I$$m providing starting code that you will need to use for this. We want to find out all the prime numbers between $1$ and some user entered value.

$*$ Algorithm explanation: we will create a boolean array that size and make all values initially true. Then we will switch all values divisible by $2$ to false. Then we will repeat for $3.$ We will continue until we have checked them all. You need to think hard about what it means to "have checked them all". Be as efficient as you can.

NOTE: you might think that n$/2$ is the upper limit for which you must test to see whether a number n is prime, but you need only go as high as the square root of n$.$ Think about it$...$

import java.util.Scanner;

$/*//$ We want to find out all the prime numbers between $1$ and some user entered value

$*$ Algorithm explanation : we will create a boolean array that size and make all values

$*$ initially true. Then we will switch all values divisible by $2$ to false. Then we will

$*$ repeat for $3.$ We will continue until we have checked them all. You need to think hard

$*$ about what it means to "have checked them all". Be as efficient as you can

$*/$

public class Primes$\{$

public static void main$($String$[]$ args$)\{$

Scanner scanner $=$ new Scanner$($System$.$in$)$;

System.out.println$("$This program will create all the prime numbers for you: $")$;

System.out.println$("$What is your maximum number?"$)$;

int max $=$ scanner.nextInt$()$;

scanner.close$()$;

$//$ create a boolean array that is one size larger than the max variable

$//($ex if I want to check primes for $1-10,$ I want to set up a boolean array with index $0-10)$

$//$ we will ignore the zeroth location

$//$ loop through the array that you made and make each value initally equal to true

$//$ utilize a for loop to switch all non prime locations to false.

$//$ I used a for loop inside of an if that was inside of my main for loop

$//$ so starting with $2,$ I want to switch $4,6,8,10,$ etc. up to less than max

$//$ then do the same for $3.$ Switch $3,6($which is already switched$),9,12,$ up to less than max

$//$ etc.

$//$see if you can optimize your algorithm.

$//$ call your printPrime$()$ method $-$ see below $--$ to print the prime numbers

$\}$

$//$write a method printPrime$($int n$,$ boolean$[]$ nums$)$ that passes in the max number and the

$//$boolean array. Have it print only the prime numbers, all on one line. See sample output$/$

$\}$

SAMPLE OUTPUT:

This program will create all the prime numbers for you:

What is your maximum number?

$50$

Prime numbers smaller than $50$:

$23571113171923293137414347$