148 lines
3.4 KiB
Plaintext
148 lines
3.4 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "9c45cbb8",
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"metadata": {},
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"source": [
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"# [Prime Permutations](https://projecteuler.net/problem=49)\n",
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"\n",
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"An easy way to approach this problem is to first find [arithmetic progressions of primes](https://en.wikipedia.org/wiki/Primes_in_arithmetic_progression), then check if any of those progressions have numbers that are permutations of each other.\n",
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"\n",
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"To start, we'll generate all the four-digit 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": 1,
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"id": "d278b9e4",
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"metadata": {},
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"outputs": [],
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"source": [
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"primes = prime_range(1000, 10000)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "97dab665",
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"metadata": {},
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"source": [
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"Here's where we find arithmetic progressions. Given two primes $p < q$, we can calculate their difference $d = q - p$ and check if $q + d$ is prime - if it is, we have a three-number progression."
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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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"id": "0eaf16ac",
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"metadata": {},
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"outputs": [],
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"source": [
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"from itertools import combinations\n",
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"\n",
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"progressions = set()\n",
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"for (p, q) in combinations(primes, 2):\n",
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" d = q - p\n",
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" r = q + d\n",
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" if r < 10000 and is_prime(r):\n",
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" progressions.add((p, q, r))"
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]
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},
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{
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"cell_type": "markdown",
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"id": "bbbcab4f",
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"metadata": {},
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"source": [
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"Here's how many of these progressions there are."
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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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"id": "8c87fea2",
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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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"42994"
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]
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},
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"execution_count": 3,
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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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"len(progressions)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "da3a48f3",
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"metadata": {},
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"source": [
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"Now we'll check each progression to find one where the digits of the numbers are permutations of each other."
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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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"id": "89cb3dd0",
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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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"(2969, 6299, 9629)"
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]
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},
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"execution_count": 4,
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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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"for (p, q, r) in progressions:\n",
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" if p == 1487 and q == 4817 and r == 8147:\n",
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" continue\n",
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" \n",
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" if sorted(p.digits()) == sorted(q.digits()) == sorted(r.digits()):\n",
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" break\n",
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" \n",
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"p, q, r"
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]
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},
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{
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"cell_type": "markdown",
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"id": "929e777d",
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"metadata": {},
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"source": [
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"#### Copyright (C) 2025 filifa\n",
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"\n",
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"This work is licensed under the [Creative Commons Attribution-ShareAlike 4.0 International license](https://creativecommons.org/licenses/by-sa/4.0/) and the [BSD Zero Clause license](https://spdx.org/licenses/0BSD.html)."
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "SageMath 9.5",
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"language": "sage",
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"name": "sagemath"
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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": "3.11.2"
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}
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"nbformat": 4,
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"nbformat_minor": 5
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