It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 509 497 314 is not a prime number.
For example, 509 497 314 can be divided by 2: 509 497 314 / 2 = 254 748 657.
For 509 497 314 to be a prime number, it would have been required that 509 497 314 has only two divisors, i.e., itself and 1.
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509 497 314 is an even number, because it is evenly divisible by 2: 509 497 314 / 2 = 254 748 657.
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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 509 497 314 is about 22 572.047.
Thus, the square root of 509 497 314 is not an integer, and therefore 509 497 314 is not a square number.
The square of a number (here 509 497 314) is the result of the product of this number (509 497 314) by itself (i.e., 509 497 314 × 509 497 314); the square of 509 497 314 is sometimes called "raising 509 497 314 to the power 2", or "509 497 314 squared".
The square of 509 497 314 is 259 587 512 973 214 592 because 509 497 314 × 509 497 314 = 509 497 3142 = 259 587 512 973 214 592.
As a consequence, 509 497 314 is the square root of 259 587 512 973 214 592.
509 497 314 is a number with 9 digits.
The multiples of 509 497 314 are all integers evenly divisible by 509 497 314, that is all numbers such that the remainder of the division by 509 497 314 is zero. There are infinitely many multiples of 509 497 314. The smallest multiples of 509 497 314 are: