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

Home > Numbers
A fun prime number (Posted on 2011-02-15) Difficulty: 2 of 5
Find a prime number such that every two consecutive digits are a square number.

See The Solution Submitted by Math Man    
Rating: 5.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution solution (spoiler) | Comment 1 of 4

The only 2-digit squares are 16, 25, 36, 49, 64 and 81.

These can be chained together in two ways before no longer being able to add to the chain: 81649 and 3649, as there is no 2-digit square beginning with a 9 or ending with an 8 or a 3.  A choice had come up before the 649, as two squares end with 6: 16 and 36.

Obviously any prime subset of these strings must have at least three digits, as any two digits constitute a square rather than a prime, and of course it must end in an odd digit. Candidates are the two strings themselves, 81649 and 3649, and 1649 and 649. Of these, only 81649 is prime, and is the answer.

3649 = 41*89
1649 = 17*97
649 = 11*59
81649 is prime.

  Posted by Charlie on 2011-02-15 19:12:02
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 (4)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

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