It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 509 507 is not a prime number.
For example, 509 507 can be divided by 17: 509 507 / 17 = 29 971.
For 509 507 to be a prime number, it would have been required that 509 507 has only two divisors, i.e., itself and 1.
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509 507 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 509 507 is about 713.798.
Thus, the square root of 509 507 is not an integer, and therefore 509 507 is not a square number.
The square of a number (here 509 507) is the result of the product of this number (509 507) by itself (i.e., 509 507 × 509 507); the square of 509 507 is sometimes called "raising 509 507 to the power 2", or "509 507 squared".
The square of 509 507 is 259 597 383 049 because 509 507 × 509 507 = 509 5072 = 259 597 383 049.
As a consequence, 509 507 is the square root of 259 597 383 049.
The multiples of 509 507 are all integers evenly divisible by 509 507, that is all numbers such that the remainder of the division by 509 507 is zero. There are infinitely many multiples of 509 507. The smallest multiples of 509 507 are: