It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 138 503 is not a prime number.
For example, 138 503 can be divided by 43: 138 503 / 43 = 3 221.
For 138 503 to be a prime number, it would have been required that 138 503 has only two divisors, i.e., itself and 1.
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138 503 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 138 503 is about 372.160.
Thus, the square root of 138 503 is not an integer, and therefore 138 503 is not a square number.
The square of a number (here 138 503) is the result of the product of this number (138 503) by itself (i.e., 138 503 × 138 503); the square of 138 503 is sometimes called "raising 138 503 to the power 2", or "138 503 squared".
The square of 138 503 is 19 183 081 009 because 138 503 × 138 503 = 138 5032 = 19 183 081 009.
As a consequence, 138 503 is the square root of 19 183 081 009.
The multiples of 138 503 are all integers evenly divisible by 138 503, that is all numbers such that the remainder of the division by 138 503 is zero. There are infinitely many multiples of 138 503. The smallest multiples of 138 503 are: