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fix: align Dusart lemma_5_10a with 1-indexed prime numbering#1512

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fix: align Dusart lemma_5_10a with 1-indexed prime numbering#1512
Chessing234 wants to merge 1 commit into
AlexKontorovich:mainfrom
Chessing234:fix/dusart-lemma-5-10a-indexing

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Fixes #1129

Bug

lemma_5_10a used nth_prime' k with paper index k ≥ 4, but nth_prime' is 0-indexed. At k = 4 this claims 11 ≤ 4 log 11, which is false.

Root cause

Dusart's p_k is 1-indexed; the Lean formalization used the paper index directly as the nth_prime' argument.

Why this fix is correct

The k-th prime in the paper is nth_prime' (k - 1). For k = 4 this gives p_4 = 7 and 7 ≤ 4 log 7, matching Lemma 5.10.

Test plan

  • lake build PrimeNumberTheoremAnd.IEANTN.Dusart

Made with Cursor

Co-authored-by: Cursor <cursoragent@cursor.com>
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[MISFORMALISATION]: lemma_5_10a statement is false for k=4

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