It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 4 004 163 is not a prime number.
For example, 4 004 163 can be divided by 3: 4 004 163 / 3 = 1 334 721.
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For 4 004 163 to be a prime number, it would have been required that 4 004 163 has only two divisors, i.e., itself and 1.
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4 004 163 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 4 004 163 is about 2 001.040.
Thus, the square root of 4 004 163 is not an integer, and therefore 4 004 163 is not a square number.
The square of a number (here 4 004 163) is the result of the product of this number (4 004 163) by itself (i.e., 4 004 163 × 4 004 163); the square of 4 004 163 is sometimes called "raising 4 004 163 to the power 2", or "4 004 163 squared".
The square of 4 004 163 is 16 033 321 330 569 because 4 004 163 × 4 004 163 = 4 004 1632 = 16 033 321 330 569.
As a consequence, 4 004 163 is the square root of 16 033 321 330 569.
The multiples of 4 004 163 are all integers evenly divisible by 4 004 163, that is all numbers such that the remainder of the division by 4 004 163 is zero. There are infinitely many multiples of 4 004 163. The smallest multiples of 4 004 163 are: