It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 509 231 is not a prime number.
For example, 509 231 can be divided by 37: 509 231 / 37 = 13 763.
For 509 231 to be a prime number, it would have been required that 509 231 has only two divisors, i.e., itself and 1.
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509 231 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 509 231 is about 713.604.
Thus, the square root of 509 231 is not an integer, and therefore 509 231 is not a square number.
The square of a number (here 509 231) is the result of the product of this number (509 231) by itself (i.e., 509 231 × 509 231); the square of 509 231 is sometimes called "raising 509 231 to the power 2", or "509 231 squared".
The square of 509 231 is 259 316 211 361 because 509 231 × 509 231 = 509 2312 = 259 316 211 361.
As a consequence, 509 231 is the square root of 259 316 211 361.
The multiples of 509 231 are all integers evenly divisible by 509 231, that is all numbers such that the remainder of the division by 509 231 is zero. There are infinitely many multiples of 509 231. The smallest multiples of 509 231 are: