A formally verified proof of the prime number theorem
Jeremy Avigad, Kevin Donnelly, David Gray, Paul Raff
Abstract
The prime number theorem, established by Hadamard and de la Vall'ee Poussin independently in 1896, asserts that the density of primes in the positive integers is asymptotic to 1 / ln x. Whereas their proofs made serious use of the methods of complex analysis, elementary proofs were provided by Selberg and Erd"os in 1948. We describe a formally verified version of Selberg's proof, obtained using the Isabelle proof assistant.
Create a lesson
Related papers
OSGR: Observation-Support Graph Reasoning for Earth Observation Question Answering
Dazhou Yu, Zerong Wang, Riyang Bao et al.
Bidirectional Centered Score Matching for Discrete Diffusion Distillation
Peng Tu, Baoyou Chen, Haoyuan Xia et al.
Harness-S: Learning from Sibling Harnesses for Generalizable Agent Training
Kangning Zhang, Wenxiang Jiao, Bowen Fang et al.
Reliability Stress Testing of RAG Retrieval under Query-Relevant Corpus Poisoning
Janet Sung, Kainan Zhou, Gangzhen Qian et al.
Neologism Inoculation Prompting
David Demitri Africa, Cameron Holmes
AceAction-5M: Hierarchical Goals for Generalist Action Learning Across 3D Game Worlds
Kailing Li, Ruoxuan Zhang, Zheyuan Zhou et al.