It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 509 526 is not a prime number.
For example, 509 526 can be divided by 2: 509 526 / 2 = 254 763.
For 509 526 to be a prime number, it would have been required that 509 526 has only two divisors, i.e., itself and 1.
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509 526 is an even number, because it is evenly divisible by 2: 509 526 / 2 = 254 763.
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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 509 526 is about 713.811.
Thus, the square root of 509 526 is not an integer, and therefore 509 526 is not a square number.
The square of a number (here 509 526) is the result of the product of this number (509 526) by itself (i.e., 509 526 × 509 526); the square of 509 526 is sometimes called "raising 509 526 to the power 2", or "509 526 squared".
The square of 509 526 is 259 616 744 676 because 509 526 × 509 526 = 509 5262 = 259 616 744 676.
As a consequence, 509 526 is the square root of 259 616 744 676.
The multiples of 509 526 are all integers evenly divisible by 509 526, that is all numbers such that the remainder of the division by 509 526 is zero. There are infinitely many multiples of 509 526. The smallest multiples of 509 526 are: