It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 413 509 is not a prime number.
For example, 413 509 can be divided by 31: 413 509 / 31 = 13 339.
For 413 509 to be a prime number, it would have been required that 413 509 has only two divisors, i.e., itself and 1.
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413 509 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 413 509 is about 643.047.
Thus, the square root of 413 509 is not an integer, and therefore 413 509 is not a square number.
The square of a number (here 413 509) is the result of the product of this number (413 509) by itself (i.e., 413 509 × 413 509); the square of 413 509 is sometimes called "raising 413 509 to the power 2", or "413 509 squared".
The square of 413 509 is 170 989 693 081 because 413 509 × 413 509 = 413 5092 = 170 989 693 081.
As a consequence, 413 509 is the square root of 170 989 693 081.
The multiples of 413 509 are all integers evenly divisible by 413 509, that is all numbers such that the remainder of the division by 413 509 is zero. There are infinitely many multiples of 413 509. The smallest multiples of 413 509 are: