Problem

The sum of the primes below 10 is $2 + 3 + 5 + 7 = 17$.

Find the sum of all the primes below two million.

Answer

142913828922

---

Python

#!/usr/bin/env python
from itertools import takewhile

def eratosthenes():
    '''Yields the sequence of prime numbers via the Sieve of Eratosthenes.'''
    D = {}  # map composite integers to primes witnessing their compositeness
    q = 2   # first integer to test for primality
    while 1:
        if q not in D:
            yield q        # not marked composite, must be prime
            D[q*q] = [q]   # first multiple of q not already marked
        else:
            for p in D[q]: # move each witness to its next multiple
                D.setdefault(p+q,[]).append(p)
            del D[q]       # no longer need D[q], free memory
        q += 1

print(sum(takewhile(lambda x: x < 2000000, eratosthenes())))

---

JavaScript

const sieve = {}
let s = 0
for (let q = 2; q < 2000000; q++) {
  if (sieve[q]) {
    sieve[q].forEach((p) => {
      const list = sieve[p + q] || []
      list.push(p)
      sieve[p + q] = list
    })
    delete sieve[q]
  } else {
    s += q
    sieve[q * q] = [q]
  }
}
console.log(s)

---

Go

package main

import "fmt"
import "math"

func PrimeSieve(n int64) []int64 {
	result := make([]int64, 0, n/int64(math.Log(float64(n))))
	sieve := make([]bool, n+1)
	sn := int64(math.Sqrt(float64(n)))
	var i, j int64
	for i = 2; i <= sn; i++ {
		if !sieve[i] {
			for j = i * i; j <= n; j += i {
				sieve[j] = true
			}
		}
	}
	for i = 2; i <= n; i++ {
		if !sieve[i] {
			result = append(result, i)
		}
	}
	return result
}

func main() {
	primes := PrimeSieve(2000000)
	var sum int64 = 0
	for _, p := range primes {
		sum += p
	}
	fmt.Println(sum)
}

---

Ruby

#!/usr/bin/env ruby
require 'mathn'
puts Prime.take_while{ |n| n < 2000000 }.reduce(:+)

---

Haskell

primes :: [Integer]
primes = 2 : sieve primes [3,5..] where
    sieve (p:ps) xs = h ++ sieve ps [x | x <- t, rem x p /= 0]
                      where (h, t) = span (< p*p) xs

main :: IO ()
main = print $ sum $ takeWhile (< 2000000) primes

---

Clojure

#!/usr/bin/env clojure
(defn primes [n]
  (defn improve [p nums]
    (filter #(or 
               (not (= (rem % p) 0))
               (= % p))
            nums))
  (defn prime-iter [p nums i]
    (if (> (* p p) n)
      nums
      (prime-iter (nth nums (+ i 1)) (improve (nth nums (+ i 1)) nums) (+ i 1))))
  (prime-iter 2 (range 2 (+ n 1)) -1))

(println (reduce + (primes 2000000)))

---

Mathematica

(* Use Mathematica's built-in functions for easy problem-solving. *)
Total[Select[Range[1999999], PrimeQ]]

---

Java

public final class p010 implements EulerSolution {
	
	public static void main(String[] args) {
		System.out.println(new p010().run());
	}
	
	
	/* 
	 * Call the sieve of Eratosthenes and sum the primes found.
	 * A conservative upper bound for the sum is 2000000^2, which fits in a Java long type.
	 */
	private static final int LIMIT = 2000000;
	
	public String run() {
		long sum = 0;
		for (int p : Library.listPrimes(LIMIT - 1))
			sum += p;
		return Long.toString(sum);
	}
	
}