Nombres_Premiers-Copy1-checkpoint.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Nombres premiers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Critère d'arrêt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from math import*\n",
    "\n",
    "def plus_petit_diviseur_premier(n):\n",
    "    r=int(floor(sqrt(n)))\n",
    "    d=2\n",
    "    while n%d!=0 and d<=r:\n",
    "        d+=1\n",
    "    if d<=r:\n",
    "        return ...\n",
    "    else :\n",
    "        return ..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def liste_nb_premiers_inferieurs_ou_egaux_a_(n):\n",
    "    return [plus_petit_diviseur_premier(i) for i in range(2,n+1) if plus_petit_diviseur_premier(i)==...]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: numpy in c:\\programdata\\anaconda3\\lib\\site-packages (1.16.2)\n",
      "Note: you may need to restart the kernel to use updated packages.\n"
     ]
    }
   ],
   "source": [
    "pip install numpy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: matplotlib in c:\\programdata\\anaconda3\\lib\\site-packages (3.0.3)\n",
      "Requirement already satisfied: numpy>=1.10.0 in c:\\programdata\\anaconda3\\lib\\site-packages (from matplotlib) (1.16.2)\n",
      "Requirement already satisfied: cycler>=0.10 in c:\\programdata\\anaconda3\\lib\\site-packages (from matplotlib) (0.10.0)\n",
      "Requirement already satisfied: kiwisolver>=1.0.1 in c:\\programdata\\anaconda3\\lib\\site-packages (from matplotlib) (1.0.1)\n",
      "Requirement already satisfied: pyparsing!=2.0.4,!=2.1.2,!=2.1.6,>=2.0.1 in c:\\programdata\\anaconda3\\lib\\site-packages (from matplotlib) (2.3.1)\n",
      "Requirement already satisfied: python-dateutil>=2.1 in c:\\programdata\\anaconda3\\lib\\site-packages (from matplotlib) (2.8.0)\n",
      "Requirement already satisfied: six in c:\\programdata\\anaconda3\\lib\\site-packages (from cycler>=0.10->matplotlib) (1.12.0)\n",
      "Requirement already satisfied: setuptools in c:\\programdata\\anaconda3\\lib\\site-packages (from kiwisolver>=1.0.1->matplotlib) (40.8.0)\n",
      "Note: you may need to restart the kernel to use updated packages.\n"
     ]
    }
   ],
   "source": [
    "pip install matplotlib"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from math import*\n",
    "\n",
    "def fonction_pi(n): #liste de pi(i) pour i allant de 0 à n\n",
    "    l=[0,0]\n",
    "    for i in range(2,n+1):\n",
    "        if plus_petit_diviseur_premier(i)<i:\n",
    "            l.append(l[i-1])\n",
    "        else :\n",
    "            l.append(l[i-1]+1)\n",
    "    return l\n",
    "\n",
    "def graphique_fonction_pi(n):\n",
    "    plt.scatter([i for i in range(n+1)],fonction_pi(n),c='b')\n",
    "    plt.scatter([i for i in range(2,n+1)],[i/log(i) for i in range(2,n+1)],c='r')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Décomposition en produit de facteurs premiers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def decomposition(n):\n",
    "    l=[]\n",
    "    d=2\n",
    "    while n>1:\n",
    "        i=0\n",
    "        while n%d==0:\n",
    "            i+=...\n",
    "            n=...\n",
    "        if i>0:\n",
    "            l.append([d,i])\n",
    "        d+=1\n",
    "    return l"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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