Is 259 a prime number?

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

For 259, the answer is: No, 259 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 259) is as follows: 1, 7, 37, 259.

For 259 to be a prime number, it would have been required that 259 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

259 is a multiple of 1
259 is a multiple of 7
259 is a multiple of 37

For 259 to be a prime number, it would have been required that 259 has only two divisors, i.e., itself and 1.

However, 259 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 259 = 7 x 37, where 7 and 37 are both prime numbers.

Is 259 a deficient number?

Yes, 259 is a deficient number, that is to say 259 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 259 without 259 itself (that is 1 + 7 + 37 = 45).

Parity of 259

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

Find out more:

What is an even number?

Is 259 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 259 is about 16.093.

Thus, the square root of 259 is not an integer, and therefore 259 is not a square number.

What is the square number of 259?

The square of a number (here 259) is the result of the product of this number (259) by itself (i.e., 259 × 259); the square of 259 is sometimes called "raising 259 to the power 2", or "259 squared".

The square of 259 is 67 081 because 259 × 259 = 259² = 67 081.

As a consequence, 259 is the square root of 67 081.

Number of digits of 259

259 is a number with 3 digits.

What are the multiples of 259?

The multiples of 259 are all integers evenly divisible by 259, that is all numbers such that the remainder of the division by 259 is zero. There are infinitely many multiples of 259. The smallest multiples of 259 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 259 too, since 0 × 259 = 0
259: indeed, 259 is a multiple of itself, since 259 is evenly divisible by 259 (we have 259 / 259 = 1, so the remainder of this division is indeed zero)
518: indeed, 518 = 259 × 2
777: indeed, 777 = 259 × 3
1 036: indeed, 1 036 = 259 × 4
1 295: indeed, 1 295 = 259 × 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 259). 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 16.093). 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 259

Preceding numbers: …257, 258
Following numbers: 260, 261…

Nearest numbers from 259

Preceding prime number: 257
Following prime number: 263