Question

Prime numbers can be generated by an algorithm known as the Sieve of Eratosthenes. The algorithm for this procedure is presented here. Write a program called primes.js that implements this algorithm. Have the program find and display all the prime numbers up to n = 150.

Sieve of Eratosthenes Algorithm
To Display All Prime Numbers Between 1 and n
Step 1: We need to start with all the numbers representing the range of numbers that are possible candidate primes. So, create an array of consecutive integers from 2 to n: (2,3,4,..n). I wouldn't hand-code this. I would use a loop to populate the array.
Step 2: At each step we select the smallest number and remove all it's multiples. So we'll start with an outer loop that goes from 2 to n. initially, let p equal 2, the first prime number.
Step 3: In an inner loop we need to iterate over all the numbers that are multiples of p, i.e for 2, that's 2,4,6,8 etc. Each time, setting it's value to false in the original array.
Step 4: Find the first number greater than p in the list that is not marked False. If there was no such number, stop. Otherwise, let p now equal this number( which is the next prime), and repeat from step 3.
When the algorithm terminates, all the numbers in the list that are not marked False are prime
Example: Let us take an example when n = 50. So we need to print all print numbers smaller than or equal to 50. We create list of all numbers from 2 to 50.
2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50

Answer 1

const MAXNR=150;

let candidates = {};

for(let i=2; i<=MAXNR; i++) {

candidates[i] = true;

}

for(let p=2; p <= MAXNR; p++) {

if (candidates[p]) {

process.stdout.write(`${p} `);

// Now flag all multiples of p as false

i=2;

while(p*i <= MAXNR) {

candidates[p*i] = false;

i++;

}

}

}