It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 137 137 is not a prime number.
For example, 137 137 can be divided by 7: 137 137 / 7 = 19 591.
For 137 137 to be a prime number, it would have been required that 137 137 has only two divisors, i.e., itself and 1.
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137 137 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 137 137 is about 370.320.
Thus, the square root of 137 137 is not an integer, and therefore 137 137 is not a square number.
The square of a number (here 137 137) is the result of the product of this number (137 137) by itself (i.e., 137 137 × 137 137); the square of 137 137 is sometimes called "raising 137 137 to the power 2", or "137 137 squared".
The square of 137 137 is 18 806 556 769 because 137 137 × 137 137 = 137 1372 = 18 806 556 769.
As a consequence, 137 137 is the square root of 18 806 556 769.
The multiples of 137 137 are all integers evenly divisible by 137 137, that is all numbers such that the remainder of the division by 137 137 is zero. There are infinitely many multiples of 137 137. The smallest multiples of 137 137 are: