It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 509 527 is not a prime number.
For example, 509 527 can be divided by 37: 509 527 / 37 = 13 771.
For 509 527 to be a prime number, it would have been required that 509 527 has only two divisors, i.e., itself and 1.
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509 527 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 509 527 is about 713.812.
Thus, the square root of 509 527 is not an integer, and therefore 509 527 is not a square number.
The square of a number (here 509 527) is the result of the product of this number (509 527) by itself (i.e., 509 527 × 509 527); the square of 509 527 is sometimes called "raising 509 527 to the power 2", or "509 527 squared".
The square of 509 527 is 259 617 763 729 because 509 527 × 509 527 = 509 5272 = 259 617 763 729.
As a consequence, 509 527 is the square root of 259 617 763 729.
The multiples of 509 527 are all integers evenly divisible by 509 527, that is all numbers such that the remainder of the division by 509 527 is zero. There are infinitely many multiples of 509 527. The smallest multiples of 509 527 are: