It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 509 353 is not a prime number.
For example, 509 353 can be divided by 13: 509 353 / 13 = 39 181.
For 509 353 to be a prime number, it would have been required that 509 353 has only two divisors, i.e., itself and 1.
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509 353 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 509 353 is about 713.690.
Thus, the square root of 509 353 is not an integer, and therefore 509 353 is not a square number.
The square of a number (here 509 353) is the result of the product of this number (509 353) by itself (i.e., 509 353 × 509 353); the square of 509 353 is sometimes called "raising 509 353 to the power 2", or "509 353 squared".
The square of 509 353 is 259 440 478 609 because 509 353 × 509 353 = 509 3532 = 259 440 478 609.
As a consequence, 509 353 is the square root of 259 440 478 609.
The multiples of 509 353 are all integers evenly divisible by 509 353, that is all numbers such that the remainder of the division by 509 353 is zero. There are infinitely many multiples of 509 353. The smallest multiples of 509 353 are: