add problem 35
This commit is contained in:
parent
0058ffe8cf
commit
0d858b90ed
|
@ -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
|
||||
}
|
Loading…
Reference in New Issue