Inside Primesieve: The Ultimate C/C++ Prime Number Library

Primesieve is a highly optimized, open-source C/C++ library and command-line program recognized as one of the fastest prime number generators in the world. It is capable of generating primes and prime -tuplets up to 2642 to the 64th power

at blistering speeds, processing billions of numbers per second by maximizing hardware efficiency. Core Algorithm & Time Complexity

Instead of using complex or exotic math, primesieve achieves its legendary speed by taking a traditional algorithm and optimizing it to the absolute limit of modern CPU architectures.

Segmented Sieve of Eratosthenes: The traditional Sieve of Eratosthenes requires a massive amount of memory to hold the entire range of numbers. primesieve breaks the desired range into small segments. It sieves one segment at a time, bringing memory consumption down from to a tiny fraction.

Algorithmic Complexity: It operates with a runtime complexity of operations while utilizing only bits of memory. Key Optimization Techniques

Cache-Conscious Design: A standard sieve constantly encounters CPU cache misses when accessing memory. primesieve automatically detects your CPU’s L1 and L2 cache sizes. It explicitly sizes its sieve segments so that the data structures fit entirely within the fastest CPU cache levels, enabling lightning-fast memory access.

Wheel Factorization: To prevent wasting cycles, primesieve uses modulo 30 and modulo 210 wheel factorization. This allows the algorithm to automatically skip testing numbers that are multiples of small primes like 2, 3, 5, and 7, eliminating up to 77% of the elements before sieving even starts.

Tomás Oliveira e Silva’s Bucket Sieve: When generating primes larger than 2322 to the 32nd power

, storing all sieving primes becomes a memory bottleneck. primesieve implements a bucket list algorithm that groups sieving primes into specific memory buckets associated with upcoming segments. This prevents the program from scanning unnecessary primes during a segment check.

Native Multi-Threading: The architecture is multi-threaded by default. It distributes separate intervals of the target range across all available CPU cores via std::async, scaling its speed almost linearly with your hardware. Practical Performance To put its efficiency into perspective: kimwalisch/primesieve: Fast prime number generator – GitHub