It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 509 409 is not a prime number.
For example, 509 409 can be divided by 3: 509 409 / 3 = 169 803.
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For 509 409 to be a prime number, it would have been required that 509 409 has only two divisors, i.e., itself and 1.
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509 409 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 509 409 is about 713.729.
Thus, the square root of 509 409 is not an integer, and therefore 509 409 is not a square number.
The square of a number (here 509 409) is the result of the product of this number (509 409) by itself (i.e., 509 409 × 509 409); the square of 509 409 is sometimes called "raising 509 409 to the power 2", or "509 409 squared".
The square of 509 409 is 259 497 529 281 because 509 409 × 509 409 = 509 4092 = 259 497 529 281.
As a consequence, 509 409 is the square root of 259 497 529 281.
The multiples of 509 409 are all integers evenly divisible by 509 409, that is all numbers such that the remainder of the division by 509 409 is zero. There are infinitely many multiples of 509 409. The smallest multiples of 509 409 are: