Performance Differences with Python Versions

Just a few notes on differences I observed using this program with different Python versions.

With an empty primenumbers.zip store I invoked method nextprime for parameter number 5 million. This forces the primes array to be built from scratch up to a prime number exceeding 5 million (5'001'001). Performance differences between Python versions and their bitness, as well as different primality test algorithms are quite remarkable.

Test machine was Windows 10 64bit, AMD 4 GHz, 8 GB memory.

Interestingly, about the same profile came out, when using an Intel-based (i7-6700) Win 10 laptop with only 2.6 GHz, but 16 GB memory and a Win system SSD. The (Intel) laptop even showed a slightly better performance, which probably goes back to the Python versions being installed on the SSD system disk.

Py Version	Eratosthenes	Miller-Rabin
2.7 x86	71 sec	40 sec
3.5 x64	45 sec	24 sec
3.6 x64	29 sec	21 sec

Conclusion

Python 3.x 64bit is about twice as fast as Python 2.7, especially when using the Miller-Rabin-Test. Some minor but noticable differences do exist between Python 3.5 and 3.6 - as was to be expected according to remarks accompanying the 3.6 release.

I also did performance tests after porting the primes.py module to Cython (v 0.25.2) and then using the primes.pyd version. The above Miller-Rabin-Tests showed very significant speed improvements by a factor of more than 20 (both, for Python 2 and 3). This means that prime numbers up to about 5 million can be calculated and stored in an array in just 1 second using Python 3!

Improvement factors for other methods of the module range from 1.8 to 6.

The Cython source is provided in primes.pyx, the generated C sources are primes.c27and primes.c3x.