It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 508 507 is not a prime number.
For example, 508 507 can be divided by 23: 508 507 / 23 = 22 109.
For 508 507 to be a prime number, it would have been required that 508 507 has only two divisors, i.e., itself and 1.
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508 507 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 508 507 is about 713.097.
Thus, the square root of 508 507 is not an integer, and therefore 508 507 is not a square number.
The square of a number (here 508 507) is the result of the product of this number (508 507) by itself (i.e., 508 507 × 508 507); the square of 508 507 is sometimes called "raising 508 507 to the power 2", or "508 507 squared".
The square of 508 507 is 258 579 369 049 because 508 507 × 508 507 = 508 5072 = 258 579 369 049.
As a consequence, 508 507 is the square root of 258 579 369 049.
The multiples of 508 507 are all integers evenly divisible by 508 507, that is all numbers such that the remainder of the division by 508 507 is zero. There are infinitely many multiples of 508 507. The smallest multiples of 508 507 are: