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Last modified: January 15, 2020

First, let's go over some basic theory.

Simply put, a number is prime if it's only divisible by one and by the number itself. The non-prime numbers are called composite numbers. And number one is neither prime nor composite.

In this article, we'll have a look at different ways to check the primality of a number in Java.

With this approach, we can check if a number between 2 and (square root of the number) can accurately divide the number.

The following logic will return *true* if the number is prime:

```
public boolean isPrime(int number) {
return number > 1
&& IntStream.rangeClosed(2, (int) Math.sqrt(number))
.noneMatch(n -> (number % n == 0));
}
```

*BigInteger* class is generally used for storing large sized integers, i.e., those greater than 64bits. It provides a few useful APIs for working with *int* and *long* values.

One of those APIs is the *isProbablePrime*. This API returns *false* if the number is definitely a composite and returns *true* if there is some probability of it being prime. It is useful when dealing with large integers because it can be quite an intensive computation to verify these fully.

**A quick side-note** – the *isProbablePrime* API uses what's known as “Miller – Rabin and Lucas – Lehmer” primality tests to check if the number is probably prime. In cases where the number is less than 100 bits, only the “Miller – Rabin” test is used, otherwise, both tests are used for checking the primality of a number.

“Miller-Rabin” test iterates a fixed number of times to determine the primality of number and this iteration count is determined by a simple check which involves the bit length of the number and the certainty value passed to the API:

```
public boolean isPrime(int number) {
BigInteger bigInt = BigInteger.valueOf(number);
return bigInt.isProbablePrime(100);
}
```

Apache Commons Math API provides a method named *org.apache.commons.math3.primes.Primes,* which we will use for checking the primality of a number.

First, we need to import the Apache Commons Math library by adding the following dependency in our *pom.xml*:

```
<dependency>
<groupId>org.apache.commons</groupId>
<artifactId>commons-math3</artifactId>
<version>3.6.1</version>
</dependency>
```

The latest version of the commons-math3 can be found here.

We could do the check just by calling the method:

`Primes.isPrime(number);`

In this quick write-up, we have seen three ways of checking for the primality of the number.

The code for this can be found in the package *com.baeldung.algorithms.primechecker* over on Github.