[Java] Find prime numbers with an Eratosthenes sieve

Introduction

In my usual development, I don't have a chance to touch the textbook algorithm, so I wrote a code to find a prime number using "Eratosthenes Sieve" as a brain teaser.

code

• [Wikipedia](https://ja.wikipedia.org/wiki/%E3%82%A8%E3%83%A9%E3%83%88%E3%82%B9%E3%83%86%E3% The algorithm written in 83% 8D% E3% 82% B9% E3% 81% AE% E7% AF% A9) was transcribed into Java code as it is.
• The most troublesome part was converting IntStream to List.
• It took a long time because it had nothing to do with the essence of the algorithm ...

PrimeNumberFinder.java

static void printPrimeNumbers(int maxNumber) {

	//Step 1: Put "integer from 2 to upper limit" in the search list.
	List<Integer> targetNumbers = IntStream.rangeClosed(2, maxNumber).boxed().collect(Collectors.toList());

	//Prime number list
	List<Integer> primeNumbers = new ArrayList<Integer>();

	int sqrt = (int) Math.sqrt(maxNumber);

	//Step 3: Continue the sieving operation until the first value in the search list reaches the square root of the argument.
	while(targetNumbers.get(0)<=sqrt) {
		//Step 2: Put the first number in the search list into the prime number list and screen multiples from the search list.
		int firstNum = targetNumbers.get(0);
		primeNumbers.add(firstNum);
		targetNumbers.removeIf(num -> (num % firstNum == 0));
	}

	//Step 4: Move the values remaining in the search list to the prime number list and finish the process.
	primeNumbers.addAll(targetNumbers);

	//Display of prime numbers
	System.out.println(primeNumbers.stream().map(pNum -> pNum.toString()).collect(Collectors.joining("\t")));
}

//Output result when 100 is specified in the argument of printPrimeNumbers
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	

Digression

• Mie Nakao is singing a song called "Eratostenes's Sieve", but the lyrics show the above. I was surprised that it was almost the same as the explanation on the Wikipedia page.
• The difference is that there is no restriction that "the sieving operation is continued until the first value of the search list reaches the square root of the argument".
• Apparently, it seems to be a song used on NHK's E-tele, but I was surprised at the solid content even though it was for children.