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May 3rd, 2017, 02:47 AM   #1
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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.
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May 3rd, 2017, 04:19 AM   #2
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101
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May 3rd, 2017, 09:41 AM   #3
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101, 107, 113, ..... , 797, 919, 929

Total of 29 cases in range 100 to 999
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May 4th, 2017, 01:35 AM   #4
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Quote:
Originally Posted by dannyh532 View Post
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 01:38 AM.
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May 4th, 2017, 02:34 AM   #5
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You're missing the point. The primes 37 and 73 are the 12th and 21st primes.
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May 4th, 2017, 09:09 AM   #6
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Quote:
Originally Posted by skipjack View Post
You're missing the point. The primes 37 and 73 are the 12th and 21st primes.
Ok , why is $ \ \ 7 \ \ $ on his list?
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May 4th, 2017, 11:43 AM   #7
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Any single-digit number is its own "mirror".
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May 4th, 2017, 04:44 PM   #8
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Quote:
Originally Posted by skipjack View Post
Any single-digit number is its own "mirror".
Ok , why is $ \ \ 13 \ \ $ not on his list?
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May 4th, 2017, 05:15 PM   #9
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Originally Posted by agentredlum View Post
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.
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May 4th, 2017, 07:35 PM   #10
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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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