## Concatenations: (A,B,C) squares and primes — Part 2

Find triples   $(A, \; B, \; C)$   such that

$A$   is a perfect square.
$B$   and   $C$   are prime numbers,   and

$A \; || \; B$   and   $A \; || \; C$   are prime numbers and
$B \; || \; A$   and   $C \; || \; A$   are perfect squares

For example,

$3481956 \; = \; 1866^2$   is a perfect square.
$9649$   is a prime number.
$624067$   is a prime number.

$3481956 \; || \; 9649 \; = \; 34819569649$   is a prime number.
$3481956 \; || \; 624067 \; = \; 3481956624067$   is a prime number.

$9649 \; || \; 3481956 \; = \; 96493481956 \; = \; 310634^2$   is a perfect square.
$624067 \; || \; 3481956 \; = \; 6240673481956 \; = \; 2498134^2$   is a perfect square.