{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "104743"
      ]
     },
     "execution_count": 1,
     "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": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[2, 3, 5]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(0...(0+3)).map{|i| $primes[i]}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       ":prime_slice"
      ]
     },
     "execution_count": 3,
     "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": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       ":sum_primes"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def sum_primes(start, len)\n",
    "  prime_slice(start, len).sum\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[2, 3, 5, 7, 11]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prime_slice(0, 5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "28"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum_primes(0, 5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[3, 543, 997651]"
      ]
     },
     "execution_count": 8,
     "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"
  }
 },
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