It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 5 052 013 is not a prime number.
For example, 5 052 013 can be divided by 53: 5 052 013 / 53 = 95 321.
For 5 052 013 to be a prime number, it would have been required that 5 052 013 has only two divisors, i.e., itself and 1.
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5 052 013 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 5 052 013 is about 2 247.668.
Thus, the square root of 5 052 013 is not an integer, and therefore 5 052 013 is not a square number.
The square of a number (here 5 052 013) is the result of the product of this number (5 052 013) by itself (i.e., 5 052 013 × 5 052 013); the square of 5 052 013 is sometimes called "raising 5 052 013 to the power 2", or "5 052 013 squared".
The square of 5 052 013 is 25 522 835 352 169 because 5 052 013 × 5 052 013 = 5 052 0132 = 25 522 835 352 169.
As a consequence, 5 052 013 is the square root of 25 522 835 352 169.
The multiples of 5 052 013 are all integers evenly divisible by 5 052 013, that is all numbers such that the remainder of the division by 5 052 013 is zero. There are infinitely many multiples of 5 052 013. The smallest multiples of 5 052 013 are: