Omkar_Pradhan_25Jan_Programming Tasks.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Programming Tasks"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 25/01/2023"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Omkar Pradhan"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "233168"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Completed\n",
    "'''\n",
    "1)\"If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23.\n",
    "Find the sum of all the multiples of 3 or 5 below 1000.\"\n",
    "'''\n",
    "def multi():\n",
    "    x = []\n",
    "    for i in range(0,1000):\n",
    "        if i%3==0 or i%5==0:\n",
    "            x.append(i)\n",
    "    return sum(x)\n",
    "\n",
    "multi()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Question 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4613732"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Completed\n",
    "'''\n",
    "2)\"Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2, the first 10 terms will be:\n",
    "1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...\n",
    "By considering the terms in the Fibonacci sequence whose values do not exceed four million, find the sum of the even-valued terms.\"\n",
    "'''\n",
    "def fibo():\n",
    "    a = 0\n",
    "    b = 1\n",
    "    x= []\n",
    "    i=1\n",
    "    while(i<4000000):\n",
    "        a,b=b,a+b\n",
    "        i=b\n",
    "        if(i%2==0):\n",
    "            x.append(i)\n",
    "    \n",
    "    return sum(x)\n",
    "fibo()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Question 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Completed\n",
    "'''\n",
    "3)\"The prime factors of 13195 are 5, 7, 13 and 29.\n",
    "What is the largest prime factor of the number 600851475143 ?\"\n",
    "\n",
    "'''\n",
    "\n",
    "\n",
    "def prime_check(n):\n",
    "    #using fernats little theorem\n",
    "    return ((2**n)-2)%n\n",
    "\n",
    "def largest_factor(n):\n",
    "    lf = 0\n",
    "    for i in range(2,n):\n",
    "        if (n%i==0 and prime_check(i)==0):\n",
    "            lf=i\n",
    "            \n",
    "    return lf\n",
    "\n",
    "\n",
    "\n",
    "largest_factor(600851475143)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "71\n",
      "839\n",
      "1471\n",
      "6857\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "6857"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Question3 Working\n",
    "def prime_factors(n):\n",
    "    c=2\n",
    "    pf = []\n",
    "    while(n>1):\n",
    "        if(n%c==0):\n",
    "            pf.append(c)\n",
    "            print(c)\n",
    "            n=n/c\n",
    "        else:\n",
    "            c+=1\n",
    "    return pf[len(pf)-1]\n",
    "\n",
    "prime_factors(600851475143)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Question 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "913  X  993  :  906609\n"
     ]
    }
   ],
   "source": [
    "#Completed\n",
    "'''\n",
    "4)\"A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 × 99.\n",
    "Find the largest palindrome made from the product of two 3-digit numbers.\"\n",
    "'''\n",
    "\n",
    "def pal_num(u,l):\n",
    "    lg = 0\n",
    "    a = 0\n",
    "    b = 0\n",
    "    for i in range(u,l):\n",
    "        for j in range(l,u,-1):\n",
    "            if(str(i*j)==str(i*j)[::-1]):\n",
    "                if (i*j)>lg:\n",
    "                    lg=i*j\n",
    "                    a=i\n",
    "                    b=j\n",
    "                    \n",
    "    print(a,\" X \",b,\" : \",lg)\n",
    "pal_num(100,1000)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Question 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "232792560"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Completed\n",
    "'''\n",
    "5)\"2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder.\n",
    "What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20?\"\n",
    "'''\n",
    "\n",
    "def small():\n",
    "    i=1\n",
    "    s = 0\n",
    "    while i>0:\n",
    "        if (i%2==0 and i%3==0 and i%4==0 and i%5==0 and i%6==0 and i%7==0 and i%8==0 and i%9==0 and i%10==0 and i%11==0 and i%12==0 and i%13==0 and i%14==0 and i%15==0 and i%16==0 and i%17==0 and i%18==0 and i%19==0 and i%20==0):\n",
    "            s=i\n",
    "            i=-1\n",
    "        else:\n",
    "            i+=1\n",
    "    return s\n",
    "            \n",
    "    \n",
    "\n",
    "small()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Question 6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "25164150"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Completed\n",
    "'''\n",
    "6)\"The sum of the squares of the first ten natural numbers is,\n",
    "12 + 22 + ... + 102 = 385\n",
    "The square of the sum of the first ten natural numbers is,\n",
    "(1 + 2 + ... + 10)2 = 552 = 3025\n",
    "Hence the difference between the sum of the squares of the first ten natural numbers and the square of the sum is 3025 − 385 = 2640.\n",
    "Find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum.\"\n",
    "\n",
    "'''\n",
    "\n",
    "def diff():\n",
    "    sums_sq = 0\n",
    "    sq_sum = 0\n",
    "    for i in range(1,101):\n",
    "        sums_sq+=(i*i)\n",
    "        sq_sum+=i\n",
    "    return (sq_sum**2)-sums_sq\n",
    "\n",
    "diff()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Question 7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 : 2\n",
      "2 : 3\n",
      "3 : 5\n",
      "4 : 7\n",
      "5 : 11\n",
      "6 : 13\n",
      "7 : 17\n",
      "8 : 19\n",
      "9 : 23\n",
      "10 : 29\n",
      "11 : 31\n",
      "12 : 37\n",
      "13 : 41\n",
      "14 : 43\n",
      "15 : 47\n",
      "16 : 53\n",
      "17 : 59\n",
      "18 : 61\n",
      "19 : 67\n",
      "20 : 71\n",
      "21 : 73\n",
      "22 : 79\n",
      "23 : 83\n",
      "24 : 89\n",
      "25 : 97\n",
      "26 : 101\n",
      "27 : 103\n",
      "28 : 107\n",
      "29 : 109\n",
      "30 : 113\n",
      "31 : 127\n",
      "32 : 131\n",
      "33 : 137\n",
      "34 : 139\n",
      "35 : 149\n",
      "36 : 151\n",
      "37 : 157\n",
      "38 : 163\n",
      "39 : 167\n",
      "40 : 173\n",
      "41 : 179\n",
      "42 : 181\n",
      "43 : 191\n",
      "44 : 193\n",
      "45 : 197\n",
      "46 : 199\n",
      "47 : 211\n",
      "48 : 223\n",
      "49 : 227\n",
      "50 : 229\n",
      "51 : 233\n",
      "52 : 239\n",
      "53 : 241\n",
      "54 : 251\n",
      "55 : 257\n",
      "56 : 263\n",
      "57 : 269\n",
      "58 : 271\n",
      "59 : 277\n",
      "60 : 281\n",
      "61 : 283\n",
      "62 : 293\n",
      "63 : 307\n",
      "64 : 311\n",
      "65 : 313\n",
      "66 : 317\n",
      "67 : 331\n",
      "68 : 337\n",
      "69 : 341\n",
      "70 : 347\n",
      "71 : 349\n",
      "72 : 353\n",
      "73 : 359\n",
      "74 : 367\n",
      "75 : 373\n",
      "76 : 379\n",
      "77 : 383\n",
      "78 : 389\n",
      "79 : 397\n",
      "80 : 401\n",
      "81 : 409\n",
      "82 : 419\n",
      "83 : 421\n",
      "84 : 431\n",
      "85 : 433\n",
      "86 : 439\n",
      "87 : 443\n",
      "88 : 449\n",
      "89 : 457\n",
      "90 : 461\n",
      "91 : 463\n",
      "92 : 467\n",
      "93 : 479\n",
      "94 : 487\n",
      "95 : 491\n",
      "96 : 499\n",
      "97 : 503\n",
      "98 : 509\n",
      "99 : 521\n",
      "100 : 523\n",
      "101 : 541\n",
      "102 : 547\n",
      "103 : 557\n",
      "104 : 561\n",
      "105 : 563\n",
      "106 : 569\n",
      "107 : 571\n",
      "108 : 577\n",
      "109 : 587\n",
      "110 : 593\n",
      "111 : 599\n",
      "112 : 601\n",
      "113 : 607\n",
      "114 : 613\n",
      "115 : 617\n",
      "116 : 619\n",
      "117 : 631\n",
      "118 : 641\n",
      "119 : 643\n",
      "120 : 645\n",
      "121 : 647\n",
      "122 : 653\n",
      "123 : 659\n",
      "124 : 661\n",
      "125 : 673\n",
      "126 : 677\n",
      "127 : 683\n",
      "128 : 691\n",
      "129 : 701\n",
      "130 : 709\n",
      "131 : 719\n",
      "132 : 727\n",
      "133 : 733\n",
      "134 : 739\n",
      "135 : 743\n",
      "136 : 751\n",
      "137 : 757\n",
      "138 : 761\n",
      "139 : 769\n",
      "140 : 773\n",
      "141 : 787\n",
      "142 : 797\n",
      "143 : 809\n",
      "144 : 811\n",
      "145 : 821\n",
      "146 : 823\n",
      "147 : 827\n",
      "148 : 829\n",
      "149 : 839\n",
      "150 : 853\n",
      "151 : 857\n",
      "152 : 859\n",
      "153 : 863\n",
      "154 : 877\n",
      "155 : 881\n",
      "156 : 883\n",
      "157 : 887\n",
      "158 : 907\n",
      "159 : 911\n",
      "160 : 919\n",
      "161 : 929\n",
      "162 : 937\n",
      "163 : 941\n",
      "164 : 947\n",
      "165 : 953\n",
      "166 : 967\n",
      "167 : 971\n",
      "168 : 977\n",
      "169 : 983\n",
      "170 : 991\n",
      "171 : 997\n",
      "172 : 1009\n",
      "173 : 1013\n",
      "174 : 1019\n",
      "175 : 1021\n",
      "176 : 1031\n",
      "177 : 1033\n",
      "178 : 1039\n",
      "179 : 1049\n",
      "180 : 1051\n",
      "181 : 1061\n",
      "182 : 1063\n",
      "183 : 1069\n",
      "184 : 1087\n",
      "185 : 1091\n",
      "186 : 1093\n",
      "187 : 1097\n",
      "188 : 1103\n",
      "189 : 1105\n",
      "190 : 1109\n",
      "191 : 1117\n",
      "192 : 1123\n",
      "193 : 1129\n",
      "194 : 1151\n",
      "195 : 1153\n",
      "196 : 1163\n",
      "197 : 1171\n",
      "198 : 1181\n",
      "199 : 1187\n",
      "200 : 1193\n",
      "201 : 1201\n",
      "202 : 1213\n",
      "203 : 1217\n",
      "204 : 1223\n",
      "205 : 1229\n",
      "206 : 1231\n",
      "207 : 1237\n",
      "208 : 1249\n",
      "209 : 1259\n",
      "210 : 1277\n",
      "211 : 1279\n",
      "212 : 1283\n",
      "213 : 1289\n",
      "214 : 1291\n",
      "215 : 1297\n",
      "216 : 1301\n",
      "217 : 1303\n",
      "218 : 1307\n",
      "219 : 1319\n",
      "220 : 1321\n",
      "221 : 1327\n",
      "222 : 1361\n",
      "223 : 1367\n",
      "224 : 1373\n",
      "225 : 1381\n",
      "226 : 1387\n",
      "227 : 1399\n",
      "228 : 1409\n",
      "229 : 1423\n",
      "230 : 1427\n",
      "231 : 1429\n",
      "232 : 1433\n",
      "233 : 1439\n",
      "234 : 1447\n",
      "235 : 1451\n",
      "236 : 1453\n",
      "237 : 1459\n",
      "238 : 1471\n",
      "239 : 1481\n",
      "240 : 1483\n",
      "241 : 1487\n",
      "242 : 1489\n",
      "243 : 1493\n",
      "244 : 1499\n",
      "245 : 1511\n",
      "246 : 1523\n",
      "247 : 1531\n",
      "248 : 1543\n",
      "249 : 1549\n",
      "250 : 1553\n",
      "251 : 1559\n",
      "252 : 1567\n",
      "253 : 1571\n",
      "254 : 1579\n",
      "255 : 1583\n",
      "256 : 1597\n",
      "257 : 1601\n",
      "258 : 1607\n",
      "259 : 1609\n",
      "260 : 1613\n",
      "261 : 1619\n",
      "262 : 1621\n",
      "263 : 1627\n",
      "264 : 1637\n",
      "265 : 1657\n",
      "266 : 1663\n",
      "267 : 1667\n",
      "268 : 1669\n",
      "269 : 1693\n",
      "270 : 1697\n",
      "271 : 1699\n",
      "272 : 1709\n",
      "273 : 1721\n",
      "274 : 1723\n",
      "275 : 1729\n",
      "276 : 1733\n",
      "277 : 1741\n",
      "278 : 1747\n",
      "279 : 1753\n",
      "280 : 1759\n",
      "281 : 1777\n",
      "282 : 1783\n",
      "283 : 1787\n",
      "284 : 1789\n",
      "285 : 1801\n",
      "286 : 1811\n",
      "287 : 1823\n",
      "288 : 1831\n",
      "289 : 1847\n",
      "290 : 1861\n",
      "291 : 1867\n",
      "292 : 1871\n",
      "293 : 1873\n",
      "294 : 1877\n",
      "295 : 1879\n",
      "296 : 1889\n",
      "297 : 1901\n",
      "298 : 1905\n",
      "299 : 1907\n",
      "300 : 1913\n",
      "301 : 1931\n",
      "302 : 1933\n",
      "303 : 1949\n",
      "304 : 1951\n",
      "305 : 1973\n",
      "306 : 1979\n",
      "307 : 1987\n",
      "308 : 1993\n",
      "309 : 1997\n",
      "310 : 1999\n",
      "311 : 2003\n",
      "312 : 2011\n",
      "313 : 2017\n",
      "314 : 2027\n",
      "315 : 2029\n",
      "316 : 2039\n",
      "317 : 2047\n",
      "318 : 2053\n",
      "319 : 2063\n",
      "320 : 2069\n",
      "321 : 2081\n",
      "322 : 2083\n",
      "323 : 2087\n",
      "324 : 2089\n",
      "325 : 2099\n",
      "326 : 2111\n",
      "327 : 2113\n",
      "328 : 2129\n",
      "329 : 2131\n",
      "330 : 2137\n",
      "331 : 2141\n",
      "332 : 2143\n",
      "333 : 2153\n",
      "334 : 2161\n",
      "335 : 2179\n",
      "336 : 2203\n",
      "337 : 2207\n",
      "338 : 2213\n",
      "339 : 2221\n",
      "340 : 2237\n",
      "341 : 2239\n",
      "342 : 2243\n",
      "343 : 2251\n",
      "344 : 2267\n",
      "345 : 2269\n",
      "346 : 2273\n",
      "347 : 2281\n",
      "348 : 2287\n",
      "349 : 2293\n",
      "350 : 2297\n",
      "351 : 2309\n",
      "352 : 2311\n",
      "353 : 2333\n",
      "354 : 2339\n",
      "355 : 2341\n",
      "356 : 2347\n",
      "357 : 2351\n",
      "358 : 2357\n",
      "359 : 2371\n",
      "360 : 2377\n",
      "361 : 2381\n",
      "362 : 2383\n",
      "363 : 2389\n",
      "364 : 2393\n",
      "365 : 2399\n",
      "366 : 2411\n",
      "367 : 2417\n",
      "368 : 2423\n",
      "369 : 2437\n",
      "370 : 2441\n",
      "371 : 2447\n",
      "372 : 2459\n",
      "373 : 2465\n",
      "374 : 2467\n",
      "375 : 2473\n",
      "376 : 2477\n",
      "377 : 2503\n",
      "378 : 2521\n",
      "379 : 2531\n",
      "380 : 2539\n",
      "381 : 2543\n",
      "382 : 2549\n",
      "383 : 2551\n",
      "384 : 2557\n",
      "385 : 2579\n",
      "386 : 2591\n",
      "387 : 2593\n",
      "388 : 2609\n",
      "389 : 2617\n",
      "390 : 2621\n",
      "391 : 2633\n",
      "392 : 2647\n",
      "393 : 2657\n",
      "394 : 2659\n",
      "395 : 2663\n",
      "396 : 2671\n",
      "397 : 2677\n",
      "398 : 2683\n",
      "399 : 2687\n",
      "400 : 2689\n",
      "401 : 2693\n",
      "402 : 2699\n",
      "403 : 2701\n",
      "404 : 2707\n",
      "405 : 2711\n",
      "406 : 2713\n",
      "407 : 2719\n",
      "408 : 2729\n",
      "409 : 2731\n",
      "410 : 2741\n",
      "411 : 2749\n",
      "412 : 2753\n",
      "413 : 2767\n",
      "414 : 2777\n",
      "415 : 2789\n",
      "416 : 2791\n",
      "417 : 2797\n",
      "418 : 2801\n",
      "419 : 2803\n",
      "420 : 2819\n",
      "421 : 2821\n",
      "422 : 2833\n",
      "423 : 2837\n",
      "424 : 2843\n",
      "425 : 2851\n",
      "426 : 2857\n",
      "427 : 2861\n",
      "428 : 2879\n",
      "429 : 2887\n",
      "430 : 2897\n",
      "431 : 2903\n",
      "432 : 2909\n",
      "433 : 2917\n",
      "434 : 2927\n",
      "435 : 2939\n",
      "436 : 2953\n",
      "437 : 2957\n",
      "438 : 2963\n",
      "439 : 2969\n",
      "440 : 2971\n",
      "441 : 2999\n",
      "442 : 3001\n",
      "443 : 3011\n",
      "444 : 3019\n",
      "445 : 3023\n",
      "446 : 3037\n",
      "447 : 3041\n",
      "448 : 3049\n",
      "449 : 3061\n",
      "450 : 3067\n",
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      "9858 : 102103\n",
      "9859 : 102107\n",
      "9860 : 102121\n",
      "9861 : 102139\n",
      "9862 : 102149\n",
      "9863 : 102161\n",
      "9864 : 102181\n",
      "9865 : 102191\n",
      "9866 : 102197\n",
      "9867 : 102199\n",
      "9868 : 102203\n",
      "9869 : 102217\n",
      "9870 : 102229\n",
      "9871 : 102233\n",
      "9872 : 102241\n",
      "9873 : 102251\n",
      "9874 : 102253\n",
      "9875 : 102259\n",
      "9876 : 102293\n",
      "9877 : 102299\n",
      "9878 : 102301\n",
      "9879 : 102317\n",
      "9880 : 102329\n",
      "9881 : 102337\n",
      "9882 : 102359\n",
      "9883 : 102367\n",
      "9884 : 102397\n",
      "9885 : 102407\n",
      "9886 : 102409\n",
      "9887 : 102433\n",
      "9888 : 102437\n",
      "9889 : 102451\n",
      "9890 : 102461\n",
      "9891 : 102481\n",
      "9892 : 102497\n",
      "9893 : 102499\n",
      "9894 : 102503\n",
      "9895 : 102523\n",
      "9896 : 102533\n",
      "9897 : 102539\n",
      "9898 : 102547\n",
      "9899 : 102551\n",
      "9900 : 102559\n",
      "9901 : 102563\n",
      "9902 : 102587\n",
      "9903 : 102593\n",
      "9904 : 102607\n",
      "9905 : 102611\n",
      "9906 : 102643\n",
      "9907 : 102647\n",
      "9908 : 102653\n",
      "9909 : 102667\n",
      "9910 : 102673\n",
      "9911 : 102677\n",
      "9912 : 102679\n",
      "9913 : 102701\n",
      "9914 : 102761\n",
      "9915 : 102763\n",
      "9916 : 102769\n",
      "9917 : 102793\n",
      "9918 : 102797\n",
      "9919 : 102811\n",
      "9920 : 102829\n",
      "9921 : 102841\n",
      "9922 : 102859\n",
      "9923 : 102871\n",
      "9924 : 102877\n",
      "9925 : 102881\n",
      "9926 : 102911\n",
      "9927 : 102913\n",
      "9928 : 102929\n",
      "9929 : 102931\n",
      "9930 : 102953\n",
      "9931 : 102967\n",
      "9932 : 102983\n",
      "9933 : 103001\n",
      "9934 : 103007\n",
      "9935 : 103043\n",
      "9936 : 103049\n",
      "9937 : 103067\n",
      "9938 : 103069\n",
      "9939 : 103079\n",
      "9940 : 103087\n",
      "9941 : 103091\n",
      "9942 : 103093\n",
      "9943 : 103099\n",
      "9944 : 103123\n",
      "9945 : 103141\n",
      "9946 : 103171\n",
      "9947 : 103177\n",
      "9948 : 103183\n",
      "9949 : 103217\n",
      "9950 : 103231\n",
      "9951 : 103237\n",
      "9952 : 103289\n",
      "9953 : 103291\n",
      "9954 : 103307\n",
      "9955 : 103319\n",
      "9956 : 103333\n",
      "9957 : 103349\n",
      "9958 : 103357\n",
      "9959 : 103387\n",
      "9960 : 103391\n",
      "9961 : 103393\n",
      "9962 : 103399\n",
      "9963 : 103409\n",
      "9964 : 103421\n",
      "9965 : 103423\n",
      "9966 : 103451\n",
      "9967 : 103457\n",
      "9968 : 103471\n",
      "9969 : 103483\n",
      "9970 : 103511\n",
      "9971 : 103529\n",
      "9972 : 103549\n",
      "9973 : 103553\n",
      "9974 : 103561\n",
      "9975 : 103567\n",
      "9976 : 103573\n",
      "9977 : 103577\n",
      "9978 : 103583\n",
      "9979 : 103591\n",
      "9980 : 103613\n",
      "9981 : 103619\n",
      "9982 : 103643\n",
      "9983 : 103651\n",
      "9984 : 103657\n",
      "9985 : 103669\n",
      "9986 : 103681\n",
      "9987 : 103687\n",
      "9988 : 103699\n",
      "9989 : 103703\n",
      "9990 : 103723\n",
      "9991 : 103769\n",
      "9992 : 103787\n",
      "9993 : 103801\n",
      "9994 : 103811\n",
      "9995 : 103813\n",
      "9996 : 103837\n",
      "9997 : 103841\n",
      "9998 : 103843\n",
      "9999 : 103867\n",
      "10000 : 103889\n",
      "10001 : 103903\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "103903"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Completed\n",
    "'''\n",
    "\"By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13.\n",
    "What is the 10 001st prime number?\"\n",
    "\n",
    "'''\n",
    "\n",
    "\n",
    "def nth_prime(n):\n",
    "    c = 1\n",
    "    i=1\n",
    "    while c<n+1:\n",
    "        i+=1\n",
    "        if (((2**i)-2)%i)==0:\n",
    "            print(c,\":\",i)\n",
    "            c+=1\n",
    "    return i\n",
    "        \n",
    "\n",
    "nth_prime(10001)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Question 8 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "23514624000\n"
     ]
    }
   ],
   "source": [
    "#Completed\n",
    "'''\n",
    "\"The four adjacent digits in the 1000-digit number that have the greatest product are 9 × 9 × 8 × 9 = 5832.\n",
    "73167176531330624919225119674426574742355349194934\n",
    "96983520312774506326239578318016984801869478851843\n",
    "85861560789112949495459501737958331952853208805511\n",
    "12540698747158523863050715693290963295227443043557\n",
    "66896648950445244523161731856403098711121722383113\n",
    "62229893423380308135336276614282806444486645238749\n",
    "30358907296290491560440772390713810515859307960866\n",
    "70172427121883998797908792274921901699720888093776\n",
    "65727333001053367881220235421809751254540594752243\n",
    "52584907711670556013604839586446706324415722155397\n",
    "53697817977846174064955149290862569321978468622482\n",
    "83972241375657056057490261407972968652414535100474\n",
    "82166370484403199890008895243450658541227588666881\n",
    "16427171479924442928230863465674813919123162824586\n",
    "17866458359124566529476545682848912883142607690042\n",
    "24219022671055626321111109370544217506941658960408\n",
    "07198403850962455444362981230987879927244284909188\n",
    "84580156166097919133875499200524063689912560717606\n",
    "05886116467109405077541002256983155200055935729725\n",
    "71636269561882670428252483600823257530420752963450\n",
    "Find the thirteen adjacent digits in the 1000-digit number that have the greatest product. What is the value of this product?\"\n",
    "\n",
    "'''\n",
    "\n",
    "thou = \"7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450\"\n",
    "\n",
    "start = 0\n",
    "l = 13\n",
    "\n",
    "prods = []\n",
    "\n",
    "while start<len(thou)-13:\n",
    "    x = 1\n",
    "    for i in range(start,start+l):\n",
    "        x*=int(thou[i])\n",
    "    prods.append(x)\n",
    "    start+=1\n",
    "\n",
    "print(max(prods))\n",
    "\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Question 9"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "200 375 425 31875000\n"
     ]
    }
   ],
   "source": [
    "#Completed\n",
    "'''\n",
    "\"A Pythagorean triplet is a set of three natural numbers, a < b < c, for which,\n",
    "a2 + b2 = c2\n",
    "For example, 32 + 42 = 9 + 16 = 25 = 52.\n",
    "There exists exactly one Pythagorean triplet for which a + b + c = 1000.\n",
    "Find the product abc.\"\n",
    "\n",
    "'''\n",
    "\n",
    "possible_trips = []\n",
    "for i in range(1,999):\n",
    "    for j in range(1,1000-i):\n",
    "        if sum([i,1000-i-j,j])==1000:\n",
    "            if i<(1000-i-j):\n",
    "                if (1000-i-j)<j:\n",
    "                    possible_trips.append((i,1000-i-j,j))\n",
    "\n",
    "for i in possible_trips:\n",
    "    a = i[0]\n",
    "    b = i[1]\n",
    "    c = i[2]\n",
    "    \n",
    "    if (a**2 + b**2)==c**2:\n",
    "        print(a,b,c,a*b*c)\n",
    "\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Question 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "142913828922"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Completed\n",
    "'''\n",
    "\"The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.\n",
    "Find the sum of all the primes below two million.\"\n",
    "'''\n",
    "def prime_checker(n):\n",
    "    if n==1:\n",
    "        return False\n",
    "    for i in range(2,int(n**0.5)+1):\n",
    "        if n%i==0:\n",
    "            return False\n",
    "    return True\n",
    "        \n",
    "    \n",
    "\n",
    "\n",
    "def sum_prime(n):\n",
    "    sumofprimes = 0\n",
    "    for i in range(2,n):\n",
    "        if prime_checker(i):\n",
    "            sumofprimes+=i\n",
    "    return sumofprimes\n",
    "\n",
    "sum_prime(2000000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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