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

  • Thread starter mathmadx
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  • #1
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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.
 

Answers and Replies

  • #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.
 
  • #3
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An interesting, but probably useless fact from http://en.wikipedia.org/wiki/Repunit" [Broken]:
It is easy to show that if n is divisible by a, then [itex]R_n[/itex] is divisible by [itex]R_a[/itex]:
where [itex]R_i[/itex] is the repunit with i ones. Unfortunately, you're dealing with [itex] R_{13} [/itex] and 13 is prime...
 
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