Actually, one can immediately see that 105 386 405 cannot be prime, because 5 is one of its divisors: indeed, a number ending with 0 or 5 has necessarily 5 among its divisors.
The last digit of 105 386 405 is 5, so it is divisible by 5 and is therefore not prime.
For 105 386 405 to be a prime number, it would have been required that 105 386 405 has only two divisors, i.e., itself and 1.
A number is a perfect square (or a square number) if its square root is an integer; that is to say, it is the product of an integer with itself. Here, the square root of 105 386 405 is about 10 265.788.