It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 504 409 is not a prime number.
For example, 504 409 can be divided by 61: 504 409 / 61 = 8 269.
For 504 409 to be a prime number, it would have been required that 504 409 has only two divisors, i.e., itself and 1.
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504 409 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 504 409 is about 710.218.
Thus, the square root of 504 409 is not an integer, and therefore 504 409 is not a square number.
The square of a number (here 504 409) is the result of the product of this number (504 409) by itself (i.e., 504 409 × 504 409); the square of 504 409 is sometimes called "raising 504 409 to the power 2", or "504 409 squared".
The square of 504 409 is 254 428 439 281 because 504 409 × 504 409 = 504 4092 = 254 428 439 281.
As a consequence, 504 409 is the square root of 254 428 439 281.
The multiples of 504 409 are all integers evenly divisible by 504 409, that is all numbers such that the remainder of the division by 504 409 is zero. There are infinitely many multiples of 504 409. The smallest multiples of 504 409 are: