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Find a prime divisor of 1111 (13 1's)

  1. Oct 30, 2011 #1
    Hello friends,
    The problem I am trying to solve sounds simple, but I still haven't been able to find the solution:
    Find a prime divisor of 1111111111111 (13 ones), also known as a repunit.
    I know the answer(53, 79 and some big prime), but I have no idea how Mathematica calculated those values.
    Can anyone help me out? :)

    I am afraid I should've posted this question in the number theory forums, sorry for that.
  2. jcsd
  3. Oct 30, 2011 #2

    I like Serena

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    Hi mathmadx! :smile:

    As far as I know we're still stuck with trial and error to find prime divisors.
    Try each odd number up to the square root and see if it's a divisor.
    If you've found one, divide the number and repeat.
  4. Oct 30, 2011 #3
    An interesting, but probably useless fact from http://en.wikipedia.org/wiki/Repunit" [Broken]:
    where [itex]R_i[/itex] is the repunit with i ones. Unfortunately, you're dealing with [itex] R_{13} [/itex] and 13 is prime...
    Last edited by a moderator: May 5, 2017
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