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Most integers are not a sum of two palindromes

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Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
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Dmitrii Zakharov

Number Theory · Submitted 16 Feb 2024

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim For $g \ge 2$, we show that the number of positive integers at most $X$ which can be written as sum of two base $g$ palindromes is at most $\frac{X}{\log^c X}$.

how it is stated · asserted 1.00 read the record →

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arXiv ID2402.10808 (version 1)
Pith IDLYJ7WWA7, Pith's permanent record of this paper and its review
CitationDmitrii Zakharov. "Most integers are not a sum of two palindromes." arXiv:2402.10808 (2024). https://pith.science/paper/LYJ7WWA7
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,273 input tokens.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.26 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.98 · compares with prior results 0.19 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

For $g \ge 2$, we show that the number of positive integers at most $X$ which can be written as sum of two base $g$ palindromes is at most $\frac{X}{\log^c X}$. This answers a question of Baxter, Cilleruelo and Luca.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 For $g \ge 2$, we show that the number of positive integers at most $X$ which can be written as sum of two base $g$ palindromes is at most $\frac{X}{\log^c X}$. result 0.99 0.96 0.95 asserted 1.00
s1 This answers a question of Baxter, Cilleruelo and Luca. interpretation 0.53 0.29 0.04 asserted 0.92

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

For $g \ge 2$, we show that the number of positive integers at most $X$ which can be written as sum of two base $g$ palindromes is at most $\frac{X}{\log^c X}$. This answers a question of Baxter, Cilleruelo and Luca.

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