# Java program to find prime numbers from 2 to N

Learn to write program for finding all the prime numbers from 1 and N, using Java 8 stream API, where N is any given input number to the application.

## 1. Prime number algorithm

A prime number (P) is a number greater than 1 whose only factors are 1 and the number (P) itself. Generally, we can determine a number is prime or not in below steps:

1. 2 is only prime number which is also even number. So, if given number N is 2 the it is PRIME number.
2. If given number N is even number then it is NOT PRIME number.
3. Find out square root on N. Traverse all odd numbers up to the `sqrt(N)` and try to divide the N with current odd number. If remainder is 0 for any odd number then number is NOT PRIME.
4. Else – number is PRIME.
```static boolean isPrime(int number) {
if(number <= 2)
return number == 2;
else
return  (number % 2) != 0
&&
IntStream.rangeClosed(3, (int) Math.sqrt(number))
.filter(n -> n % 2 != 0)
.noneMatch(n -> (number % n == 0));
}
```

## 2. Java program to find prime numbers between 2 and N

In given below program, we have used `IntStream` to iterate from 2 to 100 and find all prime numbers between them.

```package com.howtodoinjava.example;

import java.util.List;
import java.util.Scanner;
import java.util.stream.Collectors;
import java.util.stream.IntStream;

public class Main
{
public static void main(String[] args)
{
//Read input from console - optional
Scanner scan= new Scanner(System.in);
System. out.println("Enter a number : ");
int number = scan.nextInt();
scan.close();

List<Integer> primes = IntStream.rangeClosed(2, number)
.filter(n -> isPrime(n))
.boxed()
.collect(Collectors.toList());

System.out.println(primes);
}

static boolean isPrime(int number) {
if(number <= 2)
return number == 2;
else
return  (number % 2) != 0
&&
IntStream.rangeClosed(3, (int) Math.sqrt(number))
.filter(n -> n % 2 != 0)
.noneMatch(n -> (number % n == 0));
}
}
```

Program output.

```Enter a number :
100

[2, 3, 5, 7, 11, 13, 17, 19,
23, 29, 31, 37, 41, 43, 47, 53,
59, 61, 67, 71, 73, 79, 83, 89, 97]
```

It’s clear from output that program is able to print all prime numbers between 2 to 100.

Happy Learning !!

References:

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