CPrime, fast prime number generator

Description

CPrime is a Python extension, written in Cython, that implements a function to return all prime numbers below a passed maximum.

import pyximport;
pyximport.install()
import CPrime

for x in CPrime.prime_numbers(10 ** 8):
  print('{} is prime'.format(x))

The implementations takes advantage of the following:

• two order of magnitude faster: thanks to Cython's' ability to generate native it is about 100 times faster than a reference implementation (see test_CPrime.prime_numbers_reference)
• few memory, huge numbers: it lazily calculates prime number so that does not need huge buffers up front for huge ranges. Actual memory requirements are at most tens of megabytes.
• parallel execution: internally it splits the job into tasks of up to one million elements and can execute them in parallel when needed. GIL is not taken in performance critical loops so that it can also work fine with other parallel tasks.
• keep it simple: the code is essentially Python with some borrowed constructs from C: structs, malloc/free, base types, static typing.

Compiling extensions

You can compile CPrime extensions and its companion CDividends with the following command:

python3 setup.py build_ext --inplace

Performances

As a benchmark we execute the following in a python console:

import timeit
import CPrime
timeit.timeit('import CPrime; CPrime.free_run(10**9)', number=1)
timeit.timeit('import CPrime; CPrime.free_run(10**10)', number=1)

Results:

Tag	CPU	Host OS	Guest OS	Python	C compiler	10 ^ 9	10 ^ 10
v0.2	Intel i5-3335S @2.7GHz, 4 cores	Windows 10	-	Python 3.4.3	msvc 10	1.119s	11.730s
v0.2	Intel i5-3335S @2.7GHz, 4 cores	OSX 10.10.4	-	Python 3.4.1	Apple LLVM 6.1.0 (LLVM 3.6) no OpenMP	2.447s	25.321s
v0.2	Intel i5-3335S @2.7GHz, 4 cores	OSX 10.10.4	-	Python 2.7.2	Apple LLVM 6.1.0 (LLVM 3.6) no OpenMP	2.653s	27.167s
v0.2	Intel i5-3335S @2.7GHz, 4 cores	OSX 10.10.4	Ubuntu 12.04	Python 3.4.0	gcc 4.8.2	2.439s	23.201s
v0.2	Intel i5-3335S @2.7GHz, 4 cores	OSX 10.10.4	Ubuntu 12.04	Python 2.7.6	gcc 4.8.2	2.394s	23.971s
v0.2	Intel i5-3335S @2.7GHz, 4 cores	OSX 10.10.4	Ubuntu 14.04	Python 3.4.3	gcc 4.9.2	1.727s	16.911s
v0.2	Intel i5-3335S @2.7GHz, 4 cores	OSX 10.10.4	Ubuntu 14.04	Python 2.7.9	gcc 4.9.2	1.696s	16.850s
v0.2	AMD Ryzen7 3800X @3.89GHz, 8 cores	Windows 10	-	Python 3.8.10	msvc 14.29.30037	0.458s	3.936s