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‎exercise-16.ipynb‎

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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# **Check whether a number is prime or not by defining a function.**"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### **METHOD 1 - Using range(2, num) (Check All Numbers Up to n-1)**"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Number 23489991 is Prime number!\n"
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]
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}
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],
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"source": [
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"def prime_check(num):\n",
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" if num <= 1:\n",
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" print(\"1 is neither a prime nor a composite number\")\n",
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" else:\n",
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" prime = True\n",
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" for i in range(2, num):\n",
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" if num%i == 0:\n",
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" prime = False\n",
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" break\n",
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"\n",
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" if prime == True:\n",
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" print(f\"Number {n} is Prime number!\")\n",
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" else:\n",
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" print(f\"Number {n} is Prime number!\")\n",
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"\n",
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"\n",
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"n = int(input(\"Enter a no : \"))\n",
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"prime_check(n)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### **METHOD 2 - Using range(2, ceil(num/2) + 1) (Check Up to Half of the Number)**"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Number 34578 is not prime!\n"
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]
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}
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],
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"source": [
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"import math\n",
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"\n",
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"def prime_check(num):\n",
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" if num <= 1:\n",
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" prime = False\n",
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" print(\"1 is neither prime nor composite\")\n",
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" else:\n",
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" prime = True\n",
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" for i in range(2, math.ceil(num/2)+1):\n",
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" if num%i == 0:\n",
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" prime = False\n",
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" break\n",
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" \n",
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" if prime:\n",
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" print(f\"Number {n} is Prime!\")\n",
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" else:\n",
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" print(f\"Number {n} is not prime!\")\n",
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"\n",
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"\n",
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"n = int(input(\"Enter a no : \"))\n",
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"prime_check(n)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### **METHOD 3 - Using range(2, ceil(sqrt(num)) + 1) (Check Up to Square Root)**"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 8,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Number 2347899172 is not Prime number!\n"
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]
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}
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],
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"source": [
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"from math import sqrt, ceil\n",
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"\n",
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"def prime_checker(num):\n",
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" if num <= 1:\n",
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" prime = False\n",
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" print(\"1 is neither prime nor composite\")\n",
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" else:\n",
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" prime = True\n",
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" for i in range(2, ceil(sqrt(num)) + 1):\n",
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" if num%i == 0:\n",
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" prime = False\n",
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" break\n",
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"\n",
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" if prime:\n",
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" print(f\"Number {n} is Prime number!\")\n",
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" else:\n",
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" print(f\"Number {n} is not Prime number!\")\n",
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"\n",
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"\n",
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"n = int(input(\"Enter a no : \"))\n",
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"prime_checker(n)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### **METHOD 4 - Optimised approach for even numbers**"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"* Immediately handles even numbers.\n",
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"* Checks only odd divisors starting from 3, skipping unnecessary checks."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 10,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Number 25127617911 is not a Prime!\n"
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]
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}
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],
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"source": [
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"from math import ceil, sqrt\n",
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"\n",
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"def prime_check(num):\n",
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" if num <1:\n",
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" prime = False\n",
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" print(\"1 is neither prime nor composite!\")\n",
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" elif num == 2:\n",
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" prime = True\n",
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" print(f\"Number {n} is Prime!\")\n",
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" elif num%2 == 0:\n",
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" prime = False\n",
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" print(f\"Number {n} is not a Prime!\")\n",
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" else:\n",
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" prime = True\n",
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" for i in range(3, ceil(sqrt(num))+1, 2):\n",
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" if num%i == 0:\n",
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" prime = False\n",
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" break\n",
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" \n",
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" if prime:\n",
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" print(f\"Number {n} is Prime!\")\n",
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" else:\n",
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" print(f\"Number {n} is not a Prime!\")\n",
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"\n",
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"n = int(input(\"enter a number : \"))\n",
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"prime_check(n)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": []
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.11.0"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 2
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}

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