It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 5 108 123 is not a prime number.
For example, 5 108 123 can be divided by 179: 5 108 123 / 179 = 28 537.
For 5 108 123 to be a prime number, it would have been required that 5 108 123 has only two divisors, i.e., itself and 1.
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5 108 123 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 5 108 123 is about 2 260.116.
Thus, the square root of 5 108 123 is not an integer, and therefore 5 108 123 is not a square number.
The square of a number (here 5 108 123) is the result of the product of this number (5 108 123) by itself (i.e., 5 108 123 × 5 108 123); the square of 5 108 123 is sometimes called "raising 5 108 123 to the power 2", or "5 108 123 squared".
The square of 5 108 123 is 26 092 920 583 129 because 5 108 123 × 5 108 123 = 5 108 1232 = 26 092 920 583 129.
As a consequence, 5 108 123 is the square root of 26 092 920 583 129.
The multiples of 5 108 123 are all integers evenly divisible by 5 108 123, that is all numbers such that the remainder of the division by 5 108 123 is zero. There are infinitely many multiples of 5 108 123. The smallest multiples of 5 108 123 are: