All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Numbers
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.)
re(2): Another proof | Comment 9 of 10 |
(In reply to re: Another proof - not a proof by Ady TZIDON)

I don't understand the problem. In this case, "q=p(y) with x-1 zeroes placed between each pair of adjacent ones" results in q depending on x and y.

If you set x=3, y=2, then p(x)=111 as you mention. However q=1001 in this case, as p(y)=11 and placing x-1=2 zeroes between each pair of ones results in 1001.

  Posted by Gamer on 2011-01-11 14:16:32

Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (1)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2018 by Animus Pactum Consulting. All rights reserved. Privacy Information