{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "load 'primes.rb'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       ":gb_test_one"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def gb_test_one(n, s)\n",
    "  p = n - 2 * s ** 2\n",
    "  p.prime?\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       ":other_goldbach"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def other_goldbach(n)\n",
    "  s_limit = Math.sqrt(n / 2).floor\n",
    "  (1..s_limit).any? {|s| gb_test_one n, s}\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "other_goldbach(9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       ":sequence"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def sequence(&generator)\n",
    "  Enumerator.new do |yielder|\n",
    "    n = 0\n",
    "    loop do\n",
    "      yielder.yield generator.call(n)\n",
    "      n = n + 1\n",
    "    end\n",
    "  end\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "#<Enumerator::Lazy: #<Enumerator::Lazy: #<Enumerator::Lazy: #<Enumerator: #<Enumerator::Generator:0x00557af0bf6f10>:each>>:drop(1)>:select>"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "odds = sequence {|i| 2 * i + 1}\n",
    "candidates = odds.lazy.drop(1).select {|i| !i.prime?}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[9, 15, 21, 25, 27, 33, 35, 39, 45, 49]"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "candidates.take(10).force"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[5777]"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "candidates.reject {|i| other_goldbach i}.take(1).force"
   ]
  },
  {
   "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
}