It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 514 509 is not a prime number.
For example, 514 509 can be divided by 3: 514 509 / 3 = 171 503.
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For 514 509 to be a prime number, it would have been required that 514 509 has only two divisors, i.e., itself and 1.
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514 509 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 514 509 is about 717.293.
Thus, the square root of 514 509 is not an integer, and therefore 514 509 is not a square number.
The square of a number (here 514 509) is the result of the product of this number (514 509) by itself (i.e., 514 509 × 514 509); the square of 514 509 is sometimes called "raising 514 509 to the power 2", or "514 509 squared".
The square of 514 509 is 264 719 511 081 because 514 509 × 514 509 = 514 5092 = 264 719 511 081.
As a consequence, 514 509 is the square root of 264 719 511 081.
The multiples of 514 509 are all integers evenly divisible by 514 509, that is all numbers such that the remainder of the division by 514 509 is zero. There are infinitely many multiples of 514 509. The smallest multiples of 514 509 are: