You are making the Sieve of Eratosthenes much slower by making use of array manipulation functions such as Array#indexOf
and Array#splice
which runs in linear time. When you can have O(1) for both operations involved.
Below is the Sieve of Eratosthenes following conventional programming practices:
var eratosthenes = function(n) {
// Eratosthenes algorithm to find all primes under n
var array = [], upperLimit = Math.sqrt(n), output = [];
// Make an array from 2 to (n - 1)
for (var i = 0; i < n; i++) {
array.push(true);
}
// Remove multiples of primes starting from 2, 3, 5,...
for (var i = 2; i <= upperLimit; i++) {
if (array[i]) {
for (var j = i * i; j < n; j += i) {
array[j] = false;
}
}
}
// All array[i] set to true are primes
for (var i = 2; i < n; i++) {
if(array[i]) {
output.push(i);
}
}
return output;
};
You can see a live example for n = 1 000 000
here.