It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 258 263 is not a prime number.
For example, 258 263 can be divided by 271: 258 263 / 271 = 953.
For 258 263 to be a prime number, it would have been required that 258 263 has only two divisors, i.e., itself and 1.
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258 263 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 258 263 is about 508.196.
Thus, the square root of 258 263 is not an integer, and therefore 258 263 is not a square number.
The square of a number (here 258 263) is the result of the product of this number (258 263) by itself (i.e., 258 263 × 258 263); the square of 258 263 is sometimes called "raising 258 263 to the power 2", or "258 263 squared".
The square of 258 263 is 66 699 777 169 because 258 263 × 258 263 = 258 2632 = 66 699 777 169.
As a consequence, 258 263 is the square root of 66 699 777 169.
The multiples of 258 263 are all integers evenly divisible by 258 263, that is all numbers such that the remainder of the division by 258 263 is zero. There are infinitely many multiples of 258 263. The smallest multiples of 258 263 are: