It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 5 124 311 is not a prime number.
For example, 5 124 311 can be divided by 877: 5 124 311 / 877 = 5 843.
For 5 124 311 to be a prime number, it would have been required that 5 124 311 has only two divisors, i.e., itself and 1.
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5 124 311 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 5 124 311 is about 2 263.694.
Thus, the square root of 5 124 311 is not an integer, and therefore 5 124 311 is not a square number.
The square of a number (here 5 124 311) is the result of the product of this number (5 124 311) by itself (i.e., 5 124 311 × 5 124 311); the square of 5 124 311 is sometimes called "raising 5 124 311 to the power 2", or "5 124 311 squared".
The square of 5 124 311 is 26 258 563 224 721 because 5 124 311 × 5 124 311 = 5 124 3112 = 26 258 563 224 721.
As a consequence, 5 124 311 is the square root of 26 258 563 224 721.
The multiples of 5 124 311 are all integers evenly divisible by 5 124 311, that is all numbers such that the remainder of the division by 5 124 311 is zero. There are infinitely many multiples of 5 124 311. The smallest multiples of 5 124 311 are: