It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 509 461 is not a prime number.
For example, 509 461 can be divided by 673: 509 461 / 673 = 757.
For 509 461 to be a prime number, it would have been required that 509 461 has only two divisors, i.e., itself and 1.
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509 461 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 509 461 is about 713.765.
Thus, the square root of 509 461 is not an integer, and therefore 509 461 is not a square number.
The square of a number (here 509 461) is the result of the product of this number (509 461) by itself (i.e., 509 461 × 509 461); the square of 509 461 is sometimes called "raising 509 461 to the power 2", or "509 461 squared".
The square of 509 461 is 259 550 510 521 because 509 461 × 509 461 = 509 4612 = 259 550 510 521.
As a consequence, 509 461 is the square root of 259 550 510 521.
The multiples of 509 461 are all integers evenly divisible by 509 461, that is all numbers such that the remainder of the division by 509 461 is zero. There are infinitely many multiples of 509 461. The smallest multiples of 509 461 are: