Skip to content

Instantly share code, notes, and snippets.

@mozz100

mozz100/big-primes.ipynb

Created September 25, 2017 21:37
Show Gist options
  • Save mozz100/69ae347cda4b92b8996b75349c796491 to your computer and use it in GitHub Desktop.
Save mozz100/69ae347cda4b92b8996b75349c796491 to your computer and use it in GitHub Desktop.
Download ZIP
Prime numbers
Display the source blob
Display the rendered blob
Raw
big-primes.ipynb
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Credits\n",
"\n",
"Prime number functions from https://inventwithpython.com/hacking/chapter23.html\n",
"\n",
"Trinity Hall Prime from https://math.stackexchange.com/questions/2420488/what-is-trinity-hall-prime-number\n",
"\n",
"Prior art and inspiration from https://friendlyfieldsandopenmaps.com/2017/09/08/the-corpus-christi-prime/\n",
"\n",
"Prime number checking at https://www.alpertron.com.ar/ECM.HTM\n"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# Primality Testing with the Rabin-Miller Algorithm\n",
"# http://inventwithpython.com/hacking (BSD Licensed)\n",
"import random\n",
"\n",
"\n",
"def rabinMiller(num):\n",
" # Returns True if num is a prime number.\n",
" s = num - 1\n",
" t = 0\n",
" while s % 2 == 0:\n",
" # keep halving s while it is even (and use t\n",
" # to count how many times we halve s)\n",
" s = s // 2\n",
" t += 1\n",
" for trials in range(5): # try to falsify num's primality 5 times\n",
" a = random.randrange(2, num - 1)\n",
" v = pow(a, s, num)\n",
" if v != 1: # this test does not apply if v is 1.\n",
" i = 0\n",
" while v != (num - 1):\n",
" if i == t - 1:\n",
" return False\n",
" else:\n",
" i = i + 1\n",
" v = (v ** 2) % num\n",
" return True\n",
"\n",
"def isPrime(num):\n",
" # Return True if num is a prime number. This function does a quicker\n",
" # prime number check before calling rabinMiller().\n",
" if (num < 2):\n",
" return False # 0, 1, and negative numbers are not prime\n",
" # About 1/3 of the time we can quickly determine if num is not prime\n",
" # by dividing by the first few dozen prime numbers. This is quicker\n",
" # than rabinMiller(), but unlike rabinMiller() is not guaranteed to\n",
" # prove that a number is prime.\n",
" lowPrimes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997]\n",
" if num in lowPrimes:\n",
" return True\n",
" # See if any of the low prime numbers can divide num\n",
" for prime in lowPrimes:\n",
" if (num % prime == 0):\n",
" return False\n",
" # If all else fails, call rabinMiller() to determine if num is a prime.\n",
" return rabinMiller(num)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Draw ascii with:\n",
"```\n",
">$ jp2a --height=20 -i --chars=\"18\" /Users/mozz/Desktop/angentbw.jpg --invert\n",
"```\n",
"\n",
"```88888888888888888888881111118888888888888888888888\n",
"88888888888888888881111111111118888888888888888888\n",
"88888888888888888111111111111111188888888888888888\n",
"88888888888888881111111111111111118888888888888888\n",
"88888888888888811111111111111111111888888888888888\n",
"88888888888888111111118888881111111188888888888888\n",
"88888888888888111118888111188881111188888888888888\n",
"88888888888881111188811111111888111118888888888888\n",
"88888888888881111888111111111188811118888888888888\n",
"88888888888811111188811111111888111111888888888888\n",
"88888888888811111118888111188881111111888888888888\n",
"88888888888111111111188888888111111111188888888888\n",
"88888888881111111111111111111111111111118888888888\n",
"88888888111111111111111111111111111111111188888888\n",
"88888111111111111111111111111111111111111111188888\n",
"11111111111111111111188888888111111111111111111111\n",
"11111111111111111118888888888881111111111111111111\n",
"11111111111111111888888888888888811111111111111111\n",
"11111111111111118888888888888888881111111111111111\n",
"11111111111111888888888888888888888811111111111111\n",
"00000000000000000000000000000000000000000000000000\n",
"00000000000000000000000000000000000000000000000000\n",
"```\n"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Trying n=0\n",
"Trying n=100\n",
"Trying n=200\n",
"Trying n=300\n",
"Success\n"
]
}
],
"source": [
"angent0 = 88888888888888888888881111118888888888888888888888888888888888888888811111111111188888888888888888888888888888888888811111111111111118888888888888888888888888888888881111111111111111118888888888888888888888888888888111111111111111111118888888888888888888888888888811111111888888111111118888888888888888888888888888111118888111188881111188888888888888888888888888811111888111111118881111188888888888888888888888888111188811111111118881111888888888888888888888888811111188811111111888111111888888888888888888888888111111188881111888811111118888888888888888888888811111111118888888811111111118888888888888888888881111111111111111111111111111118888888888888888881111111111111111111111111111111111888888888888811111111111111111111111111111111111111118888811111111111111111111188888888111111111111111111111111111111111111111188888888888811111111111111111111111111111111111188888888888888881111111111111111111111111111111118888888888888888881111111111111111111111111111118888888888888888888888111111111111110000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\n",
"def angent_prime():\n",
" n = 0\n",
" while True:\n",
" if n % 100 == 0:\n",
" print(\"Trying n=%d\" % n)\n",
" num = angent0 + 1 + n*2\n",
" if isPrime(num):\n",
" print(\"Success\")\n",
" return num\n",
" n += 1\n",
"angent_result = angent_prime()"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"88888888888888888888881111118888888888888888888888\n",
"88888888888888888881111111111118888888888888888888\n",
"88888888888888888111111111111111188888888888888888\n",
"88888888888888881111111111111111118888888888888888\n",
"88888888888888811111111111111111111888888888888888\n",
"88888888888888111111118888881111111188888888888888\n",
"88888888888888111118888111188881111188888888888888\n",
"88888888888881111188811111111888111118888888888888\n",
"88888888888881111888111111111188811118888888888888\n",
"88888888888811111188811111111888111111888888888888\n",
"88888888888811111118888111188881111111888888888888\n",
"88888888888111111111188888888111111111188888888888\n",
"88888888881111111111111111111111111111118888888888\n",
"88888888111111111111111111111111111111111188888888\n",
"88888111111111111111111111111111111111111111188888\n",
"11111111111111111111188888888111111111111111111111\n",
"11111111111111111118888888888881111111111111111111\n",
"11111111111111111888888888888888811111111111111111\n",
"11111111111111118888888888888888881111111111111111\n",
"11111111111111888888888888888888888811111111111111\n",
"00000000000000000000000000000000000000000000000000\n",
"00000000000000000000000000000000000000000000000621\n",
"\n"
]
}
],
"source": [
"# Function for pretty printing long numbers\n",
"def pp(num, line_len):\n",
" s = str(num)\n",
" for l in range(0,1 + len(s)//line_len):\n",
" print(s[line_len*l:line_len*(l+1)])\n",
"\n",
"pp(angent_result, 50)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Trying n=0\n",
"Trying n=100\n",
"Trying n=200\n",
"Trying n=300\n",
"Trying n=400\n",
"Trying n=500\n",
"Trying n=600\n",
"Trying n=700\n",
"Trying n=800\n",
"Trying n=900\n",
"Trying n=1000\n",
"Trying n=1100\n",
"Trying n=1200\n",
"Trying n=1300\n",
"Trying n=1400\n",
"Success\n"
]
}
],
"source": [
"# Owlstone logo by a similar method. Line length 45 this time\n",
"owl1 = 111111111111118111111111111111111111111111111111111111111118881111111111111111111111111111111111111111111888888111111111111111111111111111111111111888111118888811111111111111111111111111111118881111111111111111111111111111111111111111188811111111111111111111111111111111111111111111111111111111111111188811111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111188888888111111111111111111118111111111188888888888888888811111111188111888111111111111111888888888888888111111188118888111111111111111111888888888888881111881118888811111111111111111111888888888888111881118888811111111111111111111188888888888811888118888881111111111111111111118888888888811888111888881111111111111111111111888888888811188111188888111111111111111111111188888888811118811111888811111111111111111111188811888811111881111188881111111111111111111111111888111111181111111888811111111111111111111111888111111111111111118881111111111111111111111881111111111111111111118811111111111111111118811111111111111111111111111111111111111111118811111111111111111111111111111111111111111188111111111111111111111111111111111111111111181111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111\n",
"def owl_prime():\n",
" n = 0\n",
" while True:\n",
" if n % 100 == 0:\n",
" print(\"Trying n=%d\" % n)\n",
" num = owl1 + n*2\n",
" if isPrime(num):\n",
" print(\"Success\")\n",
" return num\n",
" n += 1\n",
"owl_result = owl_prime()"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"111111111111118111111111111111111111111111111\n",
"111111111111118881111111111111111111111111111\n",
"111111111111111888888111111111111111111111111\n",
"111111111111888111118888811111111111111111111\n",
"111111111118881111111111111111111111111111111\n",
"111111111188811111111111111111111111111111111\n",
"111111111111111111111111111111188811111111111\n",
"111111111111111111111111111111111111111111111\n",
"111111111111111111111111111111111111111111111\n",
"111111111111111111111111111111111111111111111\n",
"111111111111111111111111111111111111111111111\n",
"111111111111111111111111188888888111111111111\n",
"111111118111111111188888888888888888811111111\n",
"188111888111111111111111888888888888888111111\n",
"188118888111111111111111111888888888888881111\n",
"881118888811111111111111111111888888888888111\n",
"881118888811111111111111111111188888888888811\n",
"888118888881111111111111111111118888888888811\n",
"888111888881111111111111111111111888888888811\n",
"188111188888111111111111111111111188888888811\n",
"118811111888811111111111111111111188811888811\n",
"111881111188881111111111111111111111111888111\n",
"111181111111888811111111111111111111111888111\n",
"111111111111118881111111111111111111111881111\n",
"111111111111111118811111111111111111118811111\n",
"111111111111111111111111111111111111118811111\n",
"111111111111111111111111111111111111188111111\n",
"111111111111111111111111111111111111181111111\n",
"111111111111111111111111111111111111111111111\n",
"111111111111111111111111111111111111111114027\n",
"\n"
]
}
],
"source": [
"pp(owl_result, 45)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"1350\n"
]
}
],
"source": [
"print(len(str(owl_result))) # TH"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"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": "3.5.1"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment