It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 513 523 is not a prime number.
For example, 513 523 can be divided by 37: 513 523 / 37 = 13 879.
For 513 523 to be a prime number, it would have been required that 513 523 has only two divisors, i.e., itself and 1.
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513 523 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 513 523 is about 716.605.
Thus, the square root of 513 523 is not an integer, and therefore 513 523 is not a square number.
The square of a number (here 513 523) is the result of the product of this number (513 523) by itself (i.e., 513 523 × 513 523); the square of 513 523 is sometimes called "raising 513 523 to the power 2", or "513 523 squared".
The square of 513 523 is 263 705 871 529 because 513 523 × 513 523 = 513 5232 = 263 705 871 529.
As a consequence, 513 523 is the square root of 263 705 871 529.
The multiples of 513 523 are all integers evenly divisible by 513 523, that is all numbers such that the remainder of the division by 513 523 is zero. There are infinitely many multiples of 513 523. The smallest multiples of 513 523 are: