It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 3 255 253 is not a prime number.
For example, 3 255 253 can be divided by 733: 3 255 253 / 733 = 4 441.
For 3 255 253 to be a prime number, it would have been required that 3 255 253 has only two divisors, i.e., itself and 1.
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3 255 253 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 3 255 253 is about 1 804.232.
Thus, the square root of 3 255 253 is not an integer, and therefore 3 255 253 is not a square number.
The square of a number (here 3 255 253) is the result of the product of this number (3 255 253) by itself (i.e., 3 255 253 × 3 255 253); the square of 3 255 253 is sometimes called "raising 3 255 253 to the power 2", or "3 255 253 squared".
The square of 3 255 253 is 10 596 672 094 009 because 3 255 253 × 3 255 253 = 3 255 2532 = 10 596 672 094 009.
As a consequence, 3 255 253 is the square root of 10 596 672 094 009.
The multiples of 3 255 253 are all integers evenly divisible by 3 255 253, that is all numbers such that the remainder of the division by 3 255 253 is zero. There are infinitely many multiples of 3 255 253. The smallest multiples of 3 255 253 are: