{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "from PIL import Image\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "im = Image.open('taiwan.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "arr = np.array(im.convert('L').resize((87,34)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1111111111111111111111111111111111111\n",
      "1111111111111111111111111111111111111\n",
      "1111111111111111111111111000011111111\n",
      "1111111111111111111111100000000011111\n",
      "1111111111111111111000000000000000011\n",
      "1111111111111111000000000000000000111\n",
      "1111111111111110000000000000000000111\n",
      "1111111111111100000000000000000000111\n",
      "1111111111110000000000000000000000111\n",
      "1111111111000000000000000000000000111\n",
      "1111111111000000000000000000000011111\n",
      "1111111110000000000000000000000111111\n",
      "1111111000000000000000000000000111111\n",
      "1111110000000000000000000000000011111\n",
      "1111000000000000000000000000000111111\n",
      "1100000000000000000000000000001111111\n",
      "1100000000000000000000000000001111111\n",
      "1100000000000000000000000000011111111\n",
      "1100000000000000000000000000011111111\n",
      "1100000000000000000000000000111111111\n",
      "1000000000000000000000000001111111111\n",
      "1000000000000000000000000111111111111\n",
      "1110000000000000000000001111111111111\n",
      "1111100000000000000000111111111111111\n",
      "1111100000000000000011111111111111111\n",
      "1111111000000000000111111111111111111\n",
      "1111111110000000000111111111111111111\n",
      "1111111111110000001111111111111111111\n",
      "1111111111111000001111111111111111111\n",
      "1111111111111100001111111111111111111\n",
      "1111111111111100000111111111111111111\n",
      "1111111111111111111111111111111111111\n",
      "1111111111111111111111111111111111111\n"
     ]
    }
   ],
   "source": [
    "s = \"\"\n",
    "for i in range(0,arr.shape[0]-1):\n",
    "    s0 = \"\".join(\"0\" if x else \"1\" for x in arr[i][25:-25]>5)\n",
    "    s +=s0\n",
    "    print(s0)\n",
    "    W=len(s0)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "import gmpy2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n = int(s, 2)\n",
    "n = n+1-n%2\n",
    "gmpy2.is_prime(n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1118\n",
      "36109768628918289680181237269982326836315074390373762690444804688288262200027575252299763365131812306962690821804162221273208578541930369442412178452513756440140615861198776649031195773677731825752932990810189456101069051485444236446603538346051632222803884808461872785387210706073401343398461887943541836836797791233492039274922571561154870557915420355535324418408447\n"
     ]
    }
   ],
   "source": [
    "for i in range(len(s)-2,0,-1):\n",
    "    if s[len(s)-1-i-1]!=s[len(s)-1-i+1]: # try to change edge only(if not working, comment this line and try again)\n",
    "        p = n^(1<<i)\n",
    "        if gmpy2.is_prime(p):\n",
    "            print(i)\n",
    "            print(p)\n",
    "            break\n",
    "else:\n",
    "    print(\"not working!!!!\")\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111000111111111111111111111111111111110000000001111111111111111111111110000000000000000111111111111111111000000000000000000111111111111111111000000000000000000011111111111111111000000000000000000001111111111111110000000000000000000000111111111111100000000000000000000000011111111111110000000000000000000000111111111111110000000000000000000000111111111111100000000000000000000000011111111111100000000000000000000000000111111111000000000000000000000000000111111110000000000000000000000000000111111111000000000000000000000000000011111111100000000000000000000000000011111111110000000000000000000000000001111111111000000000000000000000000001111111111000000000000000000000000001111111111100000000000000000000000011111111111111100000000000000000000011111111111111111100000000000000000111111111111111111110000000000000001111111111111111111111110000000000001111111111111111111111111110000000000111111111111111111111111111111000000111111111111111111111111111111110000011111111111111111111111111111111100001111111111111111111111111111111110000011111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111'"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s2 = bin(p)[2:]\n",
    "s2 = '0'*(len(s)-len(s2))+s2\n",
    "s2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n = int(s2, 2)\n",
    "gmpy2.is_prime(n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1111111111111111111111111111111111111\n",
      "1111111111111111111111111111111111111\n",
      "1111111111111111111111111000111111111\n",
      "1111111111111111111111100000000011111\n",
      "1111111111111111111000000000000000011\n",
      "1111111111111111000000000000000000111\n",
      "1111111111111110000000000000000000111\n",
      "1111111111111100000000000000000000111\n",
      "1111111111110000000000000000000000111\n",
      "1111111111000000000000000000000000111\n",
      "1111111111000000000000000000000011111\n",
      "1111111110000000000000000000000111111\n",
      "1111111000000000000000000000000111111\n",
      "1111110000000000000000000000000011111\n",
      "1111000000000000000000000000000111111\n",
      "1100000000000000000000000000001111111\n",
      "1100000000000000000000000000001111111\n",
      "1100000000000000000000000000011111111\n",
      "1100000000000000000000000000011111111\n",
      "1100000000000000000000000000111111111\n",
      "1000000000000000000000000001111111111\n",
      "1000000000000000000000000111111111111\n",
      "1110000000000000000000001111111111111\n",
      "1111100000000000000000111111111111111\n",
      "1111100000000000000011111111111111111\n",
      "1111111000000000000111111111111111111\n",
      "1111111110000000000111111111111111111\n",
      "1111111111110000001111111111111111111\n",
      "1111111111111000001111111111111111111\n",
      "1111111111111100001111111111111111111\n",
      "1111111111111100000111111111111111111\n",
      "1111111111111111111111111111111111111\n",
      "1111111111111111111111111111111111111\n"
     ]
    }
   ],
   "source": [
    "for i in range(0,len(s2),W):\n",
    "    print(s2[i:i+W])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.5.3"
  }
 },
 "nbformat": 4,
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}