It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 135 509 is not a prime number.
For example, 135 509 can be divided by 11: 135 509 / 11 = 12 319.
For 135 509 to be a prime number, it would have been required that 135 509 has only two divisors, i.e., itself and 1.
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135 509 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 135 509 is about 368.115.
Thus, the square root of 135 509 is not an integer, and therefore 135 509 is not a square number.
The square of a number (here 135 509) is the result of the product of this number (135 509) by itself (i.e., 135 509 × 135 509); the square of 135 509 is sometimes called "raising 135 509 to the power 2", or "135 509 squared".
The square of 135 509 is 18 362 689 081 because 135 509 × 135 509 = 135 5092 = 18 362 689 081.
As a consequence, 135 509 is the square root of 18 362 689 081.
The multiples of 135 509 are all integers evenly divisible by 135 509, that is all numbers such that the remainder of the division by 135 509 is zero. There are infinitely many multiples of 135 509. The smallest multiples of 135 509 are: