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

Home > Numbers
Prime it remains (Posted on 2013-01-15) Difficulty: 3 of 5
What is the smallest prime remaining prime when added to its reverse?

Analytical solution preferred.

No Solution Yet Submitted by Ady TZIDON    
Rating: 4.0000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Some observations and an answer | Comment 2 of 4 |
observation 1) It can't be a single digit, because the resulting sum is divisible by 2

observation 2) It can't have an even number of digits, because the resulting sum is divisible by 11.  Using a mod 11 test, the number and its reverse necessarily have opposing signs.  For instance, consider 1019. The odd digits minus the even ones = 7.  Its reverse is 9101, for which the odd digits minus the even ones = -7 .  So the sum, 10120, is necessarily divisible by 11.

observation 3) It can't have an initial odd digit, because the resulting sum is necessarily divisible by 2.

Using a prime number table, that makes the first 4 candidates 211 223 227 229 .

211 + 112 = 323, which is a multiple of 17
223 + 322 = 545, which is a multiple of 5
227 + 722 = 949, which is a multiple of 13
229 + 922 = 1151, which is prime number, so our answer is 229
 

Edited on January 15, 2013, 6:09 pm
  Posted by Steve Herman on 2013-01-15 18:08:25

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 (2)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information