It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 509 514 is not a prime number.
For example, 509 514 can be divided by 2: 509 514 / 2 = 254 757.
For 509 514 to be a prime number, it would have been required that 509 514 has only two divisors, i.e., itself and 1.
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509 514 is an even number, because it is evenly divisible by 2: 509 514 / 2 = 254 757.
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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 509 514 is about 713.802.
Thus, the square root of 509 514 is not an integer, and therefore 509 514 is not a square number.
The square of a number (here 509 514) is the result of the product of this number (509 514) by itself (i.e., 509 514 × 509 514); the square of 509 514 is sometimes called "raising 509 514 to the power 2", or "509 514 squared".
The square of 509 514 is 259 604 516 196 because 509 514 × 509 514 = 509 5142 = 259 604 516 196.
As a consequence, 509 514 is the square root of 259 604 516 196.
The multiples of 509 514 are all integers evenly divisible by 509 514, that is all numbers such that the remainder of the division by 509 514 is zero. There are infinitely many multiples of 509 514. The smallest multiples of 509 514 are: