Solved Euler 50.
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"source": [
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"# Consecutive prime sum (Euler Problem 50)"
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]
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"source": [
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"[https://projecteuler.net/problem=50](https://projecteuler.net/problem=50)\n",
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"\n",
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"The prime 41, can be written as the sum of six consecutive primes:\n",
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"\n",
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"$41 = 2 + 3 + 5 + 7 + 11 + 13$\n",
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"\n",
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"This is the longest sum of consecutive primes that adds to a prime below one-hundred.\n",
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"\n",
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"The longest sum of consecutive primes below one-thousand that adds to a prime, contains 21 terms, and is equal to 953.\n",
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"\n",
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"Which prime, below one-million, can be written as the sum of the most consecutive primes?"
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]
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {},
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"outputs": [],
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"source": [
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"def sieve_of_eratosthenes(number):\n",
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" primes = []\n",
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" prospects = [n for n in range(2, number)]\n",
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" while prospects:\n",
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" p = prospects[0]\n",
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" prospects = [x for x in prospects if x % p != 0]\n",
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" primes.append(p)\n",
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" if p * p > number:\n",
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" break\n",
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" return primes + prospects\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": 2,
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"metadata": {},
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"outputs": [],
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"source": [
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"def find_max_series(start_index, series_list, series_set): \n",
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" series_max = series_list[-1]\n",
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" total_max = 0\n",
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" total = 0 \n",
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" for i in range(start_index, len(series_list)):\n",
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" total = total + series_list[i]\n",
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" if total in series_set:\n",
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" length = i - start_index + 1\n",
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" total_max = total\n",
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" if total > series_max:\n",
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" return (length, total_max)"
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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": 3,
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"metadata": {},
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"outputs": [
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"(6, 41)\n"
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]
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}
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],
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"source": [
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"n_max = 100\n",
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"ps = sieve_of_eratosthenes(n_max)\n",
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"ps_set = set(ps)\n",
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"ps_max = max(ps)\n",
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"s = max([x for x in [find_max_series(i, ps, ps_set) for i in range(0, n_max)] if x])\n",
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"print(s)\n",
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"assert(s[1] == 41)"
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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": 4,
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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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"(21, 953)\n"
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]
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}
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],
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"source": [
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"n_max = 1000\n",
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"ps = sieve_of_eratosthenes(n_max)\n",
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"ps_set = set(ps)\n",
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"ps_max = max(ps)\n",
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"s = max([x for x in [find_max_series(i, ps, ps_set) for i in range(0, n_max)] if x])\n",
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"print(s)\n",
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"assert(s[0] == 21)\n",
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"assert(s[1] == 953)"
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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": 5,
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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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"(543, 997651)\n",
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"997651\n"
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]
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}
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],
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"source": [
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"n_max = 1000000\n",
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"ps = sieve_of_eratosthenes(n_max)\n",
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"ps_set = set(ps)\n",
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"ps_max = max(ps)\n",
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"s = max([x for x in [find_max_series(i, ps, ps_set) for i in range(0, n_max)] if x])\n",
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"print(s)\n",
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"assert(s[1] == 997651)\n",
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"print(s[1])"
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]
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}
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],
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"metadata": {
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"completion_date": "Sun, 23 Dec 2018, 02:38",
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python3.6",
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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": "3.6.5"
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},
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"tags": [
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"brute force",
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"consecutive",
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"primes",
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"search"
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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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{
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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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"# Prime digit replacements (Euler Problem 51)"
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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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"collapsed": true
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},
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"source": [
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"[https://projecteuler.net/problem=51](https://projecteuler.net/problem=51)\n",
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"\n",
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"By replacing the 1st digit of the 2-digit number x3, it turns out that six of the nine possible values: 13, 23, 43, 53, 73, and 83, are all prime.\n",
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"\n",
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"By replacing the 3rd and 4th digits of 56xx3 with the same digit, this 5-digit number is the first example having seven primes among the ten generated numbers, yielding the family: 56003, 56113, 56333, 56443, 56663, 56773, and 56993. Consequently 56003, being the first member of this family, is the smallest prime with this property.\n",
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"\n",
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"Find the smallest prime which, by replacing part of the number (not necessarily adjacent digits) with the same digit, is part of an eight prime value family."
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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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"collapsed": true
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},
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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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"completion_date": "",
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python3.6",
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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": "3.6.5"
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},
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"tags": []
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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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</tr>
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<tr>
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<td><a href="EulerProblem050.html">Problem 050</a></td>
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<td>Sun, 23 Dec 2018, 02:38</td>
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<td>
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<kbd>brute force</kbd>
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<kbd>consecutive</kbd>
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<kbd>primes</kbd>
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<kbd>search</kbd>
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</td>
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</tr>
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<tr class="table-warning">
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<td><a href="EulerProblem051.html">Problem 051</a></td>
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<td></td>
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<td>
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</td>
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</tr>
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<tr>
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<td><a href="EulerProblem067.html">Problem 067</a></td>
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