It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 503 513 is not a prime number.
For example, 503 513 can be divided by 233: 503 513 / 233 = 2 161.
For 503 513 to be a prime number, it would have been required that 503 513 has only two divisors, i.e., itself and 1.
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503 513 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 503 513 is about 709.586.
Thus, the square root of 503 513 is not an integer, and therefore 503 513 is not a square number.
The square of a number (here 503 513) is the result of the product of this number (503 513) by itself (i.e., 503 513 × 503 513); the square of 503 513 is sometimes called "raising 503 513 to the power 2", or "503 513 squared".
The square of 503 513 is 253 525 341 169 because 503 513 × 503 513 = 503 5132 = 253 525 341 169.
As a consequence, 503 513 is the square root of 253 525 341 169.
The multiples of 503 513 are all integers evenly divisible by 503 513, that is all numbers such that the remainder of the division by 503 513 is zero. There are infinitely many multiples of 503 513. The smallest multiples of 503 513 are: