Euler 035 - Circular primes.ipynb

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    "Euler Problem 35\n",
    "================\n",
    "\n",
    "The number, 197, is called a circular prime because all rotations of the digits: 197, 971, and 719, are themselves prime.\n",
    "\n",
    "There are thirteen such primes below 100: 2, 3, 5, 7, 11, 13, 17, 31, 37, 71, 73, 79, and 97.\n",
    "\n",
    "How many circular primes are there below one million?"
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      "55\n"
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    "N = 1000000\n",
    "prime = [False, False] + [True] * (N - 2)\n",
    "primes = []\n",
    "for p in range(2, N):\n",
    "    if prime[p]:\n",
    "        primes.append(p)\n",
    "        for q in range(p*p, N, p):\n",
    "            prime[q] = False\n",
    "count = 0\n",
    "pow10 = 1\n",
    "k_max = 1\n",
    "for p in primes:\n",
    "    k = len(str(p))\n",
    "    if k > k_max:\n",
    "        pow10 *= 10\n",
    "        k_max = k\n",
    "    for i in range(k-1):\n",
    "        p = p//10 + (p%10) * pow10\n",
    "        if not prime[p]:\n",
    "            break\n",
    "    else:\n",
    "        count += 1\n",
    "print(count)"
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