Is 589 a prime number?

It is possible to find out using mathematical methods whether a given integer is a prime number or not.

For 589, the answer is: No, 589 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 589) is as follows: 1, 19, 31, 589.

For 589 to be a prime number, it would have been required that 589 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

589 is a multiple of 1
589 is a multiple of 19
589 is a multiple of 31

For 589 to be a prime number, it would have been required that 589 has only two divisors, i.e., itself and 1.

However, 589 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 589 = 19 x 31, where 19 and 31 are both prime numbers.

Is 589 a deficient number?

Yes, 589 is a deficient number, that is to say 589 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 589 without 589 itself (that is 1 + 19 + 31 = 51).

Parity of 589

589 is an odd number, because it is not evenly divisible by 2.

Find out more:

What is an even number?

Is 589 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 589 is about 24.269.

Thus, the square root of 589 is not an integer, and therefore 589 is not a square number.

What is the square number of 589?

The square of a number (here 589) is the result of the product of this number (589) by itself (i.e., 589 × 589); the square of 589 is sometimes called "raising 589 to the power 2", or "589 squared".

The square of 589 is 346 921 because 589 × 589 = 589² = 346 921.

As a consequence, 589 is the square root of 346 921.

Number of digits of 589

589 is a number with 3 digits.

What are the multiples of 589?

The multiples of 589 are all integers evenly divisible by 589, that is all numbers such that the remainder of the division by 589 is zero. There are infinitely many multiples of 589. The smallest multiples of 589 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 589 too, since 0 × 589 = 0
589: indeed, 589 is a multiple of itself, since 589 is evenly divisible by 589 (we have 589 / 589 = 1, so the remainder of this division is indeed zero)
1 178: indeed, 1 178 = 589 × 2
1 767: indeed, 1 767 = 589 × 3
2 356: indeed, 2 356 = 589 × 4
2 945: indeed, 2 945 = 589 × 5
etc.

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 589). 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 24.269). 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.

Numbers near 589

Preceding numbers: …587, 588
Following numbers: 590, 591…

Nearest numbers from 589

Preceding prime number: 587
Following prime number: 593