It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 509 259 is not a prime number.
For example, 509 259 can be divided by 3: 509 259 / 3 = 169 753.
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For 509 259 to be a prime number, it would have been required that 509 259 has only two divisors, i.e., itself and 1.
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509 259 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 509 259 is about 713.624.
Thus, the square root of 509 259 is not an integer, and therefore 509 259 is not a square number.
The square of a number (here 509 259) is the result of the product of this number (509 259) by itself (i.e., 509 259 × 509 259); the square of 509 259 is sometimes called "raising 509 259 to the power 2", or "509 259 squared".
The square of 509 259 is 259 344 729 081 because 509 259 × 509 259 = 509 2592 = 259 344 729 081.
As a consequence, 509 259 is the square root of 259 344 729 081.
The multiples of 509 259 are all integers evenly divisible by 509 259, that is all numbers such that the remainder of the division by 509 259 is zero. There are infinitely many multiples of 509 259. The smallest multiples of 509 259 are: