It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 5 537 309 is not a prime number.
For example, 5 537 309 can be divided by 37: 5 537 309 / 37 = 149 657.
For 5 537 309 to be a prime number, it would have been required that 5 537 309 has only two divisors, i.e., itself and 1.
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5 537 309 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 5 537 309 is about 2 353.149.
Thus, the square root of 5 537 309 is not an integer, and therefore 5 537 309 is not a square number.
The square of a number (here 5 537 309) is the result of the product of this number (5 537 309) by itself (i.e., 5 537 309 × 5 537 309); the square of 5 537 309 is sometimes called "raising 5 537 309 to the power 2", or "5 537 309 squared".
The square of 5 537 309 is 30 661 790 961 481 because 5 537 309 × 5 537 309 = 5 537 3092 = 30 661 790 961 481.
As a consequence, 5 537 309 is the square root of 30 661 790 961 481.
The multiples of 5 537 309 are all integers evenly divisible by 5 537 309, that is all numbers such that the remainder of the division by 5 537 309 is zero. There are infinitely many multiples of 5 537 309. The smallest multiples of 5 537 309 are: