Fast prime number generator. Python bindings around C++ library primesieve
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README.md

primesieve-python

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Python bindings for the primesieve C++ library.

Generates primes orders of magnitude faster than any pure Python code!

Features:

  • Get a list of primes
  • Iterate over primes using little memory
  • Find the nth prime
  • Count/print primes and prime k-tuplets
  • Multi-threaded for counting primes and finding the nth prime
  • NumPy support

Prerequisites

You need to have installed a C++ compiler on all OSes except Windows.

# Ubuntu/Debian
sudo apt install g++ python-dev

# Fedora
sudo dnf install gcc-c++ python-devel

# macOS
xcode-select --install

Installation

pip install primesieve

Usage examples

>>> from primesieve import *

# Get a list of the primes <= 40
>>>  primes(40)
[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37]

# Get a list of the primes between 100 and 120
>>>  primes(100, 120)
[101, 103, 107, 109, 113]

# Get a list of the first 10 primes
>>>  n_primes(10)
[2, 3, 5, 7, 11, 13, 17, 19, 23, 29]

# Get a list of the first 10 primes >= 1000
>>>  n_primes(10, 1000)
[1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061]

# Get the 10th prime
>>> nth_prime(10)
29

# Count the primes below 10**9
>>> count_primes(10**9)
50847534

Here is a list of all available functions.

Iterating over primes

Instead of generating a large list of primes and then do something with the primes it is also possible to simply iterate over the primes which uses less memory.

>>> import primesieve

it = primesieve.Iterator()
prime = it.next_prime()

# Iterate over the primes below 10000
while prime < 10000:
    print prime
    prime = it.next_prime()

# Set iterator start number to 100
it.skipto(100)
prime = it.prev_prime()

# Iterate backwards over the primes below 100
while prime > 0:
    print prime
    prime = it.prev_prime()

NumPy support

Using the primesieve.numpy module you can generate an array of primes using native C++ performance!

In comparison the primesieve module generates a list of primes about 7 times slower mostly because the conversion of the C++ primes array into a python list is very slow.

>>> from primesieve.numpy import *

# Generate a numpy array with the primes below 100
>>>  primes(100)
array([ 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])

# Generate a numpy array with the first 100 primes
>>>  n_primes(100)
array([  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])

Development

You need to have installed a C++ compiler, see Prerequisites.

# Install prerequisites
pip install cython pytest numpy

# Clone repository
git clone --recursive https://github.com/hickford/primesieve-python

cd primesieve-python

# Build and install primesieve-python
pip install . --upgrade

# Run tests
py.test