It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 135 137 is not a prime number.
For example, 135 137 can be divided by 337: 135 137 / 337 = 401.
For 135 137 to be a prime number, it would have been required that 135 137 has only two divisors, i.e., itself and 1.
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135 137 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 135 137 is about 367.610.
Thus, the square root of 135 137 is not an integer, and therefore 135 137 is not a square number.
The square of a number (here 135 137) is the result of the product of this number (135 137) by itself (i.e., 135 137 × 135 137); the square of 135 137 is sometimes called "raising 135 137 to the power 2", or "135 137 squared".
The square of 135 137 is 18 262 008 769 because 135 137 × 135 137 = 135 1372 = 18 262 008 769.
As a consequence, 135 137 is the square root of 18 262 008 769.
The multiples of 135 137 are all integers evenly divisible by 135 137, that is all numbers such that the remainder of the division by 135 137 is zero. There are infinitely many multiples of 135 137. The smallest multiples of 135 137 are: