Euler 010 - Summation of primes.ipynb

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    "Euler Problem 10\n",
    "================\n",
    "\n",
    "The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.\n",
    "\n",
    "Find the sum of all the primes below two million."
   ]
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      "142913828922\n"
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    "N = 2000000\n",
    "prime = [True] * N\n",
    "prime_sum = 0\n",
    "for p in range(2, N):\n",
    "    if prime[p]:\n",
    "        prime_sum += p\n",
    "        for m in range(p*p, N, p):\n",
    "            prime[m] = False\n",
    "print(prime_sum)"
   ]
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    "*Explanation:* We use the sieve of Eratosthenes to find all primes less than two million.\n",
    "If $p$ is prime, then we add $p$ to `prime_sum`, and we mark all multiples of $p$ as composite,\n",
    "starting with $p^2$. The reason that we can start with $p^2$ is that all smaller multiples of $p$\n",
    "will have been marked already.\n",
    "\n",
    "We could speed up this program by iterating through the odd numbers.\n",
    "\n",
    "**Alternative solution:**"
   ]
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      "142913828922\n"
     ]
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   "source": [
    "from primesieve import primes\n",
    "print(sum(primes(N)))"
   ]
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