It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 509 191 is not a prime number.
For example, 509 191 can be divided by 349: 509 191 / 349 = 1 459.
For 509 191 to be a prime number, it would have been required that 509 191 has only two divisors, i.e., itself and 1.
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509 191 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 509 191 is about 713.576.
Thus, the square root of 509 191 is not an integer, and therefore 509 191 is not a square number.
The square of a number (here 509 191) is the result of the product of this number (509 191) by itself (i.e., 509 191 × 509 191); the square of 509 191 is sometimes called "raising 509 191 to the power 2", or "509 191 squared".
The square of 509 191 is 259 275 474 481 because 509 191 × 509 191 = 509 1912 = 259 275 474 481.
As a consequence, 509 191 is the square root of 259 275 474 481.
The multiples of 509 191 are all integers evenly divisible by 509 191, that is all numbers such that the remainder of the division by 509 191 is zero. There are infinitely many multiples of 509 191. The smallest multiples of 509 191 are: