It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 2 509 133 is not a prime number.
For example, 2 509 133 can be divided by 11: 2 509 133 / 11 = 228 103.
For 2 509 133 to be a prime number, it would have been required that 2 509 133 has only two divisors, i.e., itself and 1.
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2 509 133 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 2 509 133 is about 1 584.024.
Thus, the square root of 2 509 133 is not an integer, and therefore 2 509 133 is not a square number.
The square of a number (here 2 509 133) is the result of the product of this number (2 509 133) by itself (i.e., 2 509 133 × 2 509 133); the square of 2 509 133 is sometimes called "raising 2 509 133 to the power 2", or "2 509 133 squared".
The square of 2 509 133 is 6 295 748 411 689 because 2 509 133 × 2 509 133 = 2 509 1332 = 6 295 748 411 689.
As a consequence, 2 509 133 is the square root of 6 295 748 411 689.
The multiples of 2 509 133 are all integers evenly divisible by 2 509 133, that is all numbers such that the remainder of the division by 2 509 133 is zero. There are infinitely many multiples of 2 509 133. The smallest multiples of 2 509 133 are: