It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 508 506 is not a prime number.
For example, 508 506 can be divided by 2: 508 506 / 2 = 254 253.
For 508 506 to be a prime number, it would have been required that 508 506 has only two divisors, i.e., itself and 1.
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508 506 is an even number, because it is evenly divisible by 2: 508 506 / 2 = 254 253.
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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 508 506 is about 713.096.
Thus, the square root of 508 506 is not an integer, and therefore 508 506 is not a square number.
The square of a number (here 508 506) is the result of the product of this number (508 506) by itself (i.e., 508 506 × 508 506); the square of 508 506 is sometimes called "raising 508 506 to the power 2", or "508 506 squared".
The square of 508 506 is 258 578 352 036 because 508 506 × 508 506 = 508 5062 = 258 578 352 036.
As a consequence, 508 506 is the square root of 258 578 352 036.
The multiples of 508 506 are all integers evenly divisible by 508 506, that is all numbers such that the remainder of the division by 508 506 is zero. There are infinitely many multiples of 508 506. The smallest multiples of 508 506 are: