It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 512 407 is not a prime number.
For example, 512 407 can be divided by 7: 512 407 / 7 = 73 201.
For 512 407 to be a prime number, it would have been required that 512 407 has only two divisors, i.e., itself and 1.
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512 407 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 512 407 is about 715.826.
Thus, the square root of 512 407 is not an integer, and therefore 512 407 is not a square number.
The square of a number (here 512 407) is the result of the product of this number (512 407) by itself (i.e., 512 407 × 512 407); the square of 512 407 is sometimes called "raising 512 407 to the power 2", or "512 407 squared".
The square of 512 407 is 262 560 933 649 because 512 407 × 512 407 = 512 4072 = 262 560 933 649.
As a consequence, 512 407 is the square root of 262 560 933 649.
The multiples of 512 407 are all integers evenly divisible by 512 407, that is all numbers such that the remainder of the division by 512 407 is zero. There are infinitely many multiples of 512 407. The smallest multiples of 512 407 are: