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Scarce primes (Posted on 2011-01-10) Difficulty: 2 of 5
A repunit is a number consisting solely of ones (such as 11 or 11111).
Let us call p(n) a 10-base integer represented by a string of n ones, e.g. p(1)=1, p(5)=11111 etc.
Most of the repunit numbers are composite.
2, 19,23,317 are the first four indices of prime repunits.

Prove: For a prime repunit p(n) to be prime, n has to be prime.

No Solution Yet Submitted by Ady TZIDON    
Rating: 3.6667 (3 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts re(3): proof, ok! | Comment 8 of 10 |
(In reply to re(2): proof by Jer)

Nothing wrong with your proof, I agree with all your statements, as the Bard said..."to the selfsame tune and words".

 

Whatever I added was a remark , to distinguishb between necessary and sufficent-  with no claim re anything you wrote.

To sum uo:  conrapositives are of equal weight.

 


  Posted by Ady TZIDON on 2011-01-11 12:43:46
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