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Complete Challenge (LinkedInLearning#1)
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‎sudent_files/Faster Prime Finding Challenge.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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"id": "3d331168",
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"metadata": {},
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"source": [
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"## Faster Prime Finding\n",
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"\n",
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"Write a function that returns a list of all primes up to a given number.\n",
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"\n",
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"For each number, in order to determine if it is prime, take the following steps:\n",
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"1. Find the square root of the number\n",
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"2. Find all the primes up to that square root\n",
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"3. Test to see if any of those primes are divisors \n",
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"\n",
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"If a number has no prime divisors, it is prime!\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": 28,
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"id": "37687918",
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"metadata": {},
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"outputs": [],
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"source": [
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"def allPrimesUpTo(num):\n",
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" primes = [2]\n",
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" for number in range(2, num):\n",
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" sqrt = int(number ** 0.5)\n",
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" for factor in primes:\n",
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" if number % factor == 0:\n",
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" break\n",
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" else:\n",
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" if factor > sqrt:\n",
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" primes.append(number)\n",
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" \n",
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" return primes"
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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": 29,
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"id": "76e6a11b",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"[2,\n",
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" 3,\n",
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" 5,\n",
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" 7,\n",
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" 11,\n",
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" 13,\n",
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" 17,\n",
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" 23,\n",
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" 97]"
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]
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},
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"execution_count": 29,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"allPrimesUpTo(100)"
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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": 30,
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"id": "53848a3f",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"[2,\n",
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" 997]"
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]
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},
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"execution_count": 30,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"allPrimesUpTo(1000)"
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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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"id": "33e69550",
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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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"file_extension": ".py",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.12.1"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 5
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}

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