It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 509 331 is not a prime number.
For example, 509 331 can be divided by 3: 509 331 / 3 = 169 777.
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For 509 331 to be a prime number, it would have been required that 509 331 has only two divisors, i.e., itself and 1.
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509 331 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 509 331 is about 713.674.
Thus, the square root of 509 331 is not an integer, and therefore 509 331 is not a square number.
The square of a number (here 509 331) is the result of the product of this number (509 331) by itself (i.e., 509 331 × 509 331); the square of 509 331 is sometimes called "raising 509 331 to the power 2", or "509 331 squared".
The square of 509 331 is 259 418 067 561 because 509 331 × 509 331 = 509 3312 = 259 418 067 561.
As a consequence, 509 331 is the square root of 259 418 067 561.
The multiples of 509 331 are all integers evenly divisible by 509 331, that is all numbers such that the remainder of the division by 509 331 is zero. There are infinitely many multiples of 509 331. The smallest multiples of 509 331 are: