primesieve VS primerug

This is a fascinating Q&A where user GordonBGood analyzes the performance of the Sieve of Atkin and compares it to that of Eratosthenes with a view to practical implementations.

The fast prime generator project primesieve is also relevant: https://github.com/kimwalisch/primesieve

I've come across this excellent prime sieve on GitHub, and I just want to find out how it generally works. Yes, it's written in C but I plan to make a Python version that uses some of its methods to make a fairly quick prime sieve. However, I'm really not sure how it has implemented wheel factorisation, and no matter how hard I look online, I can't find a good execution of it that works with its segmented approach. Does anyone have any idea how the wheel factorisation is implemented? To my understanding it's a modulus array that tells you which numbers modulo n are definitely not prime leaving you with the candidate primes to check, but I'm not sure how you would implement this inside a segment so that you only check the candidate primes. In the prime sieve on GitHub it somehow finds the next multiple of the prime using its lookup tables, which I cannot decipher.

Implementation: https://github.com/kimwalisch/primesieve/wiki/Segmented-sieve-of-Eratosthenes

Here another version that still run fast (between 15 and 20ms). A better implementation of the sieve of Eratosthenes is primesieve. You could also use the sieve of Atkin.

Well, that's fine and all, but factually, its very slow: - https://github.com/kimwalisch/primesieve achieve over a billion prime in the same amount of time

The list of primes at primes.utm.edu contains just 50 million primes. A program like Primesieve by Kim Walisch can compute them in a fraction of a second.

There are approximately 193 million primes under 232 which is the square root of 264, you quickly generate a list of all primes using https://github.com/kimwalisch/primesieve - and then do trial division in paralelle on your input set using rayon.

Primerug is a relatively efficient prime k-tuple finder. The goal is to find large primes that have a particular user selected pattern. You can learn more about prime k-tuples here. Currently its around 2-3 times slower than the C++ equivalent so I am looking for ways to make it faster thus code review is welcome. My goal is to make it as fast as possible and potentially use it to break world records. I am relatively new to Rust so I would appreciate if anyone can point out potentially bad coding practices and/or suggest better alternatives. Thanks!