From: Neil Smith <neil.git@njae.me.uk>
Date: Fri, 17 Mar 2017 17:51:14 +0000 (+0000)
Subject: Done puzzle 50
X-Git-Url: https://git.njae.me.uk/?p=project-euler.git;a=commitdiff_plain;h=17380b005b102958fb132ea12e705e284f22f322

Done puzzle 50
---

diff --git a/euler50.ipynb b/euler50.ipynb
new file mode 100644
index 0000000..c2ae98e
--- /dev/null
+++ b/euler50.ipynb
@@ -0,0 +1,269 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {
+    "collapsed": false,
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "104743"
+      ]
+     },
+     "execution_count": 12,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "load 'primes.rb'\n",
+    "$primes = Primes.instance\n",
+    "$primes[10000]   # returns the 10,001st prime"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[2, 3, 5]"
+      ]
+     },
+     "execution_count": 13,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "(0...(0+3)).map{|i| $primes[i]}"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       ":prime_slice"
+      ]
+     },
+     "execution_count": 17,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "def prime_slice(start, len)\n",
+    "  (start...(start + len)).map{|i| $primes[i]}\n",
+    "end"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       ":sum_primes"
+      ]
+     },
+     "execution_count": 18,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "def sum_primes(start, len)\n",
+    "  prime_slice(start, len).sum\n",
+    "end"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[2, 3, 5, 7, 11]"
+      ]
+     },
+     "execution_count": 20,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "prime_slice(0, 5)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "28"
+      ]
+     },
+     "execution_count": 19,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "sum_primes(0, 5)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 30,
+   "metadata": {
+    "collapsed": false,
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0 - 2 : 5\n",
+      "0 - 4 : 17\n",
+      "0 - 6 : 41\n",
+      "0 - 12 : 197\n",
+      "0 - 14 : 281\n",
+      "0 - 60 : 7699\n",
+      "0 - 64 : 8893\n",
+      "0 - 96 : 22039\n",
+      "0 - 100 : 24133\n",
+      "0 - 102 : 25237\n",
+      "0 - 108 : 28697\n",
+      "0 - 114 : 32353\n",
+      "0 - 122 : 37561\n",
+      "0 - 124 : 38921\n",
+      "0 - 130 : 43201\n",
+      "0 - 132 : 44683\n",
+      "0 - 146 : 55837\n",
+      "0 - 152 : 61027\n",
+      "0 - 158 : 66463\n",
+      "0 - 162 : 70241\n",
+      "0 - 178 : 86453\n",
+      "0 - 192 : 102001\n",
+      "0 - 198 : 109147\n",
+      "0 - 204 : 116533\n",
+      "0 - 206 : 119069\n",
+      "0 - 208 : 121631\n",
+      "0 - 214 : 129419\n",
+      "0 - 216 : 132059\n",
+      "0 - 296 : 263171\n",
+      "0 - 308 : 287137\n",
+      "0 - 326 : 325019\n",
+      "0 - 328 : 329401\n",
+      "0 - 330 : 333821\n",
+      "0 - 332 : 338279\n",
+      "0 - 334 : 342761\n",
+      "0 - 342 : 360979\n",
+      "0 - 350 : 379667\n",
+      "0 - 356 : 393961\n",
+      "0 - 358 : 398771\n",
+      "0 - 426 : 581921\n",
+      "0 - 446 : 642869\n",
+      "0 - 458 : 681257\n",
+      "0 - 460 : 687767\n",
+      "0 - 464 : 700897\n",
+      "0 - 480 : 754573\n",
+      "0 - 484 : 768373\n",
+      "0 - 488 : 782263\n",
+      "0 - 512 : 868151\n",
+      "0 - 530 : 935507\n",
+      "0 - 536 : 958577\n",
+      "2 - 537 : 970219\n",
+      "2 - 539 : 978037\n",
+      "3 - 543 : 997651\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "[3, 543, 997651]"
+      ]
+     },
+     "execution_count": 30,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "sum_limit = 10**6\n",
+    "\n",
+    "start = 0\n",
+    "best_start = 0\n",
+    "best_length = 1\n",
+    "while primes[start] <= sum_limit\n",
+    "  # puts start\n",
+    "  length = 1\n",
+    "  sp = sum_primes(start, length)\n",
+    "  while sp <= sum_limit\n",
+    "    if sp.prime? && length > best_length\n",
+    "      best_start = start\n",
+    "      best_length = length\n",
+    "      # puts \"#{start} - #{length} : #{sum_primes(start, length)}\"\n",
+    "    end\n",
+    "    length += 1\n",
+    "    sp = sum_primes(start, length)\n",
+    "  end\n",
+    "  start += 1\n",
+    "end\n",
+    "[best_start, best_length, sum_primes(best_start, best_length)]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Ruby 2.4.0",
+   "language": "ruby",
+   "name": "ruby"
+  },
+  "language_info": {
+   "file_extension": ".rb",
+   "mimetype": "application/x-ruby",
+   "name": "ruby",
+   "version": "2.4.0"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}