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{ "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 }
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