Reversible Primes
How many two-digit primes are there between 10 and 99 which are also prime when reversed?
Age
11 to 14
Challenge level
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