It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 509 197 is not a prime number.
For example, 509 197 can be divided by 13: 509 197 / 13 = 39 169.
For 509 197 to be a prime number, it would have been required that 509 197 has only two divisors, i.e., itself and 1.
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509 197 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 509 197 is about 713.580.
Thus, the square root of 509 197 is not an integer, and therefore 509 197 is not a square number.
The square of a number (here 509 197) is the result of the product of this number (509 197) by itself (i.e., 509 197 × 509 197); the square of 509 197 is sometimes called "raising 509 197 to the power 2", or "509 197 squared".
The square of 509 197 is 259 281 584 809 because 509 197 × 509 197 = 509 1972 = 259 281 584 809.
As a consequence, 509 197 is the square root of 259 281 584 809.
The multiples of 509 197 are all integers evenly divisible by 509 197, that is all numbers such that the remainder of the division by 509 197 is zero. There are infinitely many multiples of 509 197. The smallest multiples of 509 197 are: