It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 513 993 is not a prime number.
For example, 513 993 can be divided by 3: 513 993 / 3 = 171 331.
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For 513 993 to be a prime number, it would have been required that 513 993 has only two divisors, i.e., itself and 1.
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513 993 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 513 993 is about 716.933.
Thus, the square root of 513 993 is not an integer, and therefore 513 993 is not a square number.
The square of a number (here 513 993) is the result of the product of this number (513 993) by itself (i.e., 513 993 × 513 993); the square of 513 993 is sometimes called "raising 513 993 to the power 2", or "513 993 squared".
The square of 513 993 is 264 188 804 049 because 513 993 × 513 993 = 513 9932 = 264 188 804 049.
As a consequence, 513 993 is the square root of 264 188 804 049.
The multiples of 513 993 are all integers evenly divisible by 513 993, that is all numbers such that the remainder of the division by 513 993 is zero. There are infinitely many multiples of 513 993. The smallest multiples of 513 993 are: