Benchmarks

Benchmarks — primitive vs optimized

Both methods are deterministic. The gap is engineering (wheel + Numba + threads), not weaker math on the 64-bit path.

Method	Description
Primitive	Pure Python: odds only up to isqrt(n)
Optimized	is_prime() — 30030-wheel + Numba (+ threads)

Run

NUMBA_NUM_THREADS=$(nproc) python benchmarks/compare_speed.py
NUMBA_NUM_THREADS=$(nproc) python benchmarks/compare_speed.py --include-hard

Sample speedups (indicative, 12 threads)

Case	Speedup (optimized vs primitive)
$10^9+7$ / $10^9+9$	~20×
Mersenne $2^{31}-1$	~17×
12-digit prime	~90–100×
Near $2^{63}$ prime	Optimized ~0.7s; primitive usually skipped (too slow)

Details: benchmarks/README.md