It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 509 506 is not a prime number.
For example, 509 506 can be divided by 2: 509 506 / 2 = 254 753.
For 509 506 to be a prime number, it would have been required that 509 506 has only two divisors, i.e., itself and 1.
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509 506 is an even number, because it is evenly divisible by 2: 509 506 / 2 = 254 753.
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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 509 506 is about 713.797.
Thus, the square root of 509 506 is not an integer, and therefore 509 506 is not a square number.
The square of a number (here 509 506) is the result of the product of this number (509 506) by itself (i.e., 509 506 × 509 506); the square of 509 506 is sometimes called "raising 509 506 to the power 2", or "509 506 squared".
The square of 509 506 is 259 596 364 036 because 509 506 × 509 506 = 509 5062 = 259 596 364 036.
As a consequence, 509 506 is the square root of 259 596 364 036.
The multiples of 509 506 are all integers evenly divisible by 509 506, that is all numbers such that the remainder of the division by 509 506 is zero. There are infinitely many multiples of 509 506. The smallest multiples of 509 506 are: