It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 508 509 is not a prime number.
For example, 508 509 can be divided by 3: 508 509 / 3 = 169 503.
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For 508 509 to be a prime number, it would have been required that 508 509 has only two divisors, i.e., itself and 1.
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508 509 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 508 509 is about 713.098.
Thus, the square root of 508 509 is not an integer, and therefore 508 509 is not a square number.
The square of a number (here 508 509) is the result of the product of this number (508 509) by itself (i.e., 508 509 × 508 509); the square of 508 509 is sometimes called "raising 508 509 to the power 2", or "508 509 squared".
The square of 508 509 is 258 581 403 081 because 508 509 × 508 509 = 508 5092 = 258 581 403 081.
As a consequence, 508 509 is the square root of 258 581 403 081.
The multiples of 508 509 are all integers evenly divisible by 508 509, that is all numbers such that the remainder of the division by 508 509 is zero. There are infinitely many multiples of 508 509. The smallest multiples of 508 509 are: