Author

Artur Samojluk

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Preprint Jun 2026

An Efficient Algorithm for Estimating Prime Counts

We develop the Samojluk--Siemaszko (S--S) estimator for the prime-counting function $\pi(x)$ using a non-uniform partition generated by generalized triangular numbers. A cold-start evaluation uses $\big O(\sqrt{x})$ local terms, whereas consecutive partition nodes can be processed with amortized $\big O(1)$ update cost...

Artur Samojluk, A. Siemaszko · 0 citations