It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 512 243 is not a prime number.
For example, 512 243 can be divided by 137: 512 243 / 137 = 3 739.
For 512 243 to be a prime number, it would have been required that 512 243 has only two divisors, i.e., itself and 1.
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512 243 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 512 243 is about 715.712.
Thus, the square root of 512 243 is not an integer, and therefore 512 243 is not a square number.
The square of a number (here 512 243) is the result of the product of this number (512 243) by itself (i.e., 512 243 × 512 243); the square of 512 243 is sometimes called "raising 512 243 to the power 2", or "512 243 squared".
The square of 512 243 is 262 392 891 049 because 512 243 × 512 243 = 512 2432 = 262 392 891 049.
As a consequence, 512 243 is the square root of 262 392 891 049.
The multiples of 512 243 are all integers evenly divisible by 512 243, that is all numbers such that the remainder of the division by 512 243 is zero. There are infinitely many multiples of 512 243. The smallest multiples of 512 243 are: