It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 509 497 is not a prime number.
For example, 509 497 can be divided by 467: 509 497 / 467 = 1 091.
For 509 497 to be a prime number, it would have been required that 509 497 has only two divisors, i.e., itself and 1.
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509 497 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 509 497 is about 713.791.
Thus, the square root of 509 497 is not an integer, and therefore 509 497 is not a square number.
The square of a number (here 509 497) is the result of the product of this number (509 497) by itself (i.e., 509 497 × 509 497); the square of 509 497 is sometimes called "raising 509 497 to the power 2", or "509 497 squared".
The square of 509 497 is 259 587 193 009 because 509 497 × 509 497 = 509 4972 = 259 587 193 009.
As a consequence, 509 497 is the square root of 259 587 193 009.
The multiples of 509 497 are all integers evenly divisible by 509 497, that is all numbers such that the remainder of the division by 509 497 is zero. There are infinitely many multiples of 509 497. The smallest multiples of 509 497 are: