We improve the unconditional explicit bounds for the error term in the prime counting function ψ(x). In particular, we prove that, for all x > 2, we haveand that, for all log x ≥ 3 000, |ψ(x) − x| < 4.47 • 10 −15 x. This compares to results of Platt & Trudgian (2021) who obtained 4.51 • 10 −13 x. Our approach represents a significant refinement of ideas of Pintz which had been applied by Platt and Trudgian. Improvements are obtained by splitting the zeros into additional regions, carefully estimating all of the consequent terms, and a significant use of computational methods. Results concerning π(x) will appear in a follow up work.

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