It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 4 004 001 is not a prime number.
For example, 4 004 001 can be divided by 3: 4 004 001 / 3 = 1 334 667.
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For 4 004 001 to be a prime number, it would have been required that 4 004 001 has only two divisors, i.e., itself and 1.
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4 004 001 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 4 004 001 is 2 001.
Therefore, the square root of 4 004 001 is an integer, and as a consequence 4 004 001 is a perfect square.
The square of a number (here 4 004 001) is the result of the product of this number (4 004 001) by itself (i.e., 4 004 001 × 4 004 001); the square of 4 004 001 is sometimes called "raising 4 004 001 to the power 2", or "4 004 001 squared".
The square of 4 004 001 is 16 032 024 008 001 because 4 004 001 × 4 004 001 = 4 004 0012 = 16 032 024 008 001.
As a consequence, 4 004 001 is the square root of 16 032 024 008 001.
The multiples of 4 004 001 are all integers evenly divisible by 4 004 001, that is all numbers such that the remainder of the division by 4 004 001 is zero. There are infinitely many multiples of 4 004 001. The smallest multiples of 4 004 001 are: