It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 10 013 is not a prime number.
For example, 10 013 can be divided by 17: 10 013 / 17 = 589.
For 10 013 to be a prime number, it would have been required that 10 013 has only two divisors, i.e., itself and 1.
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10 013 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 10 013 is about 100.065.
Thus, the square root of 10 013 is not an integer, and therefore 10 013 is not a square number.
The square of a number (here 10 013) is the result of the product of this number (10 013) by itself (i.e., 10 013 × 10 013); the square of 10 013 is sometimes called "raising 10 013 to the power 2", or "10 013 squared".
The square of 10 013 is 100 260 169 because 10 013 × 10 013 = 10 0132 = 100 260 169.
As a consequence, 10 013 is the square root of 100 260 169.
The multiples of 10 013 are all integers evenly divisible by 10 013, that is all numbers such that the remainder of the division by 10 013 is zero. There are infinitely many multiples of 10 013. The smallest multiples of 10 013 are: