It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 504 401 is not a prime number.
For example, 504 401 can be divided by 31: 504 401 / 31 = 16 271.
For 504 401 to be a prime number, it would have been required that 504 401 has only two divisors, i.e., itself and 1.
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504 401 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 504 401 is about 710.212.
Thus, the square root of 504 401 is not an integer, and therefore 504 401 is not a square number.
The square of a number (here 504 401) is the result of the product of this number (504 401) by itself (i.e., 504 401 × 504 401); the square of 504 401 is sometimes called "raising 504 401 to the power 2", or "504 401 squared".
The square of 504 401 is 254 420 368 801 because 504 401 × 504 401 = 504 4012 = 254 420 368 801.
As a consequence, 504 401 is the square root of 254 420 368 801.
The multiples of 504 401 are all integers evenly divisible by 504 401, that is all numbers such that the remainder of the division by 504 401 is zero. There are infinitely many multiples of 504 401. The smallest multiples of 504 401 are: