It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 5 126 509 is not a prime number.
For example, 5 126 509 can be divided by 173: 5 126 509 / 173 = 29 633.
For 5 126 509 to be a prime number, it would have been required that 5 126 509 has only two divisors, i.e., itself and 1.
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5 126 509 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 5 126 509 is about 2 264.180.
Thus, the square root of 5 126 509 is not an integer, and therefore 5 126 509 is not a square number.
The square of a number (here 5 126 509) is the result of the product of this number (5 126 509) by itself (i.e., 5 126 509 × 5 126 509); the square of 5 126 509 is sometimes called "raising 5 126 509 to the power 2", or "5 126 509 squared".
The square of 5 126 509 is 26 281 094 527 081 because 5 126 509 × 5 126 509 = 5 126 5092 = 26 281 094 527 081.
As a consequence, 5 126 509 is the square root of 26 281 094 527 081.
The multiples of 5 126 509 are all integers evenly divisible by 5 126 509, that is all numbers such that the remainder of the division by 5 126 509 is zero. There are infinitely many multiples of 5 126 509. The smallest multiples of 5 126 509 are: