It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 509 508 is not a prime number.
For example, 509 508 can be divided by 2: 509 508 / 2 = 254 754.
For 509 508 to be a prime number, it would have been required that 509 508 has only two divisors, i.e., itself and 1.
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509 508 is an even number, because it is evenly divisible by 2: 509 508 / 2 = 254 754.
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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 509 508 is about 713.798.
Thus, the square root of 509 508 is not an integer, and therefore 509 508 is not a square number.
The square of a number (here 509 508) is the result of the product of this number (509 508) by itself (i.e., 509 508 × 509 508); the square of 509 508 is sometimes called "raising 509 508 to the power 2", or "509 508 squared".
The square of 509 508 is 259 598 402 064 because 509 508 × 509 508 = 509 5082 = 259 598 402 064.
As a consequence, 509 508 is the square root of 259 598 402 064.
The multiples of 509 508 are all integers evenly divisible by 509 508, that is all numbers such that the remainder of the division by 509 508 is zero. There are infinitely many multiples of 509 508. The smallest multiples of 509 508 are: