It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 509 412 is not a prime number.
For example, 509 412 can be divided by 2: 509 412 / 2 = 254 706.
For 509 412 to be a prime number, it would have been required that 509 412 has only two divisors, i.e., itself and 1.
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509 412 is an even number, because it is evenly divisible by 2: 509 412 / 2 = 254 706.
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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 509 412 is about 713.731.
Thus, the square root of 509 412 is not an integer, and therefore 509 412 is not a square number.
The square of a number (here 509 412) is the result of the product of this number (509 412) by itself (i.e., 509 412 × 509 412); the square of 509 412 is sometimes called "raising 509 412 to the power 2", or "509 412 squared".
The square of 509 412 is 259 500 585 744 because 509 412 × 509 412 = 509 4122 = 259 500 585 744.
As a consequence, 509 412 is the square root of 259 500 585 744.
The multiples of 509 412 are all integers evenly divisible by 509 412, that is all numbers such that the remainder of the division by 509 412 is zero. There are infinitely many multiples of 509 412. The smallest multiples of 509 412 are: