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{
"cells": [
{
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"source": [
"# Euler Problem 7\n",
"\n",
"By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13.\n",
"\n",
"What is the 10 001st prime number?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We reuse our prime functions and use a trick from [stackoverflow](https://stackoverflow.com/questions/2300756/get-the-nth-item-of-a-generator-in-python) to get the nth element."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"104743\n"
]
}
],
"source": [
"import itertools\n",
"\n",
"def is_prime(n, smaller_primes):\n",
" for s in smaller_primes:\n",
" if n % s == 0:\n",
" return False\n",
" if s * s > n:\n",
" return True\n",
" return True\n",
"\n",
"def prime_generator_function():\n",
" primes = [2, 3, 5, 7]\n",
" for p in primes:\n",
" yield p\n",
" while True:\n",
" p += 2\n",
" if is_prime(p, primes):\n",
" primes.append(p)\n",
" yield p\n",
"\n",
"def get_nth_prime(n):\n",
" ps = prime_generator_function()\n",
" return next(itertools.islice(ps, n - 1, n))\n",
"\n",
"assert(get_nth_prime(6) == 13)\n",
"print(get_nth_prime(10001))"
]
}
],
"metadata": {
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"completion_date": "Wed, 20 Aug 2014, 15:40",
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"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
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"language_info": {
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"name": "ipython",
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"nbconvert_exporter": "python",
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},
"tags": [
"prime",
"nth prime",
"nth",
"generator"
]
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