It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 593, the answer is: yes, 593 is a prime number because it has only two distinct divisors: 1 and itself (593).
As a consequence, 593 is only a multiple of 1 and 593..
Since 593 is a prime number, 593 is also a deficient number, that is to say 593 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 593 without 593 itself (that is 1, by definition!).
Parity of 593
593 is an odd number, because it is not evenly divisible by 2.
Is 593 a perfect square number?
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 593 is about 24.352.
Thus, the square root of 593 is not an integer, and therefore 593 is not a square number.
Anyway, 593 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 593?
The square of a number (here 593) is the result of the product of this number (593) by itself (i.e., 593 × 593); the square of 593 is sometimes called "raising 593 to the power 2", or "593 squared".
As a consequence, 593 is the square root of 351 649.
Number of digits of 593
593 is a number with 3 digits.
What are the multiples of 593?
The multiples of 593 are all integers evenly divisible by 593, that is all numbers such that the remainder of the division by 593 is zero. There are infinitely many multiples of 593. The smallest multiples of 593 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 593 too, since 0 × 593 = 0
- 593: indeed, 593 is a multiple of itself, since 593 is evenly divisible by 593 (we have 593 / 593 = 1, so the remainder of this division is indeed zero)
- 1 186: indeed, 1 186 = 593 × 2
- 1 779: indeed, 1 779 = 593 × 3
- 2 372: indeed, 2 372 = 593 × 4
- 2 965: indeed, 2 965 = 593 × 5
How to determine whether an integer is a prime number?
To determine the primality of a number, several algorithms can be used. The most naive technique is to test all divisors strictly smaller to the number of which we want to determine the primality (here 593). First, we can eliminate all even numbers greater than 2 (and hence 4, 6, 8…). Then, we can stop this check when we reach the square root of the number of which we want to determine the primality (here the square root is about 24.352). Historically, the sieve of Eratosthenes (dating from the Greek mathematics) implements this technique in a relatively efficient manner.
More modern techniques include the sieve of Atkin, probabilistic algorithms, and the cyclotomic AKS test.