It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 509 309 is not a prime number.
For example, 509 309 can be divided by 239: 509 309 / 239 = 2 131.
For 509 309 to be a prime number, it would have been required that 509 309 has only two divisors, i.e., itself and 1.
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509 309 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 509 309 is about 713.659.
Thus, the square root of 509 309 is not an integer, and therefore 509 309 is not a square number.
The square of a number (here 509 309) is the result of the product of this number (509 309) by itself (i.e., 509 309 × 509 309); the square of 509 309 is sometimes called "raising 509 309 to the power 2", or "509 309 squared".
The square of 509 309 is 259 395 657 481 because 509 309 × 509 309 = 509 3092 = 259 395 657 481.
As a consequence, 509 309 is the square root of 259 395 657 481.
The multiples of 509 309 are all integers evenly divisible by 509 309, that is all numbers such that the remainder of the division by 509 309 is zero. There are infinitely many multiples of 509 309. The smallest multiples of 509 309 are: