Prime Sieve Visualizer

Explore the inclusion, exclusion principle, the 2^k−1 error bound, and the Hardy, Littlewood twin-prime conjecture, all in one sieve.

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Inclusion, Exclusion Formula

Actual Count vs Hardy, Littlewood Prediction

The Hardy, Littlewood conjecture estimates the count of twin primes below n as C₂ · n / (ln n)² where C₂ ≈ 1.32032. The green line shows the real count of numbers surviving your selected sieving primes; the orange line shows the theoretical twin-prime prediction. As n grows, watch how the prediction tracks the actual count.