A 2-digit integer
$\overline{ab}$
is called "
*
beautiful
*
" if:

- $\overline{ab}$ is a prime.
- There is a square has 2 last digits is $\overline{ab}$

Find the sum of possible values of $\overline{ab}$ .

**
Note:
**
$a$
can be equal
$0$
.

The answer is 220.

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First we check that if $\overline{02}$ can be a 'tail' of square, which clearly not.

So from $\overline{ab}$ is a prime, $b=1,3,7,9$ .

Since it is a tail of square, $b=1,9$ .

$\therefore a$ is even.

Check them all and we will have answer $=41+61+29+89=220$ .