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 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. Thanks from greg1313
 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
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Quote:
 Originally Posted by dannyh532 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.
Not sure I understand your definition. Are you listing primes whose mirror is also prime?

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. Thanks from greg1313
May 4th, 2017, 10:09 AM   #6
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Quote:
 Originally Posted by skipjack You're missing the point. The primes 37 and 73 are the 12th and 21st primes.
Ok , why is $\ \ 7 \ \$ on his list?

 May 4th, 2017, 12:43 PM #7 Global Moderator   Joined: Dec 2006 Posts: 18,145 Thanks: 1418 Any single-digit number is its own "mirror".
May 4th, 2017, 05:44 PM   #8
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Quote:
 Originally Posted by skipjack Any single-digit number is its own "mirror".
Ok , why is $\ \ 13 \ \$ not on his list?

May 4th, 2017, 06:15 PM   #9
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Quote:
 Originally Posted by agentredlum Ok , why is $\ \ 13 \ \$ not on his list?
If I understand this silliness properly:
13 = 6th prime
31 = 11th prime

31 is mirror of 13, but 11 is not mirror of 6.

The problem is very obscurely worded.

 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! Thanks from agentredlum

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