perplexus.info :: Numbers : Repunits and bases

Repunits and bases (Posted on 2013-07-24)

11₂=3 and 111₃=13 are prime. However, 1111₄=85=5*17 and 11111₅=781=11*71 are not prime. What is the least number n>3 such that the repunit consisting of n 1's in base n is prime?

See The Solution Submitted by Math Man

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re(2): Answer:

| Comment 4 of 6 |

(In reply to re: Answer: by Charlie)

Good question, Charlie!

It is obvious to me that only odd values of n need to be checked.

If n = 2k, then ((2k)^(2k))-1 can be factored into

(((2k)^(k))-1) * (((2k)^(k))+1),

and x is not going to be prime if k > 1

Posted by Steve Herman on 2013-07-24 12:53:15

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