Project Euler Q49 - LO Man Hei

Download notebook

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "a469358e-2f57-4bd6-9c8d-c59f3d77920b",
   "metadata": {},
   "source": [
    "### Q49\n",
    "What 12-digit number do you form by concatenating the three terms in this sequence?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "820c6f59-d5d1-4f67-a379-b41d8bb337ac",
   "metadata": {},
   "outputs": [],
   "source": [
    "def prime_numbers(min_num, max_num):\n",
    "    result = []\n",
    "    sieve = [True] * (max_num+1)\n",
    "    for p in range(2, max_num+1):\n",
    "        if (sieve[p]):\n",
    "            if p >= min_num: \n",
    "                result.append(p)\n",
    "            for i in range(p, max_num+1, p):\n",
    "                sieve[i] = False\n",
    "    return result\n",
    "\n",
    "def prime_permutations():\n",
    "    prime_permutations_map = {}\n",
    "    prime_numbers_set = prime_numbers(1000,9999)\n",
    "    for prime in prime_numbers_set:\n",
    "        sorted_num = ''.join(sorted(str(prime)))\n",
    "        prime_permutations_map[sorted_num] = prime_permutations_map.get(sorted_num,[]) + [prime]\n",
    "    for k,v in prime_permutations_map.items():\n",
    "        len_v = len(v)\n",
    "        if len_v < 3 or k == ''.join(sorted('1487')):\n",
    "            continue\n",
    "        for i in range(len_v-2):\n",
    "            for j in range(i+1,len_v-1):\n",
    "                if 2*v[j]-v[i] in v:\n",
    "                    return f\"{v[i]}{v[j]}{2*v[j]-v[i]}\"\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "af630329-9130-41b7-9eae-dbff1852f068",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 1.69 ms, sys: 326 µs, total: 2.01 ms\n",
      "Wall time: 2.02 ms\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "'296962999629'"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%%time\n",
    "prime_permutations()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "663d196a-1e20-4e4e-b065-59ff78163a78",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}

Loading