It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 509 663 is not a prime number.
For example, 509 663 can be divided by 7: 509 663 / 7 = 72 809.
For 509 663 to be a prime number, it would have been required that 509 663 has only two divisors, i.e., itself and 1.
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509 663 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 509 663 is about 713.907.
Thus, the square root of 509 663 is not an integer, and therefore 509 663 is not a square number.
The square of a number (here 509 663) is the result of the product of this number (509 663) by itself (i.e., 509 663 × 509 663); the square of 509 663 is sometimes called "raising 509 663 to the power 2", or "509 663 squared".
The square of 509 663 is 259 756 373 569 because 509 663 × 509 663 = 509 6632 = 259 756 373 569.
As a consequence, 509 663 is the square root of 259 756 373 569.
The multiples of 509 663 are all integers evenly divisible by 509 663, that is all numbers such that the remainder of the division by 509 663 is zero. There are infinitely many multiples of 509 663. The smallest multiples of 509 663 are: