add problem 49

notebooks/problem0049.ipynb

@@ -0,0 +1,138 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "9c45cbb8",
+   "metadata": {},
+   "source": [
+    "# [Prime Permutations](https://projecteuler.net/problem=49)\n",
+    "\n",
+    "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",
+    "\n",
+    "To start, we'll generate all the four-digit primes."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "d278b9e4",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "primes = prime_range(1000, 10000)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "97dab665",
+   "metadata": {},
+   "source": [
+    "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."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "id": "0eaf16ac",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "progressions = set()\n",
+    "for (i, p) in enumerate(sorted(primes)):\n",
+    "    for q in primes[i+1:]:\n",
+    "        d = q - p\n",
+    "        r = q + d\n",
+    "        if r < 10000 and is_prime(r):\n",
+    "            progressions.add((p, q, r))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "bbbcab4f",
+   "metadata": {},
+   "source": [
+    "Here's how many of these progressions there are."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "id": "8c87fea2",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "42994"
+      ]
+     },
+     "execution_count": 3,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "len(progressions)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "da3a48f3",
+   "metadata": {},
+   "source": [
+    "Now we'll check each progression to find one where the digits of the numbers are permutations of each other."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "id": "89cb3dd0",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(2969, 6299, 9629)"
+      ]
+     },
+     "execution_count": 4,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "from collections import Counter\n",
+    "\n",
+    "for (p, q, r) in progressions:\n",
+    "    if p == 1487 and q == 4817 and r == 8147:\n",
+    "        continue\n",
+    "        \n",
+    "    if Counter(p.digits()) == Counter(q.digits()) == Counter(r.digits()):\n",
+    "        break\n",
+    "        \n",
+    "p, q, r"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "SageMath 9.5",
+   "language": "sage",
+   "name": "sagemath"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.11.2"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}