124 lines
2.5 KiB
Plaintext
124 lines
2.5 KiB
Plaintext
{
|
|
"cells": [
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"# Pandigital prime (Euler Problem 41)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {
|
|
"collapsed": true
|
|
},
|
|
"source": [
|
|
"[https://projecteuler.net/problem=41]\n",
|
|
"\n",
|
|
"We shall say that an n-digit number is pandigital if it makes use of all the digits 1 to n exactly once. For example, 2143 is a 4-digit pandigital and is also prime.\n",
|
|
"\n",
|
|
"What is the largest n-digit pandigital prime that exists?"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 49,
|
|
"metadata": {
|
|
"collapsed": true
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"def expmod(base, exp, m):\n",
|
|
" if exp == 0:\n",
|
|
" return 1\n",
|
|
" if (exp % 2 == 0):\n",
|
|
" return (expmod(base, exp // 2, m) ** 2 % m)\n",
|
|
" return (base * expmod(base, exp - 1, m) % m)\n",
|
|
" \n",
|
|
"def expmod_naiv(base, exp, m):\n",
|
|
" return base ** exp % m\n",
|
|
"\n",
|
|
"def fermat_test(n):\n",
|
|
" a = n - 3\n",
|
|
" return expmod(a, n, n) == a"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 50,
|
|
"metadata": {
|
|
"collapsed": true
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"assert(expmod(2, 100000, 2143) == expmod_naiv(2, 100000, 2143))"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 51,
|
|
"metadata": {
|
|
"collapsed": true
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"assert(fermat_test(2143))"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 54,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"7652413\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"import itertools\n",
|
|
"\n",
|
|
"for pandigital in itertools.permutations(\"7654321\"):\n",
|
|
" p = int(\"\".join(pandigital))\n",
|
|
" if fermat_test(p):\n",
|
|
" s = p\n",
|
|
" break\n",
|
|
" \n",
|
|
"print(s)\n",
|
|
"assert(s == 7652413)"
|
|
]
|
|
}
|
|
],
|
|
"metadata": {
|
|
"completion_date": "Wed, 19 Dec 2018, 20:14",
|
|
"kernelspec": {
|
|
"display_name": "Python 3",
|
|
"language": "python3.6",
|
|
"name": "python3"
|
|
},
|
|
"language_info": {
|
|
"codemirror_mode": {
|
|
"name": "ipython",
|
|
"version": 3
|
|
},
|
|
"file_extension": ".py",
|
|
"mimetype": "text/x-python",
|
|
"name": "python",
|
|
"nbconvert_exporter": "python",
|
|
"pygments_lexer": "ipython3",
|
|
"version": "3.6.5"
|
|
},
|
|
"tags": [
|
|
"pandigital",
|
|
"prime",
|
|
"fermat",
|
|
"test"
|
|
]
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 2
|
|
}
|