Problems & Puzzles: Puzzles

Puzzle 586. 73 is the best prime

Perhaps you already know the popular Dr. Sheldon Cooper's claim:

"The best number is 73. Why? 73 is the 21st prime number. Its mirror (37) is the 12th and its mirror (21)

In our terms:

If n=12, p(r(n))=r(p(n))........(1)

Q. Can you get a larger solution for (1) or prove that there are no more solutions for n>12?

Note1: non-elegant solutions come when n & p(n) are both palindromes. Here we do not consider these solutions that -BTW- are the matter of our old Puzzle 51 that remains stuck since 2003!!!

Note2: I should thank to my friend Jaime Ayala for let me know about this popular claim.


Contribution came from Emmanuel Vantieghem


Emmanuel wrote:

I think there might be other 'elegant' primes like  37, but then these will be greater than  9196155337


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