Eratosthenes.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "01fd229a-7839-4564-8e6b-ec928fe51fbb",
   "metadata": {},
   "source": [
    "# Prime numbers and the sieve of Eratosthenes\n",
    "_Author: An enthusiastic scientist, a terrible programmer._\n",
    "\n",
    "The sieve of Eratosthenes is a simple and famous algorithm for factoring prime\n",
    "numbers. I was always fascinated with prime numbers, so I am very excited about new project!"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b728cbcd-e726-4ff3-a62f-98a7121c79a2",
   "metadata": {},
   "source": [
    "Let's start with a simple implementation of the Sieve or Eratosthenes:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "74dbed17-52d6-4d60-b65f-e4d4900c19ac",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 610 ms, sys: 338 ms, total: 948 ms\n",
      "Wall time: 533 ms\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53]"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%%time\n",
    "\n",
    "import sys\n",
    "import math\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sieve_tools import sieve, plots\n",
    "\n",
    "all_primes = []\n",
    "nmax = 55\n",
    "\n",
    "if nmax == 2: \n",
    "    all_primes = [2]\n",
    "else:\n",
    "    primes_head = [2]\n",
    "    first = 3\n",
    "    primes_tail = np.arange(first,nmax+1,2)\n",
    "    while first <= round(math.sqrt(primes_tail[-1])):\n",
    "        first = primes_tail[0]\n",
    "        primes_head.append(first)\n",
    "        non_primes = first * primes_tail\n",
    "        primes_tail = np.array([ n for n in primes_tail[1:]\n",
    "                                if n not in non_primes ])\n",
    "\n",
    "all_primes = primes_head + primes_tail.tolist()\n",
    "all_primes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "54a6642f-bc80-4a18-884b-2791891bd2f7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[2, 3, 5, 7, 11, 13]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sieve.get_primes(15)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bdd29d53-1ccf-44f7-8555-78bb859001c0",
   "metadata": {},
   "source": [
    "Now, let's do something a little bit more efficient. This code should give me the same than before, but in less time. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "6faf830e-76a3-49cf-a6ed-107a121b2376",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 53 µs, sys: 0 ns, total: 53 µs\n",
      "Wall time: 58.2 µs\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%%time \n",
    "\n",
    "all_primes = []\n",
    "\n",
    "if nmax == 2: \n",
    "    all_primes = [2]\n",
    "\n",
    "else:\n",
    "\n",
    "    primes_head = [2]\n",
    "    first = 3\n",
    "\n",
    "    # The primes tail will be kept both as a set and as a sorted list\n",
    "    primes_tail_lst = range(first,nmax+1,2)\n",
    "    primes_tail_set = set(primes_tail_lst)\n",
    "\n",
    "    # Now do the actual sieve\n",
    "    while first <= round(math.sqrt(primes_tail_lst[-1])):\n",
    "        # Move the first leftover prime from the set to the head list\n",
    "        first = primes_tail_lst[0]\n",
    "        primes_tail_set.remove(first)  # remove it from the set\n",
    "        primes_head.append(first) # and store it in the head list\n",
    "\n",
    "        # Now, remove from the primes tail all non-primes.  For us to be able\n",
    "        # to break as soon as a key is not found, it's crucial that the tail\n",
    "        # list is always sorted.\n",
    "        for next_candidate in primes_tail_lst:\n",
    "            try:\n",
    "                primes_tail_set.remove(first * next_candidate)\n",
    "            except KeyError:\n",
    "                break\n",
    "\n",
    "        # Build a new sorted tail list with the leftover keys\n",
    "        primes_tail_lst = list(primes_tail_set)\n",
    "        primes_tail_lst.sort()\n",
    "\n",
    "    all_primes = primes_head + primes_tail_lst\n",
    "    \n",
    "all_primes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "7369152b-6365-44ca-9bba-be40add14868",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[2, 3, 5, 7, 11, 13, 17]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sieve.slow_sieve(17)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "840d9c6e-a4f6-4ea8-b28a-00d8c56197cf",
   "metadata": {},
   "source": [
    "## Long Run: proportion of primer numbers\n",
    "\n",
    "Now I am interested in knowing what is the proportion of prime numbers smaller than some `nmax`. This next for loop runs the last implementation of the sieve of Eratosthenes for different numbers. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "ac5d3c8d-9202-4c31-99c8-58196ec328e0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 16.9 ms, sys: 5 µs, total: 16.9 ms\n",
      "Wall time: 16.8 ms\n"
     ]
    }
   ],
   "source": [
    "%%time \n",
    "\n",
    "all_nmax = np.arange(100, 5000, 100)\n",
    "all_proportions = []\n",
    "\n",
    "for nmax in all_nmax:\n",
    "    \n",
    "    all_primes = []\n",
    "\n",
    "    if nmax == 2: \n",
    "        all_primes = [2]\n",
    "\n",
    "    else:\n",
    "\n",
    "        primes_head = [2]\n",
    "        first = 3\n",
    "\n",
    "        # The primes tail will be kept both as a set and as a sorted list\n",
    "        primes_tail_lst = range(first,nmax+1,2)\n",
    "        primes_tail_set = set(primes_tail_lst)\n",
    "\n",
    "        # Now do the actual sieve\n",
    "        while first <= round(math.sqrt(primes_tail_lst[-1])):\n",
    "            # Move the first leftover prime from the set to the head list\n",
    "            first = primes_tail_lst[0]\n",
    "            primes_tail_set.remove(first)  # remove it from the set\n",
    "            primes_head.append(first) # and store it in the head list\n",
    "\n",
    "            # Now, remove from the primes tail all non-primes.  For us to be able\n",
    "            # to break as soon as a key is not found, it's crucial that the tail\n",
    "            # list is always sorted.\n",
    "            for next_candidate in primes_tail_lst:\n",
    "                try:\n",
    "                    primes_tail_set.remove(first * next_candidate)\n",
    "                except KeyError:\n",
    "                    break\n",
    "\n",
    "            # Build a new sorted tail list with the leftover keys\n",
    "            primes_tail_lst = list(primes_tail_set)\n",
    "            primes_tail_lst.sort()\n",
    "\n",
    "        all_primes = primes_head + primes_tail_lst\n",
    "\n",
    "    all_proportions.append(len(all_primes) / nmax)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "bd37b6ed-b78b-4907-a926-7e532a6607cc",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ns, props = sieve.proportion_primes(np.arange(10, 100, 10))\n",
    "\n",
    "plots.plot_props(ns, props)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "ccfc9a97-2708-4c95-8fca-b1d582d38666",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Proportion of primer numbers')"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(all_nmax, all_proportions)\n",
    "plt.xlabel(\"N\")\n",
    "plt.ylabel(\"Proportion of primer numbers\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b8c287c9-e310-4498-92ce-c59bec68b9fa",
   "metadata": {},
   "source": [
    "OIn theory this should look like $1 / ln(N)$. Let's make the plot in log scale, since it seems more meaninful in this way."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "47c05b78-ba0d-43a3-beb0-215891d9a10c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(all_nmax, all_proportions)\n",
    "plt.xlabel(\"N\")\n",
    "plt.ylabel(\"Proportion of primer numbers\")\n",
    "plt.xscale(\"log\")\n",
    "plt.yscale(\"log\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7cda3103-9645-4323-a5eb-7a14f98a60c6",
   "metadata": {},
   "source": [
    "## Performance\n",
    "\n",
    "It will be great to compare the performance of the two algorithms as we increase the window search. \n",
    "\n",
    "Write a function that computes the overall time of a program. I guess something like this should work. The function `time.perf_counter` can be useful here. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "538b8740-0820-4373-96f7-ddde241e0cd7",
   "metadata": {},
   "outputs": [],
   "source": [
    "import time\n",
    "\n",
    "def time_rng(fun, nrange, verbose=False):\n",
    "    \"\"\"\n",
    "    Time a function over a range of parameters.\n",
    "\n",
    "    Returns the list of run times.\n",
    "\n",
    "    The function should be callable with a single argument: it will be\n",
    "    called with each entry from nrange in turn.\n",
    "\n",
    "    If verbose is true, at each step the value of nrange and time for the\n",
    "    call is printed.\n",
    "    \"\"\"\n",
    "\n",
    "    # BEGIN SOLUTION\n",
    "\n",
    "\n",
    "    # END SOLUTION\n",
    "    return nrange, times"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0ee2ace0-d28a-463b-bf77-c5ca2bef75e4",
   "metadata": {},
   "source": [
    "Plot!!! Make a comparision of the two methods. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "060ccbb1-4705-426e-a1f7-0c203711abcc",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.10.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}