It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 8 109 623 is not a prime number.
For example, 8 109 623 can be divided by 37: 8 109 623 / 37 = 219 179.
For 8 109 623 to be a prime number, it would have been required that 8 109 623 has only two divisors, i.e., itself and 1.
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8 109 623 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 8 109 623 is about 2 847.740.
Thus, the square root of 8 109 623 is not an integer, and therefore 8 109 623 is not a square number.
The square of a number (here 8 109 623) is the result of the product of this number (8 109 623) by itself (i.e., 8 109 623 × 8 109 623); the square of 8 109 623 is sometimes called "raising 8 109 623 to the power 2", or "8 109 623 squared".
The square of 8 109 623 is 65 765 985 202 129 because 8 109 623 × 8 109 623 = 8 109 6232 = 65 765 985 202 129.
As a consequence, 8 109 623 is the square root of 65 765 985 202 129.
The multiples of 8 109 623 are all integers evenly divisible by 8 109 623, that is all numbers such that the remainder of the division by 8 109 623 is zero. There are infinitely many multiples of 8 109 623. The smallest multiples of 8 109 623 are: