It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 513 343 is not a prime number.
For example, 513 343 can be divided by 599: 513 343 / 599 = 857.
For 513 343 to be a prime number, it would have been required that 513 343 has only two divisors, i.e., itself and 1.
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513 343 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 513 343 is about 716.480.
Thus, the square root of 513 343 is not an integer, and therefore 513 343 is not a square number.
The square of a number (here 513 343) is the result of the product of this number (513 343) by itself (i.e., 513 343 × 513 343); the square of 513 343 is sometimes called "raising 513 343 to the power 2", or "513 343 squared".
The square of 513 343 is 263 521 035 649 because 513 343 × 513 343 = 513 3432 = 263 521 035 649.
As a consequence, 513 343 is the square root of 263 521 035 649.
The multiples of 513 343 are all integers evenly divisible by 513 343, that is all numbers such that the remainder of the division by 513 343 is zero. There are infinitely many multiples of 513 343. The smallest multiples of 513 343 are: