It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 506 508 is not a prime number.
For example, 506 508 can be divided by 2: 506 508 / 2 = 253 254.
For 506 508 to be a prime number, it would have been required that 506 508 has only two divisors, i.e., itself and 1.
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506 508 is an even number, because it is evenly divisible by 2: 506 508 / 2 = 253 254.
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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 506 508 is about 711.694.
Thus, the square root of 506 508 is not an integer, and therefore 506 508 is not a square number.
The square of a number (here 506 508) is the result of the product of this number (506 508) by itself (i.e., 506 508 × 506 508); the square of 506 508 is sometimes called "raising 506 508 to the power 2", or "506 508 squared".
The square of 506 508 is 256 550 354 064 because 506 508 × 506 508 = 506 5082 = 256 550 354 064.
As a consequence, 506 508 is the square root of 256 550 354 064.
The multiples of 506 508 are all integers evenly divisible by 506 508, that is all numbers such that the remainder of the division by 506 508 is zero. There are infinitely many multiples of 506 508. The smallest multiples of 506 508 are: