It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 500 138 is not a prime number.
For example, 500 138 can be divided by 2: 500 138 / 2 = 250 069.
For 500 138 to be a prime number, it would have been required that 500 138 has only two divisors, i.e., itself and 1.
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500 138 is an even number, because it is evenly divisible by 2: 500 138 / 2 = 250 069.
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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 500 138 is about 707.204.
Thus, the square root of 500 138 is not an integer, and therefore 500 138 is not a square number.
The square of a number (here 500 138) is the result of the product of this number (500 138) by itself (i.e., 500 138 × 500 138); the square of 500 138 is sometimes called "raising 500 138 to the power 2", or "500 138 squared".
The square of 500 138 is 250 138 019 044 because 500 138 × 500 138 = 500 1382 = 250 138 019 044.
As a consequence, 500 138 is the square root of 250 138 019 044.
The multiples of 500 138 are all integers evenly divisible by 500 138, that is all numbers such that the remainder of the division by 500 138 is zero. There are infinitely many multiples of 500 138. The smallest multiples of 500 138 are: