From 0d858b90ed4bdeb545b285c993138784527f4503 Mon Sep 17 00:00:00 2001
From: filifa <filifa.breath652@8alias.com>
Date: Thu, 17 Apr 2025 20:41:13 -0400
Subject: [PATCH] add problem 35

---
 notebooks/problem0035.ipynb | 84 +++++++++++++++++++++++++++++++++++++
 1 file changed, 84 insertions(+)
 create mode 100644 notebooks/problem0035.ipynb

diff --git a/notebooks/problem0035.ipynb b/notebooks/problem0035.ipynb
new file mode 100644
index 0000000..45378d8
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+++ b/notebooks/problem0035.ipynb
@@ -0,0 +1,84 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "f118733f",
+   "metadata": {},
+   "source": [
+    "# [Circular Primes](https://projecteuler.net/problem=35)\n",
+    "\n",
+    "We're only looking for [circular primes](https://en.wikipedia.org/wiki/Circular_prime) below one million, which makes this search not too strenuous. Obviously, being prime is a precondition for being a circular prime, so we can start our search by only checking primes below one million.\n",
+    "\n",
+    "We can then use Python's [`deque` class](https://docs.python.org/3/library/collections.html) to write a function that cycles through a prime number's digits to check if it is a circular prime."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "9d4833c5",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "55\n"
+     ]
+    }
+   ],
+   "source": [
+    "from collections import deque\n",
+    "\n",
+    "def is_circular_prime(p):\n",
+    "    d = deque(str(p))\n",
+    "    while True:\n",
+    "        d.rotate()\n",
+    "        rp = int(\"\".join(d))\n",
+    "        if rp == p:\n",
+    "            break\n",
+    "        elif not is_prime(rp):\n",
+    "            return False\n",
+    "    \n",
+    "    return True\n",
+    "\n",
+    "\n",
+    "circular_primes = set(p for p in prime_range(1000000) if is_circular_prime(p))\n",
+    "print(len(circular_primes))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "5e21d050",
+   "metadata": {},
+   "source": [
+    "There are other optimizations you can make - for instance, every multi-digit circular prime can only be composed of the digits 1, 3, 7, and 9 (since having another digit would eventually result in a rotation that ends in an even number or 5, which obviously isn't prime) - but why bother (for this problem) when it's already this fast?\n",
+    "\n",
+    "Another note - there aren't that many known circular primes, and all of the known ones greater than one million are [repunits](https://en.wikipedia.org/wiki/Repunit).\n",
+    "\n",
+    "## Relevant sequences\n",
+    "* Circular primes: [A068652](https://oeis.org/A068652)"
+   ]
+  }
+ ],
+ "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
+}