It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 509 609 is not a prime number.
For example, 509 609 can be divided by 17: 509 609 / 17 = 29 977.
For 509 609 to be a prime number, it would have been required that 509 609 has only two divisors, i.e., itself and 1.
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509 609 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 509 609 is about 713.869.
Thus, the square root of 509 609 is not an integer, and therefore 509 609 is not a square number.
The square of a number (here 509 609) is the result of the product of this number (509 609) by itself (i.e., 509 609 × 509 609); the square of 509 609 is sometimes called "raising 509 609 to the power 2", or "509 609 squared".
The square of 509 609 is 259 701 332 881 because 509 609 × 509 609 = 509 6092 = 259 701 332 881.
As a consequence, 509 609 is the square root of 259 701 332 881.
The multiples of 509 609 are all integers evenly divisible by 509 609, that is all numbers such that the remainder of the division by 509 609 is zero. There are infinitely many multiples of 509 609. The smallest multiples of 509 609 are: