It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 509 212 is not a prime number.
For example, 509 212 can be divided by 2: 509 212 / 2 = 254 606.
For 509 212 to be a prime number, it would have been required that 509 212 has only two divisors, i.e., itself and 1.
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509 212 is an even number, because it is evenly divisible by 2: 509 212 / 2 = 254 606.
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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 509 212 is about 713.591.
Thus, the square root of 509 212 is not an integer, and therefore 509 212 is not a square number.
The square of a number (here 509 212) is the result of the product of this number (509 212) by itself (i.e., 509 212 × 509 212); the square of 509 212 is sometimes called "raising 509 212 to the power 2", or "509 212 squared".
The square of 509 212 is 259 296 860 944 because 509 212 × 509 212 = 509 2122 = 259 296 860 944.
As a consequence, 509 212 is the square root of 259 296 860 944.
The multiples of 509 212 are all integers evenly divisible by 509 212, that is all numbers such that the remainder of the division by 509 212 is zero. There are infinitely many multiples of 509 212. The smallest multiples of 509 212 are: