How to make an algorithm for calculating the sum of prime numbers according to the principle of Sita Erastofen?

Question

JavaScript

Good day. I wrote a code that calculates the sum of prime numbers from zero to a given number. But everything works fine for small numbers, when I set the number 977 it should be 73156 and I have 108618. Who can help?

function sumPrimes(num) {
  let numArr = [2];
  let delLength3 = [];
  let delLength5 = [];
  let delLength7 = [];
  for (let i = 4; i <= num; i = i + 3) {
    delLength3.push(i);
  }

  for (let i = 5; i <= num; i = i + 5) {
    delLength5.push(i);
  }

  for (let i = 14; i <= num; i = i + 7) {
    delLength7.push(i);
  }

  for (let i = 2; i <= num; i++) {
    if (i % 2 !== 0) {
      numArr.push(i);
    }
  }

  delLength3.map(el => {
    numArr[el] = "x";
  });

  delLength5.map(el => {
    numArr[el] = "x";
  });

  delLength7.map(el => {
  console.log(el)
  let index = numArr.indexOf(el)
  if (index >= 0) {
    numArr[index] = 'x'
  }
  });

  let newArr = numArr.filter(el => {
    if (typeof el === "number") {
      return el;
    }
  });

  let sumArr = newArr.reduce((a, b) => {
    return a + b;
  });

  console.log(sumArr);
  return sumArr;
}

sumPrimes(977);

code link https://codesandbox.io/s/adoring-wildflower-c0rf0

Answer 1

Many questions about the code
1) Why is it starting from 4 and not from 3? 2) Why is it starting from 14, and not from 7 3) Firstly, you already have a deuce in the array, and secondly, why the condition if you can just i + = 2?

for (let i = 2; i <= num; i++) {
    if (i % 2 !== 0) {
      numArr.push(i);
    }
  }

4) Where are the other prime numbers? 11, 13, etc.?
In general, it is not visible that this code could be working
. A simple and efficient code for this case would be like this

const simpleNumbersSum = max => {
   const arr = new Array(max + 1)
   let sum = 1 + 2; //Или просто 2, если единицу не учитываем
   for (let i = 3; i <= max; i+=2) {
      if (!arr[i]) {
         sum+=i;
         for (let j = i * i; j <= max; j+=i*2) {
            arr[j] = true;
         }
      }
   }
   
   return sum
}

console.log(simpleNumbersSum(977))