prime_analysis.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Prime number analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Presentation of the algorithm generating prime numbers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A naive way to determine if a number `n` is prime would be to iteratively divide it by each of the numbers less than itself up to 2. If the number is divisible by any of them, then it is composite (not prime), if it is not divisible by any of them it is then prime. But this process, while it may be suitable for small numbers, has the disadvantage of being particularly cumbersome for large numbers. Indeed the amount of calculation required is always equal to `n-2`\n",
    "\n",
    "One way to optimize the algorithm would be to use the primality theorem which states that **a number `n` is prime if it is not divisible by any number smaller than its square root**. The iterative process can thus be greatly reduced.\n",
    "\n",
    ">If we decided to check the primality of the number 101 (which is indeed prime), the naive algorithm would require performing 99 operations (101-2), but using the primality theorem, `n` becomes equal to the square root of 101 is 10, so we only perform 8 operations (10-2) instead of 99, a saving of approximately 92% on calculation time.\n",
    "\n",
    "### Function overview\n",
    "The algorithm is divided into two functions:\n",
    "- `is_prime` allowing you to check if a number is prime\n",
    "- `prime_gen` returning a generator of an infinite sequence of prime numbers which can be iterated\n",
    "\n",
    "#### `is_prime`\n",
    "Allows you to check if a number `n` is prime using the primality theorem. In the function we raise `n` to a power of 0.5 because this amounts to calculating its square root, plus it saves us from importing modules such as `math` or `numpy`. So, the `for` loop goes through the values going from 2 to the square root of `n` and checks if `n` is divisible with at least one of them, if so the function returns False: `n` is not prime. If the function ends the sequence having failed to divide `n` with any of these values, then `n` is prime."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "def is_prime(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"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### `prime_gen`\n",
    "This is a generating function, that is to say intended to become a generator. The function creates an infinite loop going through the numbers starting from 2 and checking, using the `is_prime` function, if each of them is prime. If this is the case, the value is returned with a `yield`. At the next requested element, the function resumes where it left off until the next `yield` encountered.\n",
    "\n",
    "The generator can then be created by assigning this function to a variable, `primes` in our case."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def prime_gen():\n",
    "    n = 2\n",
    "    while True:\n",
    "        if is_prime(n):\n",
    "            yield n\n",
    "        n += 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Generator creation\n",
    "primes = prime_gen()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 "
     ]
    }
   ],
   "source": [
    "for _ in range(20):\n",
    "    print(next(primes), end=\" \")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Prime numbers are fascinating mathematical objects, which have been studied by mathematicians since ancient times. They present many interesting patterns and some curiosities, which continue to intrigue researchers and which our generating function created above can help us explore."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt \n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def percent(partial, total, rnd=2):\n",
    "    return round((partial/total) * 100, rnd)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The density of prime numbers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One of the most well-known patterns is the distribution of prime numbers. We know that the **density of prime numbers tends to zero as the number increases**, but we do not know exactly how this density behaves.\n",
    "\n",
    "To illustrate this we will create a function allowing us to generate several samples of prime numbers and to calculate for each of them, the average difference between each pair of values.\n",
    "\n",
    "The function `mean_diff()` includes 2 parameters :\n",
    "- `sample_length` : quantity of prime numbers that each sample must contain\n",
    "- `sample_quantity` : number of samples\n",
    "\n",
    "For each of these samples, the function calculates the difference between each pair of values and averages it. It is these averages which will be used to illustrate in a graph the fact that the density of prime numbers decreases as the numbers increase.\n",
    "\n",
    "The function returns a dictionary with statistics on each of the generated samples. Each element of the dictionary is composed as follows :\n",
    "- **Key** : The first and last value of the sample as a string\n",
    "- **Value** : A list with 4 elements :\n",
    "  - [0] : the first and last sample value in a `list`\n",
    "  - [1] : the prime numbers of the sample in a `list`\n",
    "  - [2] : the difference between each pair of prime numbers present in the sample in a `list`\n",
    "  - [3] : the average of the differences as `int`\n",
    "\n",
    "Here is an example function output for 5 samples of 5 prime numbers :\n",
    "```\n",
    "{'2 to 11': [[2, 11], [2, 3, 5, 7, 11], [1, 2, 2, 4], 2.25],\n",
    " '13 to 29': [[13, 29], [13, 17, 19, 23, 29], [4, 2, 4, 6], 4],\n",
    " '31 to 47': [[31, 47], [31, 37, 41, 43, 47], [6, 4, 2, 4], 4],\n",
    " '53 to 71': [[53, 71], [53, 59, 61, 67, 71], [6, 2, 6, 4], 4.5],\n",
    " '73 to 97': [[73, 97], [73, 79, 83, 89, 97], [6, 4, 6, 8], 6]}\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def mean_diff(sample_length=5, sample_quantity=5):\n",
    "    gen = prime_gen()\n",
    "    round_vals = 3\n",
    "    L = [] # Temporary storage of sampled primes\n",
    "    diffs = []\n",
    "    stats = {}\n",
    "\n",
    "    for _ in range(sample_quantity): # Number of samples\n",
    "        for _ in range(sample_length): # Elements of each sample\n",
    "            L.append(next(gen)) # Prime numbers generation\n",
    "        \n",
    "        # Calculating the difference between \n",
    "        # each pair of values in L and inserting \n",
    "        # the results into list D\n",
    "        D = []\n",
    "        for i in range(len(L) - 1):\n",
    "            diff = round(L[i + 1] - L[i], round_vals)\n",
    "            D.append(diff)\n",
    "        \n",
    "        diffs_mean = round(np.mean(D), round_vals) # Difference\n",
    "        diffs.append(diffs_mean) # Mean calculation\n",
    "\n",
    "        stats[f\"{L[0]} to {L[-1]}\"] = [[L[0], L[-1]], L, D, diffs_mean]\n",
    "\n",
    "        L=[]\n",
    "\n",
    "    return stats"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can now create a graph using the `matplotlib` module to plot the variation in mean difference values. We will also draw a linear regression line which will allow us to more clearly distinguish the trend of the graph.\n",
    "\n",
    "For this illustration we will generate 10 samples each composed of 1000 prime numbers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dict_stats = mean_diff(sample_length= 1000, sample_quantity=10)\n",
    "y_label = [val[3] for val in dict_stats.values()]\n",
    "\n",
    "x_label = [key for key in dict_stats.keys()]\n",
    "x = list(range(len(x_label)))\n",
    "y = y_label\n",
    "\n",
    "# Trend line\n",
    "coef = np.polyfit(x, y, 1)\n",
    "poly = np.poly1d(coef)\n",
    "x_trend = np.linspace(min(x), max(x), 100)\n",
    "y_trend = poly(x_trend)\n",
    "plt.plot(x_trend, y_trend, color='red', label=\"Trend line\",\n",
    "linestyle=\"dashed\")\n",
    "\n",
    "plt.plot(x, y)\n",
    "plt.xticks(x, x_label, rotation=60)\n",
    "plt.xlabel(\"Samples\")\n",
    "plt.ylabel(\"Mean difference\")\n",
    "plt.grid(True)\n",
    "\n",
    "plt.title(\"The mean difference between each pair of prime numbers in samples\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can clearly see, even if there are some local fluctuations, the further we go through the numbers, the more the average difference between each pair of prime numbers increases. \n",
    "\n",
    "The average difference between pairs of prime numbers from 2 to 7919 is approximately 8. This average difference increases to 11.5 for prime numbers from 93187 to 104729. \n",
    "\n",
    "In other words, **prime numbers become rarer as we advance through the numbers**.\n",
    "\n",
    "A more meaningful way to illustrate the decline in prime number density would be to calculate the percentage of prime numbers in different number intervals. For this we will create a new plot function called `prime_density()` (which will only contain slight modifications compared to `mean_diff()`) in order to create samples of a succession of integers, the percentage of prime numbers will be calculated for each of these samples.\n",
    "\n",
    ">We use the `count()` function of the `itertools` module as an integer iterator"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "from itertools import count\n",
    "\n",
    "def prime_density(sample_length=5, sample_quantity=5):\n",
    "    num_gen = count() # Integers generator\n",
    "    round_vals = 3\n",
    "    L = [] # Temporary storage of integers\n",
    "    stats = {}\n",
    "\n",
    "    for _ in range(sample_quantity): # Number of samples\n",
    "        for _ in range(sample_length): # Elements of each sample\n",
    "            L.append(next(num_gen)) # integers generation\n",
    "        \n",
    "        # Finding prime numbers in the sample L\n",
    "        P = []\n",
    "        for num in L:\n",
    "            if is_prime(num):\n",
    "                P.append(num)\n",
    "        \n",
    "        prime_percent = percent(len(P), len(L))\n",
    "\n",
    "        stats[f\"{L[0]} to {L[-1]}\"] = [[L[0], L[-1]], L, P, prime_percent]\n",
    "\n",
    "        L=[]\n",
    "\n",
    "    return stats"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The function returns a dictionary with statistics on each of the generated samples. Each element of the dictionary is composed as follows :\n",
    "```\n",
    "{'0 to 4': [[0, 4], [0, 1, 2, 3, 4], [2, 3], 40.0],\n",
    " '5 to 9': [[5, 9], [5, 6, 7, 8, 9], [5, 7], 40.0],\n",
    " '10 to 14': [[10, 14], [10, 11, 12, 13, 14], [11, 13], 40.0],\n",
    " '15 to 19': [[15, 19], [15, 16, 17, 18, 19], [17, 19], 40.0],\n",
    " '20 to 24': [[20, 24], [20, 21, 22, 23, 24], [23], 20.0]}\n",
    "```\n",
    "- **Key** : The first and last value of the sample as a string\n",
    "- **Value** : A list with 4 elements :\n",
    "  - [0] : the first and last sample value\n",
    "  - [1] : integers present in the sample\n",
    "  - [2] : the prime numbers of the sample\n",
    "  - [3] : the percentage of prime numbers in the sample"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dict_stats = prime_density(sample_length= 1000, sample_quantity=10)\n",
    "y_label = [val[3] for val in dict_stats.values()]\n",
    "\n",
    "x_label = [key for key in dict_stats.keys()]\n",
    "x = list(range(len(x_label)))\n",
    "y = y_label\n",
    "\n",
    "# Trend line\n",
    "coef = np.polyfit(x, y, 1)\n",
    "poly = np.poly1d(coef)\n",
    "x_trend = np.linspace(min(x), max(x), 100)\n",
    "y_trend = poly(x_trend)\n",
    "plt.plot(x_trend, y_trend, color='red', label=\"Trend line\",\n",
    "linestyle=\"dashed\")\n",
    "\n",
    "plt.plot(x, y)\n",
    "plt.xticks(x, x_label, rotation=60)\n",
    "plt.xlabel(\"Number range\")\n",
    "plt.ylabel(\"Percentage of prime numbers\")\n",
    "plt.grid(True)\n",
    "\n",
    "plt.title(\"Percentage of prime numbers in different number intervals\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here again, while there appears to be some local fluctuations, the trend is clear: prime numbers become rarer as the value of the numbers increases. There are 16.8% prime numbers in the interval [0, 999] and only 11.2% in the interval [14000, 14999]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[16.8, 13.5, 12.7, 12.0, 11.9, 11.4, 11.7, 10.7, 11.0, 11.2]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Percentage values\n",
    "L = [val[3] for val in dict_stats.values()]\n",
    "L"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can extract the values from the linear regression line displayed in our graph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.48060606, 14.45272727])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Retrieving values from linear regression\n",
    "x = np.array([i for i in range(len(L))])\n",
    "y = np.array(L)\n",
    "\n",
    "reg = np.polyfit(x, y, 1)\n",
    "reg"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The linear regression values show us that the slope is -0.48, in other words the percentage values decrease on average by -0.48 for each position in the list"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fibonacci in prime numbers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we will try to find out if the numbers composing the Fibonacci sequence are frequently encountered in the set of prime numbers. For this we will use `fibo()` a Fibonacci number generating function and `is_fibo()` a function based on the values generated by `fibo()` to determine whether or not a number is part of the sequence.\n",
    "\n",
    "We will then, in a `for` loop, go through the first 10k elements of the `prime_gen` generator and check if each of these values is a fibonacci number (by submitting it to the `is_fibo()` function), if so the value will be added into a list."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def fibo():\n",
    "    L = [0, 1]\n",
    "\n",
    "    if L[0] == 0:\n",
    "        yield L[0]\n",
    "        yield L[1]\n",
    "\n",
    "    while True:\n",
    "        fibo_num = L[0] + L[1]\n",
    "        L[0] = L[1]\n",
    "        L[1] = fibo_num\n",
    "        yield L[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def is_fibo(n):\n",
    "    gen = fibo()\n",
    "\n",
    "    while True:\n",
    "        fibo_num = next(gen)\n",
    "\n",
    "        if fibo_num == n:\n",
    "            return True\n",
    "\n",
    "        elif fibo_num < n:\n",
    "            continue\n",
    "        \n",
    "        else:\n",
    "            return False"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def fibo_in_primes():\n",
    "    first_n_primes = 10\n",
    "    multiplier = 5\n",
    "    L=[]\n",
    "    stats={}\n",
    "\n",
    "    while first_n_primes <= 10 * (multiplier**4):\n",
    "        P = prime_gen()\n",
    "        for _ in range(first_n_primes):\n",
    "            prime = next(P)\n",
    "            if is_fibo(prime):\n",
    "                L.append(prime)\n",
    "\n",
    "        ratio = percent(len(L), first_n_primes)\n",
    "        stats[first_n_primes] = [L, ratio]\n",
    "\n",
    "        L=[]\n",
    "        first_n_primes*=multiplier\n",
    "\n",
    "    return stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{10: [[2, 3, 5, 13], 40.0],\n",
       " 50: [[2, 3, 5, 13, 89], 10.0],\n",
       " 250: [[2, 3, 5, 13, 89, 233], 2.4],\n",
       " 1250: [[2, 3, 5, 13, 89, 233, 1597], 0.56],\n",
       " 6250: [[2, 3, 5, 13, 89, 233, 1597, 28657], 0.13]}"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats = fibo_in_primes()\n",
    "stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = [key for key in stats.keys()]\n",
    "y = [val[1] for val in stats.values()]\n",
    "\n",
    "plt.plot(x,y, marker=\"o\")\n",
    "for x_axis, y_axis, text in zip(x, y, y):\n",
    "    plt.text(x_axis+100, y_axis+0.5, str(text)+\"%\")\n",
    "\n",
    "plt.grid(True)\n",
    "plt.xlabel(\"First n prime numbers\")\n",
    "plt.ylabel(\"Fibonacci number percentage\")\n",
    "plt.title(\"Percentage of Fibonacci number falling \\n\"+ \n",
    "\"within different intervals of prime numbers\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the same way that the frequency of prime numbers decreases with increasing the value of the numbers, the density of Fibonacci numbers in the set of prime numbers also decreases as the value of these numbers increases, but the drop in density seems much more drastic here."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sum of digits of prime numbers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Even or odd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In 1968 a hypothesis from Alexandre Gelfond states that **the sum of the digits of a prime number has as much chance of being even as odd**. This hypothesis was later demonstrated by Christian Mauduit and Joël Rivat in 2010.\n",
    "\n",
    "To illustrate this we are going to create a function `sum_is_even()` which decomposes the digits of a number `n` in order to add them and check if their sum is even (`True`) or odd (`False`)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sum_is_even(p):\n",
    "    num_list = []\n",
    "\n",
    "    # The number is iterated as str\n",
    "    # and each element added as int\n",
    "    for n in str(p):\n",
    "        num_list.append(int(n))\n",
    "\n",
    "    # Parity check\n",
    "    if sum(num_list) % 2 == 0:\n",
    "        return True\n",
    "    else:\n",
    "        return False"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# (1 + 0 + 2) = 3 = odd = False\n",
    "sum_is_even(102)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# (1 + 0 + 3) = 4 = even = True\n",
    "sum_is_even(103)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's start by preparing the data needed to create the chart. We want :\n",
    "- Generate multiple samples, each with an equal number of prime numbers\n",
    "- Decompose each number of these samples to determine whether their sum is even or odd\n",
    "- Establish in a list the percentage represented by the even and odd numbers for each of these samples.\n",
    "\n",
    "To do this we will create the `sum_stats()` function which takes two parameters:\n",
    "- `sample_length`: the length of samples that must contain prime numbers\n",
    "- `sample_quantity`: the number of samples\n",
    "\n",
    "And which returns 3 elements:\n",
    "- A list containing the percentage values of even sums of each sample\n",
    "- A list containing the percentage values of odd sums of each sample\n",
    "- A list comprising character strings providing the minimum and maximum value of each sample of prime numbers (in other words the interval). This list will be used to name the graph x-axis labels\n",
    "\n",
    "For our example we will choose to represent 7 samples each containing 1000 prime numbers, in other words we will represent the first 7000 prime numbers divided into 7 samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sum_stats(sample_length=10, sample_quantity=7):\n",
    "    gen = prime_gen()\n",
    "\n",
    "    even_list=[] # Percentage of even numbers for each sample\n",
    "    odd_list=[] # Percentage of odd numbers for each sample\n",
    "    x_label=[]\n",
    "\n",
    "    for _ in range(sample_quantity):\n",
    "        even=0\n",
    "        odd=0\n",
    "        primes=set()\n",
    "\n",
    "        for _ in range(sample_length):\n",
    "            p = next(gen)\n",
    "            primes.add(p)\n",
    "            if sum_is_even(p):\n",
    "                even+=1\n",
    "            else:\n",
    "                odd+=1\n",
    "        \n",
    "        txt_label = f\"{min(primes)}-{max(primes)}\"\n",
    "        x_label.append(txt_label)\n",
    "        even_list.append(percent(even, sample_length))\n",
    "        odd_list.append(percent(odd, sample_length))\n",
    "\n",
    "    return even_list, odd_list, x_label"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "([50.0, 50.0, 70.0, 40.0, 20.0, 60.0, 40.0],\n",
       " [50.0, 50.0, 30.0, 60.0, 80.0, 40.0, 60.0],\n",
       " ['2-29', '31-71', '73-113', '127-173', '179-229', '233-281', '283-349'])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Output example\n",
    "sum_stats(sample_length=10, sample_quantity=7)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The idea would be to create a paired bar chart for each of the generated samples with one bar for the percentage of even numbers and another for the percentage of odd numbers.\n",
    "\n",
    "For this we will create the `sum_plot()` function which will allow us to easily create paired bar graphs from the data returned by the `sum_stats()` function mentioned above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sum_plot(sample_length=10, sample_quantity=7, rot=0, loc=1, ylim=100):\n",
    "    even_list, odd_list, samples = sum_stats(sample_length=sample_length, sample_quantity=sample_quantity)\n",
    "\n",
    "    parities = {\n",
    "        'even' : even_list,\n",
    "        'odd' : odd_list\n",
    "    }\n",
    "\n",
    "    x = np.arange(len(samples))\n",
    "    width = 0.40\n",
    "    multiplier = 0\n",
    "\n",
    "    fig, ax = plt.subplots(layout='constrained')\n",
    "\n",
    "    # Iteration of dictionary items containing percentage values\n",
    "    for parity, vals in parities.items():\n",
    "        offset = width * multiplier\n",
    "        rects = ax.bar(x + offset, vals, width, label=parity)\n",
    "        ax.bar_label(rects, padding=5)\n",
    "        multiplier += 1\n",
    "\n",
    "    primes_qty = sample_length * sample_quantity\n",
    "    ax.set_ylabel(\"Percentage\")\n",
    "    ax.set_xlabel(f\"Prime number samples ({sample_length} primes/sample)\")\n",
    "    ax.set_title(f\"Parity distribution of the sum of digits of the {primes_qty} first prime numbers\")\n",
    "    ax.set_xticks(x+0.16, samples, rotation=rot)\n",
    "    ax.legend(loc=loc)\n",
    "    ax.set_ylim(0,ylim)\n",
    "    ax.yaxis.grid(lw=0.5)\n",
    "    ax.set_axisbelow(True) # Grid background\n",
    "    fig.set_size_inches(10,5) # fig size\n",
    "\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's observe the parity distribution for the sum of the digits of the first 70 prime numbers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sum_plot(ylim=90)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We observe perfect equality in the distribution of parities for the first 2 samples (2-29) and (31-71), however strong disparities are observed for the next 5 samples, the interval [179,229] for example has 20 % of even sums and 80% of odd sums.\n",
    "\n",
    "Let's average all the even and odd percentages to get an idea of the total distribution for all 70 prime numbers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Total percentage of all samples\n",
      "Even : 47.14%\n",
      "Odd : 52.86%\n",
      "Difference : 5.72%\n"
     ]
    }
   ],
   "source": [
    "even_list, odd_list, _ = sum_stats(sample_length=10, sample_quantity=7)\n",
    "\n",
    "even_mean = round(np.mean(even_list), 2)\n",
    "odd_mean = round(np.mean(odd_list), 2)\n",
    "diff = round(abs(even_mean-odd_mean), 2)\n",
    "\n",
    "print(\"Total percentage of all samples\")\n",
    "print(f\"Even : {even_mean}%\")\n",
    "print(f\"Odd : {odd_mean}%\")\n",
    "print(f\"Difference : {diff}%\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The difference between even and odd sums seems less pronounced when calculated on all samples, odd sums are around 5.7% more frequent than even sums.\n",
    "\n",
    "Let us now try to increase the size of these samples as well as their quantity in order to observe whether these disparities are confirmed. To do this, we generate 10 samples each containing 1000 prime numbers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sum_plot(sample_length=1000, sample_quantity=10, rot=15, ylim=65)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The disparities observed in the first graphs are much less pronounced here, the differences between the percentages of even and odd sums seem to decrease as the scale of the numbers increases.\n",
    "\n",
    "here too, let's try to average all the even and odd percentages to get an idea of the total distribution for all 10000 prime numbers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Total percentage of all samples\n",
      "Even : 49.25%\n",
      "Odd : 50.75%\n",
      "Difference : 1.5%\n"
     ]
    }
   ],
   "source": [
    "even_list, odd_list, _ = sum_stats(sample_length=1000, sample_quantity=10)\n",
    "\n",
    "even_mean = round(np.mean(even_list), 2)\n",
    "odd_mean = round(np.mean(odd_list), 2)\n",
    "diff = round(abs(even_mean-odd_mean), 2)\n",
    "\n",
    "print(\"Total percentage of all samples\")\n",
    "print(f\"Even : {even_mean}%\")\n",
    "print(f\"Odd : {odd_mean}%\")\n",
    "print(f\"Difference : {diff}%\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The difference here is only 1.5%, still in favor of odd sums"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### The sum of the digits is a prime number"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Certain sums of the digits of prime numbers are also prime: for example the prime number 29 is decomposed into 2+9 which is equal to 11, also prime. We will here focus more particularly on the result of these sums in order to try to discern any pattern.\n",
    "\n",
    "For this we will create a function `sum_is_prime()` which will allow it to go through the prime numbers and decompose them into numbers in order to add them, if the result of this addition is a prime number then this result is added to a dictionary."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sum_is_prime(limit):\n",
    "    P = prime_gen()\n",
    "    prime_sums = {}\n",
    "\n",
    "    for _ in range(limit):\n",
    "        prime = next(P)\n",
    "        digits_list = []\n",
    "\n",
    "        for n in str(prime):\n",
    "            digits_list.append(int(n))\n",
    "    \n",
    "        digits_sum = sum(digits_list)\n",
    "        \n",
    "        if is_prime(digits_sum):\n",
    "            if digits_sum not in prime_sums:\n",
    "                prime_sums[digits_sum] = [1,[prime]]\n",
    "            else:\n",
    "                prime_sums[digits_sum][0] += 1\n",
    "                prime_sums[digits_sum][1].append(prime) \n",
    "    \n",
    "    return prime_sums"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{2: [3, [2, 11, 101]],\n",
       " 3: [1, [3]],\n",
       " 5: [7, [5, 23, 41, 113, 131, 311, 401]],\n",
       " 7: [9, [7, 43, 61, 151, 223, 241, 313, 331, 421]],\n",
       " 11: [13, [29, 47, 83, 137, 173, 191, 227, 263, 281, 317, 353, 443, 461]],\n",
       " 13: [10, [67, 139, 157, 193, 229, 283, 337, 373, 409, 463]],\n",
       " 17: [7, [89, 179, 197, 269, 359, 449, 467]],\n",
       " 19: [4, [199, 379, 397, 487]]}"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Exemple :\n",
    "stats = sum_is_prime(100)\n",
    "stats"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The dictionary is structured as follows:\n",
    "- **Key** : Result of the sum (which is a prime number)\n",
    "- **Value** : A list containing two elements:\n",
    "  - The number of occurrences obtained from this sum during the function traversal\n",
    "  - The prime numbers whose sum of the digits gives this result\n",
    "\n",
    "The data contained in this dictionary will allow us to draw the graph. We will use the dictionary keys (prime sums obtained) for the x axis and the first element of the lists contained in value (number of occurrences) for the y axis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "stats = sum_is_prime(1000)\n",
    "\n",
    "# Data plot\n",
    "fig = plt.figure()\n",
    "ax = fig.add_axes([0,0,1,1])\n",
    "x = [key for key in stats.keys()]\n",
    "y = [val[0] for val in stats.values()]\n",
    "ax.set_xticks(x, x)\n",
    "ax.bar(x,y)\n",
    "\n",
    "# Polynomial curve from data\n",
    "coef = np.polyfit(x, y, 5)\n",
    "poly = np.poly1d(coef)\n",
    "x_trend = np.linspace(min(x), max(x), 100)\n",
    "y_trend = poly(x_trend)\n",
    "plt.plot(x_trend, y_trend, color='red', label=\"Trend line\",\n",
    "linestyle=\"dashed\")\n",
    "\n",
    "# Set labels name and title\n",
    "ax.set_xlabel(\"Prime sums\")\n",
    "ax.set_ylabel(\"Occurrence\")\n",
    "ax.set_title(\"Distribution of the prime number digits sums \"+ \n",
    "\"when this sum is a prime number\\n\" +\n",
    "\"(1000 first prime numbers)\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The sums of the decompositions of the first 1000 prime numbers show us what appears to be a normal distribution, as the bell curve suggests. The sums 17 and 19 are particularly frequent (appearing 107 and 104x respectively) and represent the median of this distribution. \n",
    "\n",
    ">It should be noted that [2,3], [5,7], [11,13], [17,19] and [29,31] are twin prime numbers."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "lastpy",
   "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": "3.12.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}