May 3rd, 2017, 03:47 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, 05:19 AM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,641 Thanks: 959 Math Focus: Elementary mathematics and beyond 
101

May 3rd, 2017, 10:41 AM  #3 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 10,898 Thanks: 716 
101, 107, 113, ..... , 797, 919, 929 Total of 29 cases in range 100 to 999 
May 4th, 2017, 02:35 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 02:38 AM.  
May 4th, 2017, 03:34 AM  #5 
Global Moderator Joined: Dec 2006 Posts: 18,145 Thanks: 1418 
You're missing the point. The primes 37 and 73 are the 12th and 21st primes.

May 4th, 2017, 10:09 AM  #6 
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233  
May 4th, 2017, 12:43 PM  #7 
Global Moderator Joined: Dec 2006 Posts: 18,145 Thanks: 1418 
Any singledigit number is its own "mirror".

May 4th, 2017, 05:44 PM  #8 
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233  
May 4th, 2017, 06:15 PM  #9 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 10,898 Thanks: 716  
May 4th, 2017, 08:35 PM  #10 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 10,898 Thanks: 716 
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! 

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interesting, numbers, prime 
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