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

Home > Numbers
Binary Primes (Posted on 2004-02-18) Difficulty: 4 of 5
How many primes, written in usual base 10, have digits that are alternating 1s and 0s, beginning and ending with one?

For example (not necessarily prime):
1, 101, 10101, ...

  Submitted by Aaron    
Rating: 3.5000 (2 votes)
Solution: (Hide)
The numbers are (10^(2n)-1)/99 but 10^(2n)-1 = (10^n-1)*(10^n+1).

So the only way you'll get a prime is if one of those two factors is 99.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolutionPuzzle Solution K Sengupta2022-08-27 02:20:04
SolutionsolutionDej Mar2011-06-22 05:56:06
re: Another thoughtWAyne2007-09-30 06:26:58
re: Oh god! I read the question wrong.Brian Wainscott2004-02-23 15:25:28
OK I swear this is the last time!Mitch Mullings2004-02-22 21:01:21
Oh god! I read the question wrong.Mitch Mullings2004-02-22 20:59:37
It's me again adding to my previous entryMitch Mullings2004-02-22 20:57:19
It's me! Mwahahahaha. Okay I'll stop now.Mitch Mullings2004-02-22 20:54:46
re: No SubjectBrian Wainscott2004-02-18 19:03:50
SolutionNo Subjecte.g.2004-02-18 15:25:11
Second thoughtLarry2004-02-18 14:25:58
Another thoughtBrian Wainscott2004-02-18 14:25:17
First thoughtBrian Wainscott2004-02-18 14:20:32
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (13)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2024 by Animus Pactum Consulting. All rights reserved. Privacy Information