pyprimesieve
Many primes, very fast. Uses primesieve.
primesieve, one of the fastest (if not the fastest) prime sieve implementaions available, is actively maintained by Kim Walisch.
It uses a segmented sieve of Eratosthenes with wheel factorization for a complexity of O(nloglogn) operations.
Performance
Regarding primesieve for C++:
primesieve generates the first 50,847,534 primes up to 10^9 in just 0.4 seconds on a single core of an Intel Core i7-920 2.66GHz, this is about 50 times faster than an ordinary C/C++ sieve of Eratosthenes implementation and about 10,000 times faster than trial-division. primesieve outperforms [Kim's] older ecprime (fastest from 2002 to 2010) by about 30 percent and also substantially outperforms primegen the fastest sieve of Atkin implementation on the web.
For comparison, on an Intel Core i7 2GHz, pyprimesieve populates an entire Python list of the first
50,847,534 primes in 1.40 seconds. It's expected that a Python implementation would be slower than C++ but,
surprisingly, by only one second.
pyprimesieve outperforms all of the fastest prime sieving implementations for Python.
Time (ms) to generate the all primes below one million and iterate over them in Python:
| algorithm | time |
| pyprimesieve | 2.79903411865 |
| primesfrom2to | 13.1568908691 |
| primesfrom3to | 13.5800838470 |
| ambi_sieve | 16.1600112915 |
| rwh_primes2 | 38.7749671936 |
| rwh_primes1 | 48.5658645630 |
| rwh_primes | 52.0040988922 |
| sieve_wheel_30 | 59.3869686127 |
| sieveOfEratosthenes | 59.4990253448 |
| ambi_sieve_plain | 161.740064621 |
| sieveOfAtkin | 232.724905014 |
| sundaram3 | 251.194953918 |
It can be seen here that pyprimesieve is 4.7 times faster than the fastest Python alternative using Numpy and
13.85 times faster than the fastest pure Python sieve.
All benchmark scripts and algorithms are available for reproduction. Prime sieve algorithm implementations were taken from this discussion on SO.
Functions
primes(n): List of prime numbers up to n.
primes(start, n): List of prime numbers from start up to n.
primes_sum(n): The summation of prime numbers up to n. The optimal number of threads will be determined for the given number and system.
primes_sum(start, n): The summation of prime numbers from start up to n. The optimal number of threads will be determined for the given numbers and system.
primes_nth(n): The nth prime number.
factorize(n): List of tuples in the form of (prime, power) for the prime factorization of n.
Installation
pip install pyprimesieveNOTE: To enable the parallelized version of prime summation, you must use a compiler that supports OpenMP. You may need to pass a valid compiler as an environment variable.
Testing
After installation, you can make sure everything is working by running the following inside the project root folder,
python testsLicense
"Modified BSD License". See LICENSE for details. Copyright Jared Suttles, 2015.
