It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 509 337 is not a prime number.
For example, 509 337 can be divided by 3: 509 337 / 3 = 169 779.
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For 509 337 to be a prime number, it would have been required that 509 337 has only two divisors, i.e., itself and 1.
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509 337 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 509 337 is about 713.678.
Thus, the square root of 509 337 is not an integer, and therefore 509 337 is not a square number.
The square of a number (here 509 337) is the result of the product of this number (509 337) by itself (i.e., 509 337 × 509 337); the square of 509 337 is sometimes called "raising 509 337 to the power 2", or "509 337 squared".
The square of 509 337 is 259 424 179 569 because 509 337 × 509 337 = 509 3372 = 259 424 179 569.
As a consequence, 509 337 is the square root of 259 424 179 569.
The multiples of 509 337 are all integers evenly divisible by 509 337, that is all numbers such that the remainder of the division by 509 337 is zero. There are infinitely many multiples of 509 337. The smallest multiples of 509 337 are: