such in length, for example 3^7146 contains 1846678925 integers or so (this is not a real example, I just put those numbers in screen here). They may also tell us that the last integer is, say, "9".
    I would like to know, what kind is an algorithm they really use in their computers? It is hard for me to believe that they use naive repetitive multiplications time after time?
    My question consearns expecially integer or natural number base numbers and exponents.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor ebaines's Avatar
    Joined
    Jun 2008
    From
    Illinois
    Posts
    1,153
    Thanks
    348

    Re: What kind is an algorithm that opens large natural number exponents?

    You can determine the number of integers in 3^7146 by doing the following calculation:

    3^7146 = 10^y

    The value of 'y' rounded up to the next highest integer is the number of integers you are looking for.

    3^7147 = [3^(log_3 10)] ^ y = 3^[log_3 10)*y]

    So y = 7147/(log_3 10) = 7147/2.059 = 3409.986. Hence 3^7147 has 3410 digits.

    As for what the last digit is, if you write out the powers of 3 you will see a pattern where the last digit cycles through 3, 9, 7, 1, ... Since 7147 is divisible by 4 with a remainder of 3, the last digit is 7.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jan 2013
    From
    Europe
    Posts
    20

    Re: What kind is an algorithm that opens large natural number exponents?

    Thank You for quick and helpful answer.
    (My calculator says that log_3 10 is about 2,095..., not 2,059..., but I guess that is just a keyboard error?)
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor ebaines's Avatar
    Joined
    Jun 2008
    From
    Illinois
    Posts
    1,153
    Thanks
    348

    Re: What kind is an algorithm that opens large natural number exponents?

    Quote Originally Posted by kpkkpk View Post
    Thank You for quick and helpful answer.
    (My calculator says that log_3 10 is about 2,095..., not 2,059..., but I guess that is just a keyboard error?)

    Yes, keyboard error: log_3 10 = 2.095903....
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Calculate number of digits in large number
    Posted in the Advanced Math Topics Forum
    Replies: 1
    Last Post: January 2nd 2013, 07:14 AM
  2. Replies: 0
    Last Post: June 20th 2011, 02:37 PM
  3. large exponents with fermats little theorem
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: February 24th 2010, 08:53 PM
  4. Solving congruences for large exponents and mods
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: November 17th 2009, 09:01 AM
  5. perform basic operations on large numbers algorithm?
    Posted in the Advanced Math Topics Forum
    Replies: 2
    Last Post: October 17th 2008, 09:50 AM

Search Tags


/mathhelpforum @mathhelpforum