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

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In summary, the conversation discusses the problem of finding a prime divisor of 1111111111111, also known as a repunit. The asker knows the answer (53, 79 and some big prime), but is unsure how Mathematica calculated those values. The conversation also mentions using trial and error to find prime divisors and an interesting fact about repunits. The conversation concludes with the asker expressing regret for not posting the question in a number theory forum.
  • #1
mathmadx
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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.
 
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  • #2
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
An interesting, but probably useless fact from http://en.wikipedia.org/wiki/Repunit" :
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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1. What is a prime divisor?

A prime divisor is a number that evenly divides another number without leaving a remainder, and is itself a prime number. In other words, it is a factor of a number that is also a prime number.

2. How many prime divisors does 1111 (13 1's) have?

1111 (13 1's) has four prime divisors: 11, 101, 111, and 1001.

3. How do I find a prime divisor of 1111 (13 1's)?

To find a prime divisor of 1111 (13 1's), you can use a method called prime factorization. This involves breaking down the number into its prime factors until all of the factors are prime numbers. In the case of 1111 (13 1's), you could start by dividing it by 11, which is a prime number. This would leave you with 101, which is also a prime number. Therefore, 1111 (13 1's) has two prime divisors: 11 and 101.

4. Is 1111 (13 1's) a prime number?

No, 1111 (13 1's) is not a prime number. A prime number is a number that only has two divisors: 1 and itself. 1111 (13 1's) has more than two divisors, including 11, 101, 111, and 1001, therefore it is not a prime number.

5. Why is it important to find a prime divisor of 1111 (13 1's)?

Finding prime divisors of a number is important in many mathematical and scientific applications. Prime numbers and their divisors are the building blocks of all numbers, and understanding their properties can help in solving complex mathematical problems. In addition, prime numbers have many practical applications, such as in cryptography and computer security.

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