Euler 047 - Distinct prime factors.ipynb

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    "Euler Problem 47\n",
    "================\n",
    "\n",
    "The first two consecutive numbers to have two distinct prime factors are:\n",
    "\n",
    "- 14 = 2 × 7\n",
    "- 15 = 3 × 5\n",
    "\n",
    "The first three consecutive numbers to have three distinct prime factors are:\n",
    "\n",
    "- 644 = 2² × 7 × 23\n",
    "- 645 = 3 × 5 × 43\n",
    "- 646 = 2 × 17 × 19.\n",
    "\n",
    "Find the first four consecutive integers to have four distinct prime factors. What is the first of these numbers?"
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      "134043\n"
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    "N = 200000\n",
    "sieve = [0] * N\n",
    "prime_factors = [0] * N\n",
    "run = 0\n",
    "for n in range(2, N):\n",
    "    if sieve[n] == 0:\n",
    "        sieve[n] = n\n",
    "        for m in range(n*n, N, n):\n",
    "            sieve[m] = n\n",
    "    q = n // sieve[n]\n",
    "    if q % sieve[n] == 0:\n",
    "        prime_factors[n] = prime_factors[q]\n",
    "    else:\n",
    "        prime_factors[n] = prime_factors[q] + 1\n",
    "    if prime_factors[n] == 4:\n",
    "        run += 1\n",
    "        if run == 4:\n",
    "            print(n-3)\n",
    "            break\n",
    "    else:\n",
    "        run = 0"
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