May 3rd, 2017, 02:47 AM  #1 
Newbie Joined: May 2017 From: israel Posts: 4 Thanks: 1 Math Focus: number theory  interesting prime numbers
I will define the mirror of n : the mirror of 532 is 235, the mirror of 437 is 734 etc. We will say that the nth prime number is the prime in place n. I will define interesting primes as the prime in place n, which his mirror is the prime in place of the mirror of n. Examples: 2 3 5 7 11 37 73 are interesting primes. I couldn't find other interesting primes, are there? thank you very much, Danny. 
May 3rd, 2017, 04:19 AM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,574 Thanks: 931 Math Focus: Elementary mathematics and beyond 
101

May 3rd, 2017, 09:41 AM  #3 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 10,471 Thanks: 693 
101, 107, 113, ..... , 797, 919, 929 Total of 29 cases in range 100 to 999 
May 4th, 2017, 01:35 AM  #4  
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233  Quote:
If so , you missed 13 <> 31 , 17 <> 71 and 79 <> 97 Last edited by agentredlum; May 4th, 2017 at 01:38 AM.  
May 4th, 2017, 02:34 AM  #5 
Global Moderator Joined: Dec 2006 Posts: 17,919 Thanks: 1385 
You're missing the point. The primes 37 and 73 are the 12th and 21st primes.

May 4th, 2017, 09:09 AM  #6 
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233  
May 4th, 2017, 11:43 AM  #7 
Global Moderator Joined: Dec 2006 Posts: 17,919 Thanks: 1385 
Any singledigit number is its own "mirror".

May 4th, 2017, 04:44 PM  #8 
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233  
May 4th, 2017, 05:15 PM  #9 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 10,471 Thanks: 693  
May 4th, 2017, 07:35 PM  #10 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 10,471 Thanks: 693 
Leaving out the "already mirrored" (like 101), these are the only candidates using 3digit primes: prime(position): example: 107 is the 28th prime) 107(028 ),701(126) 113(030), 311(064) 149(035), 941(160) 157(037), 751(133) 167(039), 761(135) 179(041), 971(164) 199(046), 991(167) 337(068 ),733(130) 347(069), 743(132) 359(072), 953(162) 389(077), 983(166) 709(127), 907(155) 739(131), 937(159) 769(136), 967(163) Sooo....none qualify! 

Tags 
interesting, numbers, prime 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Has anyone analyzed non prime numbers? Exponents seem interesting.  Kensou77  Number Theory  13  April 30th, 2016 04:48 PM 
Interesting prime number sequence: (n^2)  (n1)  DavidGustafik  Number Theory  6  April 2nd, 2014 04:31 AM 
Mersenne Prime  Interesting Observation  curioso  Number Theory  4  January 31st, 2014 06:59 PM 
Interesting Prime Patterns  Wissam  Number Theory  20  November 1st, 2010 04:42 AM 
Interesting property of numbers?  xcloud  Number Theory  9  May 12th, 2010 04:42 AM 