It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 10 138 is not a prime number.
For example, 10 138 can be divided by 2: 10 138 / 2 = 5 069.
For 10 138 to be a prime number, it would have been required that 10 138 has only two divisors, i.e., itself and 1.
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10 138 is an even number, because it is evenly divisible by 2: 10 138 / 2 = 5 069.
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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 10 138 is about 100.688.
Thus, the square root of 10 138 is not an integer, and therefore 10 138 is not a square number.
The square of a number (here 10 138) is the result of the product of this number (10 138) by itself (i.e., 10 138 × 10 138); the square of 10 138 is sometimes called "raising 10 138 to the power 2", or "10 138 squared".
The square of 10 138 is 102 779 044 because 10 138 × 10 138 = 10 1382 = 102 779 044.
As a consequence, 10 138 is the square root of 102 779 044.
The multiples of 10 138 are all integers evenly divisible by 10 138, that is all numbers such that the remainder of the division by 10 138 is zero. There are infinitely many multiples of 10 138. The smallest multiples of 10 138 are: