It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 137 097 is not a prime number.
For example, 137 097 can be divided by 3: 137 097 / 3 = 45 699.
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For 137 097 to be a prime number, it would have been required that 137 097 has only two divisors, i.e., itself and 1.
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137 097 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 137 097 is about 370.266.
Thus, the square root of 137 097 is not an integer, and therefore 137 097 is not a square number.
The square of a number (here 137 097) is the result of the product of this number (137 097) by itself (i.e., 137 097 × 137 097); the square of 137 097 is sometimes called "raising 137 097 to the power 2", or "137 097 squared".
The square of 137 097 is 18 795 587 409 because 137 097 × 137 097 = 137 0972 = 18 795 587 409.
As a consequence, 137 097 is the square root of 18 795 587 409.
The multiples of 137 097 are all integers evenly divisible by 137 097, that is all numbers such that the remainder of the division by 137 097 is zero. There are infinitely many multiples of 137 097. The smallest multiples of 137 097 are: