It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 509 398 is not a prime number.
For example, 509 398 can be divided by 2: 509 398 / 2 = 254 699.
For 509 398 to be a prime number, it would have been required that 509 398 has only two divisors, i.e., itself and 1.
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509 398 is an even number, because it is evenly divisible by 2: 509 398 / 2 = 254 699.
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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 509 398 is about 713.721.
Thus, the square root of 509 398 is not an integer, and therefore 509 398 is not a square number.
The square of a number (here 509 398) is the result of the product of this number (509 398) by itself (i.e., 509 398 × 509 398); the square of 509 398 is sometimes called "raising 509 398 to the power 2", or "509 398 squared".
The square of 509 398 is 259 486 322 404 because 509 398 × 509 398 = 509 3982 = 259 486 322 404.
As a consequence, 509 398 is the square root of 259 486 322 404.
The multiples of 509 398 are all integers evenly divisible by 509 398, that is all numbers such that the remainder of the division by 509 398 is zero. There are infinitely many multiples of 509 398. The smallest multiples of 509 398 are: