It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 509 463 is not a prime number.
For example, 509 463 can be divided by 3: 509 463 / 3 = 169 821.
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For 509 463 to be a prime number, it would have been required that 509 463 has only two divisors, i.e., itself and 1.
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509 463 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 509 463 is about 713.767.
Thus, the square root of 509 463 is not an integer, and therefore 509 463 is not a square number.
The square of a number (here 509 463) is the result of the product of this number (509 463) by itself (i.e., 509 463 × 509 463); the square of 509 463 is sometimes called "raising 509 463 to the power 2", or "509 463 squared".
The square of 509 463 is 259 552 548 369 because 509 463 × 509 463 = 509 4632 = 259 552 548 369.
As a consequence, 509 463 is the square root of 259 552 548 369.
The multiples of 509 463 are all integers evenly divisible by 509 463, that is all numbers such that the remainder of the division by 509 463 is zero. There are infinitely many multiples of 509 463. The smallest multiples of 509 463 are: