Reversible primes
How many two-digit primes are there between 10 and 99 which are also prime when reversed?
Problem
The integer 113 is prime, and its reverse, 311, is also prime.
How many two-digit primes are there between 10 and 99 which have the same property?
This problem is taken from the UKMT Mathematical Challenges.
Student Solutions
Answer: 9
2 __, 4 __, 6 __, 8 __
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1 __
11: reverse 11
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13: reverse 31
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15 not prime
17: reverse 71
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19: reverse 91 = 7$\times$13
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31: already counted as 13
33, 35 not prime
37: reverse 73
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39 not prime
5 __
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77 not prime
79: reverse 97
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9 __ already counted via reverse (except for 99, not prime)
5 ticks which are 4 pairs plus 11
Total 9