Reversible Prime Squares

Both $169$ and $961$ are the square of a prime. $169$ is the reverse of $961$.

We call a number a reversible prime square if:

It is not a palindrome, and
It is the square of a prime, and
Its reverse is also the square of a prime.

$169$ and $961$ are not palindromes, so both are reversible prime squares.

Find the sum of the first $50$ reversible prime squares.

This is an interesting problem, but it actually can’t be solved explicitly, because currently there are not even 50 known reversible prime squares. As a matter of fact, only 4 are known so far: 13^2 = 169, 31^2 = 961, 37^2 = 1369, and 73^2 = 5329.

When the digits of these perfect squares are reversed, the resulting numbers are also perfect squares of prime numbers: 31^2 = 961, 13^2 = 169, 31^2 = 961, and 23^2 = 529.

Again, while it’s possible that more reversible prime squares exist, they’re incredibly rare and as of now, no more than these 4 have been found.

If you’re looking for the sum of the known reversible prime squares (169, 961, 1369, 5329), that would be:

169 + 961 + 1369 + 5329 = 7828.

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