It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 509 031 is not a prime number.
For example, 509 031 can be divided by 3: 509 031 / 3 = 169 677.
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For 509 031 to be a prime number, it would have been required that 509 031 has only two divisors, i.e., itself and 1.
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509 031 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 509 031 is about 713.464.
Thus, the square root of 509 031 is not an integer, and therefore 509 031 is not a square number.
The square of a number (here 509 031) is the result of the product of this number (509 031) by itself (i.e., 509 031 × 509 031); the square of 509 031 is sometimes called "raising 509 031 to the power 2", or "509 031 squared".
The square of 509 031 is 259 112 558 961 because 509 031 × 509 031 = 509 0312 = 259 112 558 961.
As a consequence, 509 031 is the square root of 259 112 558 961.
The multiples of 509 031 are all integers evenly divisible by 509 031, that is all numbers such that the remainder of the division by 509 031 is zero. There are infinitely many multiples of 509 031. The smallest multiples of 509 031 are: