Euler 046 - Goldbach's other conjecture.ipynb

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    "Euler Problem 46\n",
    "================\n",
    "\n",
    "It was proposed by Christian Goldbach that every odd composite number can be written as the sum of a prime and twice a square.\n",
    "\n",
    "- 9 = 7 + 2×1<sup>2</sup>\n",
    "- 15 = 7 + 2×2<sup>2</sup>\n",
    "- 21 = 3 + 2×3<sup>2</sup>\n",
    "- 25 = 7 + 2×3<sup>2</sup>\n",
    "- 27 = 19 + 2×2<sup>2</sup>\n",
    "- 33 = 31 + 2×1<sup>2</sup>\n",
    "\n",
    "It turns out that the conjecture was false.\n",
    "\n",
    "What is the smallest odd composite that cannot be written as the sum of a prime and twice a square?"
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      "5777\n"
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    "N = 10000\n",
    "sieve = [False, False] + [True]*N\n",
    "for p in range(N):\n",
    "    if sieve[p]:\n",
    "        for m in range(p*p, N, p):\n",
    "            sieve[m] = False\n",
    "for n in range(9, N, 2):\n",
    "    if sieve[n]:\n",
    "        continue\n",
    "    delta = 6\n",
    "    m = n - 2\n",
    "    while m > 2 and not sieve[m]:\n",
    "        m -= delta\n",
    "        delta += 4\n",
    "    if m <= 2:\n",
    "        print(n)\n",
    "        break"
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