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vendor

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sudo: required
dist: trusty
group: edge
language: php
php:
- '7.0'
- '7.1'
- nightly
- hhvm
- '5.6'
- '5.5'
- '5.4'
addons:
apt:
packages:
- python3
before_script:
- composer update --dev
script:
- "tests/testing.php"

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# PrimeModule
Prime module capable of doing prime factorization of huge numbers very quickly.
It can factorize huge numbers (even bigger than `PHP_INT_MAX` thanks to the wolfram alpha/python modules) very quickly.
## Installation:
Install with composer.
```
composer require danog/primemodule
```
Install python to enable the python module and the PHP curl extension to enable the wolfram alpha module.
## Usage:
This library has 4 prime factorization modules (ordered by speed, huge semiprime is usually a 20 digit semiprime generated by [telegram](https://core.telegram.org), see the travis ci tests for more stats):
* python - A [quadratic sieve](http://codegolf.stackexchange.com/questions/8629/fastest-semiprime-factorization) python module (usually it's faster than the pollard brent module, other times it just gets stuck (and then killed after 10 seconds by the lib), medium time 0.35134809732437 seconds calculated using 100 huge semiprimes, some of which caused the module to freeze and be killed. Usually it's 10 times faster than the pollard brent module)
* python_alt - A [pollard brent](https://stackoverflow.com/questions/4643647/fast-prime-factorization-module) module also written in python (medium time 0.1801231908798 seconds calculated using 100 huge semiprimes)
* wolfram - A [wolfram alpha](https://wolframalpha.com) module (usually takes around 2.1294961380959 seconds calculated using 100 huge semiprimes)
* native - A [native PHP lopatin](https://github.com/LonamiWebs/Telethon/blob/master/telethon/crypto/factorizator.py) module (usually takes around 2.5698633241653 seconds calculated using 100 huge semiprimes, may sometimes be faster than the wolfram module)
These modules can be used either in the single variant, which returns only one factor (useful for semiprime factorization), or the full methods, that return an array with all of the factors.
This module was created to do semiprime factorization, so it might not perform very well with composite numbers.
The python/wolframalpha modules accept numeric strings bigger than `PHP_INT_MAX`, and if the factors are bigger than `PHP_INT_MAX` they will also returned as a string.
An automatic function can also be used, which chooses automatically the module in the following order: python_alt, python, native, wolfram.
```
require 'vendor/autoload.php';
// quadratic sieve factorization
$factor = \danog\PrimeModule::python_single(2768594593405030913); // returns 1455582581 or 1902052573
// pollard brent sieve factorization
$factor = \danog\PrimeModule::python_single_alt(2768594593405030913); // returns 1455582581 or 1902052573
// native PHP single factorization
$factor = \danog\PrimeModule::native_single(2768594593405030913); // returns 1455582581 or 1902052573
// wolfram factorization
$factor = \danog\PrimeModule::wolfram_single(2768594593405030913); // returns 1455582581 or 1902052573
// automatic factorization
$factor = \danog\PrimeModule::auto_single(2768594593405030913); // returns 1455582581 or 1902052573
// quadratic sieve factorization
$factor = \danog\PrimeModule::python(15); // returns an array with 3 and 5
// pollard brent sieve factorization
$factor = \danog\PrimeModule::python_alt(15); // returns an array with 3 and 5
// native PHP factorization
$factor = \danog\PrimeModule::native(15); // returns an array with 3 and 5
// wolfram factorization
$factor = \danog\PrimeModule::wolfram(15); // returns an array with 3 and 5
// automatic factorization
$factor = \danog\PrimeModule::auto(15); // returns an array with 3 and 5
```
See `tests/testing.php` for more detailed examples.
Library created by Daniil Gentili (https://daniil.it)

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{
"name": "danog/primemodule",
"description": "Prime module capable of doing prime factorization of huge numbers very quickly.\"",
"type": "library",
"license": "AGLPV3",
"authors": [
{
"name": "Daniil Gentili",
"email": "daniil@daniil.it"
}
],
"require": {}
}

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<?php
/*
opyright 2016-2017 Daniil Gentili
(https://daniil.it)
This file is part of MadelineProto.
MadelineProto is free software: you can redistribute it and/or modify it under the terms of the GNU Affero General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.
MadelineProto is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY;
without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
See the GNU Affero General Public License for more details.
You should have received a copy of the GNU General Public License along with the MadelineProto.
If not, see <http://www.gnu.org/licenses/>.
*/
namespace danog;
class PrimeModule
{
// Uses https://github.com/LonamiWebs/Telethon/blob/master/telethon/crypto/factorizator.py, thank you so freaking much!
public static function native_single($what)
{
if (!is_int($what)) return false;
foreach ([2, 3, 5, 7, 11, 13, 17, 19, 23] as $s) {
if ($what % $s === 0) {
return $s;
}
}
$g = 0;
for ($i = 0; $i < 3; $i++) {
$q = (rand(0, 127) & 15) + 17;
$x = rand(0, 1000000000) + 1;
$y = $x;
$lim = 1 << ($i + 18);
for ($j = 1; $j <= $lim; $j++) {
list($a, $b, $c) = [$x, $x, $q];
while ($b != 0) {
if (($b & 1) != 0) {
$c += $a;
if ($c >= $what) {
$c -= $what;
}
}
$a += $a;
if ($a >= $what) {
$a -= $what;
}
$b >>= 1;
}
$x = $c;
$z = ($x < $y) ? $y - $x : $x - $y;
$g = self::gcd($z, $what);
if ($g != 1) {
break;
}
if (($j & ($j - 1)) === 0) {
$y = $x;
}
}
if ($g > 1) {
break;
}
}
$p = $what;
return min($p, $g);
}
private static function gcd($a, $b)
{
if ($a == $b) {
return $a;
}
while ($b > 0) {
list($a, $b) = [$b, self::posmod($a, $b)];
}
return $a;
}
private static function posmod($a, $b) {
$resto = $a % $b;
if ($resto < 0) {
$resto += abs($b);
}
return $resto;
}
public static function python_single($what) {
if (function_exists('shell_exec')) {
$res = shell_exec('timeout 10 python '.__DIR__.'/prime.py '.$what);
if ($res == '' || is_null($res)) return false;
$newval = intval($res);
if (is_int($newval)) $res = $newval;
if ($res === 0) return false;
return $res;
}
return false;
}
public static function python_single_alt($what) {
if (function_exists('shell_exec')) {
$res = shell_exec('python '.__DIR__.'/alt_prime.py '.$what);
if ($res == '' || is_null($res)) return false;
$newval = intval($res);
if (is_int($newval)) $res = $newval;
if ($res === 0) return false;
return $res;
}
return false;
}
public static function wolfram_single($what)
{
$query = 'Do prime factorization of '.$what;
$params = [
'async' => true,
'banners' => 'raw',
'debuggingdata' => false,
'format' => 'moutput',
'formattimeout' => 8,
'input' => $query,
'output' => 'JSON',
'proxycode' => json_decode(file_get_contents('http://www.wolframalpha.com/api/v1/code'), true)['code'],
];
$url = 'https://www.wolframalpha.com/input/json.jsp?'.http_build_query($params);
$ch = curl_init();
curl_setopt($ch, CURLOPT_RETURNTRANSFER, true);
curl_setopt($ch, CURLOPT_HTTPHEADER, ['Referer: https://www.wolframalpha.com/input/?i='.urlencode($query)]);
curl_setopt($ch, CURLOPT_URL, $url);
$res = json_decode(curl_exec($ch), true);
curl_close($ch);
$fres = false;
if (!isset($res['queryresult']['pods'])) return false;
foreach ($res['queryresult']['pods'] as $cur) {
if ($cur['id'] === 'Divisors') {
$fres = explode(', ', preg_replace(["/{\d+, /", "/, \d+}$/"], '', $cur['subpods'][0]['moutput']));
break;
}
}
if (is_array($fres)) {
$fres = $fres[0];
$newval = intval($fres);
if (is_int($newval)) $fres = $newval;
return $fres;
}
return false;
}
public static function native($what) {
$res = [self::native_single($what)];
while (array_product($res) !== $what) {
$res [] = self::native_single($what / array_product($res));
}
return $res;
}
public static function python($what) {
$res = [self::python_single($what)];
if ($res[0] === false) return false;
while (array_product($res) !== $what) {
$res [] = self::python_single($what / array_product($res));
}
return $res;
}
public static function python_alt($what) {
$res = [self::python_single_alt($what)];
if ($res[0] === false) return false;
while (array_product($res) !== $what) {
$res [] = self::python_single_alt($what / array_product($res));
}
return $res;
}
public static function wolfram($what) {
$res = [self::wolfram_single($what)];
while (array_product($res) !== $what) {
$res [] = self::wolfram_single($what / array_product($res));
}
return $res;
}
public static function auto($what) {
$res = self::python_alt($what);
if (is_array($res)) return $res;
$res = self::python($what);
if (is_array($res)) return $res;
$res = self::native((int) $what);
if (is_array($res)) return $res;
$res = self::wolfram($what);
if (is_array($res)) return $res;
return false;
}
public static function auto_single($what) {
$res = self::python_single_alt($what);
if ($res !== false) return $res;
$res = self::python_single($what);
if ($res !== false) return $res;
$res = self::native_single((int) $what);
if ($res !== false) return $res;
$res = self::wolfram_single($what);
if ($res !== false) return $res;
return false;
}
}

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# NOTICE!!! This is copied from https://stackoverflow.com/questions/4643647/fast-prime-factorization-module
import sys
import random
def primesbelow(N):
# http://stackoverflow.com/questions/2068372/fastest-way-to-list-all-primes-below-n-in-python/3035188#3035188
#""" Input N>=6, Returns a list of primes, 2 <= p < N """
correction = N % 6 > 1
N = {0:N, 1:N-1, 2:N+4, 3:N+3, 4:N+2, 5:N+1}[N%6]
sieve = [True] * (N // 3)
sieve[0] = False
for i in range(int(N ** .5) // 3 + 1):
if sieve[i]:
k = (3 * i + 1) | 1
sieve[k*k // 3::2*k] = [False] * ((N//6 - (k*k)//6 - 1)//k + 1)
sieve[(k*k + 4*k - 2*k*(i%2)) // 3::2*k] = [False] * ((N // 6 - (k*k + 4*k - 2*k*(i%2))//6 - 1) // k + 1)
return [2, 3] + [(3 * i + 1) | 1 for i in range(1, N//3 - correction) if sieve[i]]
smallprimeset = set(primesbelow(100000))
_smallprimeset = 100000
def isprime(n, precision=7):
# http://en.wikipedia.org/wiki/Miller-Rabin_primality_test#Algorithm_and_running_time
if n == 1 or n % 2 == 0:
return False
elif n < 1:
raise ValueError("Out of bounds, first argument must be > 0")
elif n < _smallprimeset:
return n in smallprimeset
d = n - 1
s = 0
while d % 2 == 0:
d //= 2
s += 1
for repeat in range(precision):
a = random.randrange(2, n - 2)
x = pow(a, d, n)
if x == 1 or x == n - 1: continue
for r in range(s - 1):
x = pow(x, 2, n)
if x == 1: return False
if x == n - 1: break
else: return False
return True
# https://comeoncodeon.wordpress.com/2010/09/18/pollard-rho-brent-integer-factorization/
def pollard_brent(n):
if n % 2 == 0: return 2
if n % 3 == 0: return 3
y, c, m = random.randint(1, n-1), random.randint(1, n-1), random.randint(1, n-1)
g, r, q = 1, 1, 1
while g == 1:
x = y
for i in range(r):
y = (pow(y, 2, n) + c) % n
k = 0
while k < r and g==1:
ys = y
for i in range(min(m, r-k)):
y = (pow(y, 2, n) + c) % n
q = q * abs(x-y) % n
g = gcd(q, n)
k += m
r *= 2
if g == n:
while True:
ys = (pow(ys, 2, n) + c) % n
g = gcd(abs(x - ys), n)
if g > 1:
break
return g
smallprimes = primesbelow(10000) # might seem low, but 1000*1000 = 1000000, so this will fully factor every composite < 1000000
def primefactors(n, sort=False):
factors = []
limit = int(n ** .5) + 1
for checker in smallprimes:
if checker > limit: break
while n % checker == 0:
factors.append(checker)
n //= checker
limit = int(n ** .5) + 1
if checker > limit: break
if n < 2: return factors
while n > 1:
if isprime(n):
factors.append(n)
break
factor = pollard_brent(n) # trial division did not fully factor, switch to pollard-brent
factors.extend(primefactors(factor)) # recurse to factor the not necessarily prime factor returned by pollard-brent
n //= factor
if sort: factors.sort()
return factors
def factorization(n):
factors = {}
for p1 in primefactors(n):
try:
factors[p1] += 1
except KeyError:
factors[p1] = 1
return factors
totients = {}
def totient(n):
if n == 0: return 1
try: return totients[n]
except KeyError: pass
tot = 1
for p, exp in factorization(n).items():
tot *= (p - 1) * p ** (exp - 1)
totients[n] = tot
return tot
def gcd(a, b):
if a == b: return a
while b > 0: a, b = b, a % b
return a
def lcm(a, b):
return abs(a * b) // gcd(a, b)
print(primefactors(int(sys.argv[1]))[0])

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from math import log
from argparse import ArgumentParser
# Multiple Polynomial Quadratic Sieve
def mpqs(n, verbose=False):
if verbose:
time1 = clock()
root_n = isqrt(n)
root_2n = isqrt(n+n)
# formula chosen by experimentation
# seems to be close to optimal for n < 10^50
bound = int(5 * log(n, 10)**2)
prime = []
mod_root = []
log_p = []
num_prime = 0
# find a number of small primes for which n is a quadratic residue
p = 2
while p < bound or num_prime < 3:
# legendre (n|p) is only defined for odd p
if p > 2:
leg = legendre(n, p)
else:
leg = n & 1
if leg == 1:
prime += [p]
mod_root += [int(mod_sqrt(n, p))]
log_p += [log(p, 10)]
num_prime += 1
elif leg == 0:
return p
p = next_prime(p)
# size of the sieve
x_max = len(prime)*60
# maximum value on the sieved range
m_val = (x_max * root_2n) >> 1
# fudging the threshold down a bit makes it easier to find powers of primes as factors
# as well as partial-partial relationships, but it also makes the smoothness check slower.
# there's a happy medium somewhere, depending on how efficient the smoothness check is
thresh = log(m_val, 10) * 0.735
# skip small primes. they contribute very little to the log sum
# and add a lot of unnecessary entries to the table
# instead, fudge the threshold down a bit, assuming ~1/4 of them pass
min_prime = int(thresh*3)
fudge = sum(log_p[i] for i,p in enumerate(prime) if p < min_prime)/4
thresh -= fudge
smooth = []
used_prime = set()
partial = {}
num_smooth = 0
num_used_prime = 0
num_partial = 0
num_poly = 0
root_A = isqrt(root_2n / x_max)
while True:
# find an integer value A such that:
# A is =~ sqrt(2*n) / x_max
# A is a perfect square
# sqrt(A) is prime, and n is a quadratic residue mod sqrt(A)
while True:
root_A = next_prime(root_A)
leg = legendre(n, root_A)
if leg == 1:
break
elif leg == 0:
return root_A
A = root_A * root_A
# solve for an adequate B
# B*B is a quadratic residue mod n, such that B*B-A*C = n
# this is unsolvable if n is not a quadratic residue mod sqrt(A)
b = mod_sqrt(n, root_A)
B = (b + (n - b*b) * mod_inv(b + b, root_A))%A
# B*B-A*C = n <=> C = (B*B-n)/A
C = (B*B - n) / A
num_poly += 1
# sieve for prime factors
sums = [0.0]*(2*x_max)
i = 0
for p in prime:
if p < min_prime:
i += 1
continue
logp = log_p[i]
inv_A = mod_inv(A, p)
# modular root of the quadratic
a = int(((mod_root[i] - B) * inv_A)%p)
b = int(((p - mod_root[i] - B) * inv_A)%p)
k = 0
while k < x_max:
if k+a < x_max:
sums[k+a] += logp
if k+b < x_max:
sums[k+b] += logp
if k:
sums[k-a+x_max] += logp
sums[k-b+x_max] += logp
k += p
i += 1
# check for smooths
i = 0
for v in sums:
if v > thresh:
x = x_max-i if i > x_max else i
vec = set()
sqr = []
# because B*B-n = A*C
# (A*x+B)^2 - n = A*A*x*x+2*A*B*x + B*B - n
# = A*(A*x*x+2*B*x+C)
# gives the congruency
# (A*x+B)^2 = A*(A*x*x+2*B*x+C) (mod n)
# because A is chosen to be square, it doesn't need to be sieved
val = sieve_val = A*x*x + 2*B*x + C
if sieve_val < 0:
vec = set([-1])
sieve_val = -sieve_val
for p in prime:
while sieve_val%p == 0:
if p in vec:
# keep track of perfect square factors
# to avoid taking the sqrt of a gigantic number at the end
sqr += [p]
vec ^= set([p])
sieve_val = int(sieve_val / p)
if sieve_val == 1:
# smooth
smooth += [(vec, (sqr, (A*x+B), root_A))]
used_prime |= vec
elif sieve_val in partial:
# combine two partials to make a (xor) smooth
# that is, every prime factor with an odd power is in our factor base
pair_vec, pair_vals = partial[sieve_val]
sqr += list(vec & pair_vec) + [sieve_val]
vec ^= pair_vec
smooth += [(vec, (sqr + pair_vals[0], (A*x+B)*pair_vals[1], root_A*pair_vals[2]))]
used_prime |= vec
num_partial += 1
else:
# save partial for later pairing
partial[sieve_val] = (vec, (sqr, A*x+B, root_A))
i += 1
num_smooth = len(smooth)
num_used_prime = len(used_prime)
if num_smooth > num_used_prime:
used_prime_list = sorted(list(used_prime))
# set up bit fields for gaussian elimination
masks = []
mask = 1
bit_fields = [0]*num_used_prime
for vec, vals in smooth:
masks += [mask]
i = 0
for p in used_prime_list:
if p in vec: bit_fields[i] |= mask
i += 1
mask <<= 1
# row echelon form
col_offset = 0
null_cols = []
for col in xrange(num_smooth):
pivot = col-col_offset == num_used_prime or bit_fields[col-col_offset] & masks[col] == 0
for row in xrange(col+1-col_offset, num_used_prime):
if bit_fields[row] & masks[col]:
if pivot:
bit_fields[col-col_offset], bit_fields[row] = bit_fields[row], bit_fields[col-col_offset]
pivot = False
else:
bit_fields[row] ^= bit_fields[col-col_offset]
if pivot:
null_cols += [col]
col_offset += 1
# reduced row echelon form
for row in xrange(num_used_prime):
# lowest set bit
mask = bit_fields[row] & -bit_fields[row]
for up_row in xrange(row):
if bit_fields[up_row] & mask:
bit_fields[up_row] ^= bit_fields[row]
# check for non-trivial congruencies
for col in null_cols:
all_vec, (lh, rh, rA) = smooth[col]
lhs = lh # sieved values (left hand side)
rhs = [rh] # sieved values - n (right hand side)
rAs = [rA] # root_As (cofactor of lhs)
i = 0
for field in bit_fields:
if field & masks[col]:
vec, (lh, rh, rA) = smooth[i]
lhs += list(all_vec & vec) + lh
all_vec ^= vec
rhs += [rh]
rAs += [rA]
i += 1
factor = gcd(list_prod(rAs)*list_prod(lhs) - list_prod(rhs), n)
if factor != 1 and factor != n:
break
else:
continue
break
return factor
# divide and conquer list product
def list_prod(a):
size = len(a)
if size == 1:
return a[0]
return list_prod(a[:size>>1]) * list_prod(a[size>>1:])
# greatest common divisor of a and b
def gcd(a, b):
while b:
a, b = b, a%b
return a
# modular inverse of a mod m
def mod_inv(a, m):
a = int(a%m)
x, u = 0, 1
while a:
x, u = u, x - (m/a)*u
m, a = a, m%a
return x
# legendre symbol (a|m)
# note: returns m-1 if a is a non-residue, instead of -1
def legendre(a, m):
return pow(a, (m-1) >> 1, m)
# modular sqrt(n) mod p
# p must be prime
def mod_sqrt(n, p):
a = n%p
if p%4 == 3:
return pow(a, (p+1) >> 2, p)
elif p%8 == 5:
v = pow(a << 1, (p-5) >> 3, p)
i = ((a*v*v << 1) % p) - 1
return (a*v*i)%p
elif p%8 == 1:
# Shank's method
q = p-1
e = 0
while q&1 == 0:
e += 1
q >>= 1
n = 2
while legendre(n, p) != p-1:
n += 1
w = pow(a, q, p)
x = pow(a, (q+1) >> 1, p)
y = pow(n, q, p)
r = e
while True:
if w == 1:
return x
v = w
k = 0
while v != 1 and k+1 < r:
v = (v*v)%p
k += 1
if k == 0:
return x
d = pow(y, 1 << (r-k-1), p)
x = (x*d)%p
y = (d*d)%p
w = (w*y)%p
r = k
else: # p == 2
return a
#integer sqrt of n
def isqrt(n):
c = n*4/3
d = c.bit_length()
a = d>>1
if d&1:
x = 1 << a
y = (x + (n >> a)) >> 1
else:
x = (3 << a) >> 2
y = (x + (c >> a)) >> 1
if x != y:
x = y
y = (x + n/x) >> 1
while y < x:
x = y
y = (x + n/x) >> 1
return x
# strong probable prime
def is_sprp(n, b=2):
if n < 2: return False
d = n-1
s = 0
while d&1 == 0:
s += 1
d >>= 1
x = pow(b, d, n)
if x == 1 or x == n-1:
return True
for r in xrange(1, s):
x = (x * x)%n
if x == 1:
return False
elif x == n-1:
return True
return False
# lucas probable prime
# assumes D = 1 (mod 4), (D|n) = -1
def is_lucas_prp(n, D):
P = 1
Q = (1-D) >> 2
# n+1 = 2**r*s where s is odd
s = n+1
r = 0
while s&1 == 0:
r += 1
s >>= 1
# calculate the bit reversal of (odd) s
# e.g. 19 (10011) <=> 25 (11001)
t = 0
while s:
if s&1:
t += 1
s -= 1
else:
t <<= 1
s >>= 1
# use the same bit reversal process to calculate the sth Lucas number
# keep track of q = Q**n as we go
U = 0
V = 2
q = 1
# mod_inv(2, n)
inv_2 = (n+1) >> 1
while t:
if t&1:
# U, V of n+1
U, V = ((U + V) * inv_2)%n, ((D*U + V) * inv_2)%n
q = (q * Q)%n
t -= 1
else:
# U, V of n*2
U, V = (U * V)%n, (V * V - 2 * q)%n
q = (q * q)%n
t >>= 1
# double s until we have the 2**r*sth Lucas number
while r:
U, V = (U * V)%n, (V * V - 2 * q)%n
q = (q * q)%n
r -= 1
# primality check
# if n is prime, n divides the n+1st Lucas number, given the assumptions
return U == 0
# primes less than 212
small_primes = set([
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])
# pre-calced sieve of eratosthenes for n = 2, 3, 5, 7
indices = [
1, 11, 13, 17, 19, 23, 29, 31, 37, 41,
43, 47, 53, 59, 61, 67, 71, 73, 79, 83,
89, 97,101,103,107,109,113,121,127,131,
137,139,143,149,151,157,163,167,169,173,
179,181,187,191,193,197,199,209]
# distances between sieve values
offsets = [
10, 2, 4, 2, 4, 6, 2, 6, 4, 2, 4, 6,
6, 2, 6, 4, 2, 6, 4, 6, 8, 4, 2, 4,
2, 4, 8, 6, 4, 6, 2, 4, 6, 2, 6, 6,
4, 2, 4, 6, 2, 6, 4, 2, 4, 2,10, 2]
max_int = 2147483647
# an 'almost certain' primality check
def is_prime(n):
if n < 212:
return n in small_primes
for p in small_primes:
if n%p == 0:
return False
# if n is a 32-bit integer, perform full trial division
if n <= max_int:
i = 211
while i*i < n:
for o in offsets:
i += o
if n%i == 0:
return False
return True
# Baillie-PSW
# this is technically a probabalistic test, but there are no known pseudoprimes
if not is_sprp(n, 2): return False
# idea shamelessly stolen from Mathmatica
# if n is a 2-sprp and a 3-sprp, n is necessarily square-free
if not is_sprp(n, 3): return False
a = 5
s = 2
# if n is a perfect square, this will never terminate
while legendre(a, n) != n-1:
s = -s
a = s-a
return is_lucas_prp(n, a)
# next prime strictly larger than n
def next_prime(n):
if n < 2:
return 2
# first odd larger than n
n = (n + 1) | 1
if n < 212:
while True:
if n in small_primes:
return n
n += 2
# find our position in the sieve rotation via binary search
x = int(n%210)
s = 0
e = 47
m = 24
while m != e:
if indices[m] < x:
s = m
m = (s + e + 1) >> 1
else:
e = m
m = (s + e) >> 1
i = int(n + (indices[m] - x))
# adjust offsets
offs = offsets[m:] + offsets[:m]
while True:
for o in offs:
if is_prime(i):
return i
i += o
if __name__ == "__main__":
parser =ArgumentParser(description='Uses a MPQS to factor a composite number')
parser.add_argument('composite', metavar='number_to_factor', type=long,
help='the composite number to factor')
parser.add_argument('--verbose', dest='verbose', action='store_true',
help="enable verbose output")
args = parser.parse_args()
print mpqs(args.composite)

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#!/usr/bin/env php
<?php
require 'vendor/autoload.php';
function get_time($callable, $param) {
$a = microtime(true);
$result = $callable($param);
$time = microtime(true) - $a;
if (is_array($result)) $result = json_encode($result);
return [$time, $result];
}
function test($n) {
$init = '| '.str_pad('result', strlen($n), " ", STR_PAD_RIGHT).' | type | time |';
echo '|'.str_pad('', strlen($init)-2, "-", STR_PAD_RIGHT).'|'.PHP_EOL;
echo '|'.str_pad('Multiple factorization of '.$n, strlen($init)-2, " ", STR_PAD_BOTH).'|'.PHP_EOL;
echo '|'.str_pad('', strlen($init)-2, "_", STR_PAD_RIGHT).'|'.PHP_EOL;
echo $init.PHP_EOL;
list($time, $result) = get_time(['\danog\PrimeModule', 'python_alt'], $n, true);
$GLOBALS['medium']['python_alt'] += $time;
echo '| '.str_pad($result, 6, " ", STR_PAD_RIGHT).' | python alt | '.str_pad($time, 20, " ", STR_PAD_RIGHT).' |'.PHP_EOL;
list($time, $result) = get_time(['\danog\PrimeModule', 'python'], $n);
$GLOBALS['medium']['python'] += $time;
echo '| '.str_pad($result, 6, " ", STR_PAD_RIGHT).' | wolfram | '.str_pad($time, 20, " ", STR_PAD_RIGHT).' |'.PHP_EOL;
list($time, $result) = get_time(['\danog\PrimeModule', 'native'], $n);
$GLOBALS['medium']['native'] += $time;
echo '| '.str_pad($result, 6, " ", STR_PAD_RIGHT).' | python | '.str_pad($time, 20, " ", STR_PAD_RIGHT).' |'.PHP_EOL;
list($time, $result) = get_time(['\danog\PrimeModule', 'wolfram'], $n);
$GLOBALS['medium']['wolfram'] += $time;
echo '| '.str_pad($result, 6, " ", STR_PAD_RIGHT).' | native | '.str_pad($time, 20, " ", STR_PAD_RIGHT).' |'.PHP_EOL;
//echo '| '.str_pad($n, 6, " ", STR_PAD_RIGHT).' | auto | '.str_pad(get_time(['\danog\PrimeModule', 'auto'], $n), 20, " ", STR_PAD_RIGHT).' |'.PHP_EOL;
echo '|'.str_pad('', strlen($init)-2, "-", STR_PAD_RIGHT).'|'.PHP_EOL.PHP_EOL;
}
function test_single($n, $messy = false) {
$init = '| '.str_pad('result', strlen($n), " ", STR_PAD_RIGHT).' | type | time |';
echo '|'.str_pad('', strlen($init)-2, "-", STR_PAD_RIGHT).'|'.PHP_EOL;
echo '|'.str_pad('Single factorization of '.$n, strlen($init)-2, " ", STR_PAD_BOTH).'|'.PHP_EOL;
echo '|'.str_pad('', strlen($init)-2, "_", STR_PAD_RIGHT).'|'.PHP_EOL;
echo $init.PHP_EOL;
list($time, $result) = get_time(['\danog\PrimeModule', 'python_single_alt'], $n);
$GLOBALS['medium']['python_alt'] += $time;
echo '| '.str_pad($result, strlen($n), " ", STR_PAD_RIGHT).' | python alt | '.str_pad($time, 20, " ", STR_PAD_RIGHT).' |'.PHP_EOL;
if (!$messy) {
list($time, $result) = get_time(['\danog\PrimeModule', 'python_single'], $n);
$GLOBALS['medium']['python'] += $time;
echo '| '.str_pad($result, strlen($n), " ", STR_PAD_RIGHT).' | python | '.str_pad($time, 20, " ", STR_PAD_RIGHT).' |'.PHP_EOL;
}
list($time, $result) = get_time(['\danog\PrimeModule', 'native_single'], $n);
$GLOBALS['medium']['native'] += $time;
echo '| '.str_pad($result, strlen($n), " ", STR_PAD_RIGHT).' | native | '.str_pad($time, 20, " ", STR_PAD_RIGHT).' |'.PHP_EOL;
list($time, $result) = get_time(['\danog\PrimeModule', 'wolfram_single'], $n);
$GLOBALS['medium']['wolfram'] += $time;
echo '| '.str_pad($result, strlen($n), " ", STR_PAD_RIGHT).' | wolfram | '.str_pad($time, 20, " ", STR_PAD_RIGHT).' |'.PHP_EOL;
echo '|'.str_pad('', strlen($init)-2, "-", STR_PAD_RIGHT).'|'.PHP_EOL.PHP_EOL;
}
function random_string($length) {
if (function_exists('random_bytes')) return random_bytes($length);
$s = '';
for ($x = 0; $x < $length; $x++) {
$s .= chr(rand(0, 255));
}
return $s;
}
function gen_payload() {
return pack('CPPVV', 10, 0, (int) (time() << 32), 20, 1615239032).random_string(16);
}
echo PHP_EOL.'----------- HUGE SEMIPRIME TESTS (100 semiprimes) ----------'.PHP_EOL;
$GLOBALS['medium'] = ['python' => 0, 'python_alt' => 0, 'wolfram' => 0, 'native' => 0];
$tg = fsockopen('tcp://149.154.167.40:443');
fwrite($tg, chr(239));
stream_set_timeout($tg, 1);
$tot = 100;
for ($x = 0; $x < $tot; $x++) {
fwrite($tg, gen_payload());
$packet_length = ord(stream_get_contents($tg, 1));
if ($packet_length < 127) {
$packet_length <<= 2;
} else {
$packet_length_data = stream_get_contents($tg, 3);
$packet_length = unpack('V', $packet_length_data.pack('x'))[0] << 2;
}
$number = unpack('J', substr(stream_get_contents($tg, $packet_length), 57, 8))[1];
test_single($number);
}
fclose($tg);
foreach ($medium as $type => $total) {
echo $type.': total time '.$total.', medium time '.($total/$tot).PHP_EOL;
}
echo PHP_EOL.'------------------- SMALL MULTIPLE FACTOR TESTS -------------------'.PHP_EOL;
$GLOBALS['medium'] = ['python' => 0, 'python_alt' => 0, 'wolfram' => 0, 'native' => 0];
foreach ([200, 327, 35, 13589] as $multiple) {
test($multiple);
}
foreach ($medium as $type => $total) {
echo $type.': total time '.$total.', medium time '.($total/4).PHP_EOL;
}
echo PHP_EOL.'------------------- HUGE SEMIPRIME TESTS (MESSY) ------------------'.PHP_EOL;
$GLOBALS['medium'] = ['python' => 0, 'python_alt' => 0, 'wolfram' => 0, 'native' => 0];
$m = [1724114033281923457, 2189285106422392999, 3510535493073971807, 1756377470921216651, 1767867620107504387, 2149465210997855797];
foreach ($m as $messy) {
test_single($messy, true);
}
foreach ($medium as $type => $total) {
echo $type.': total time '.$total.', medium time '.($total/count($m)).PHP_EOL;
}