It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 8 125 001 is not a prime number.
For example, 8 125 001 can be divided by 353: 8 125 001 / 353 = 23 017.
For 8 125 001 to be a prime number, it would have been required that 8 125 001 has only two divisors, i.e., itself and 1.
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8 125 001 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 8 125 001 is about 2 850.439.
Thus, the square root of 8 125 001 is not an integer, and therefore 8 125 001 is not a square number.
The square of a number (here 8 125 001) is the result of the product of this number (8 125 001) by itself (i.e., 8 125 001 × 8 125 001); the square of 8 125 001 is sometimes called "raising 8 125 001 to the power 2", or "8 125 001 squared".
The square of 8 125 001 is 66 015 641 250 001 because 8 125 001 × 8 125 001 = 8 125 0012 = 66 015 641 250 001.
As a consequence, 8 125 001 is the square root of 66 015 641 250 001.
The multiples of 8 125 001 are all integers evenly divisible by 8 125 001, that is all numbers such that the remainder of the division by 8 125 001 is zero. There are infinitely many multiples of 8 125 001. The smallest multiples of 8 125 001 are: