It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 125 123 is not a prime number.
For example, 125 123 can be divided by 211: 125 123 / 211 = 593.
For 125 123 to be a prime number, it would have been required that 125 123 has only two divisors, i.e., itself and 1.
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125 123 is an odd number, because it is not evenly divisible by 2.
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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 125 123 is about 353.727.
Thus, the square root of 125 123 is not an integer, and therefore 125 123 is not a square number.
The square of a number (here 125 123) is the result of the product of this number (125 123) by itself (i.e., 125 123 × 125 123); the square of 125 123 is sometimes called "raising 125 123 to the power 2", or "125 123 squared".
The square of 125 123 is 15 655 765 129 because 125 123 × 125 123 = 125 1232 = 15 655 765 129.
As a consequence, 125 123 is the square root of 15 655 765 129.
The multiples of 125 123 are all integers evenly divisible by 125 123, that is all numbers such that the remainder of the division by 125 123 is zero. There are infinitely many multiples of 125 123. The smallest multiples of 125 123 are: