Runbo Li

About Me

I am an undergraduate student in the Department of Mathematics at Imperial College London.

Education

B.Sc.
Department of Mathematics, Imperial College London
2026–Present

High School
International Curriculum Center, The High School Affiliated to Renmin University of China
2023–2026

Publications and Preprints

• 35. On the largest prime factor of integers in short intervals IV. Preprint. Download. Cambridge Open Engage
• 34. The number of Piatetski-Shapiro primes in short intervals. Preprint. Download. Cambridge Open Engage
• 33. Primes in arithmetic progressions to large moduli and refinements of Harman's sieve. Preprint. Download. arXiv
• 32. On the largest prime factor of integers in short intervals III. Preprint. Download. arXiv
• 31. Sums of two squares of primes in short intervals. Preprint. Download. Cambridge Open Engage
• 30. Bombieri–Vinogradov Theorem in shorter intervals. Preprint. Download. Preprints
• 29. Primes in almost all short intervals II. Preprint. Download. Cambridge Open Engage
• 28. On Chen's theorem, Goldbach's conjecture and almost prime twins III. Preprint. Download. Cambridge Open Engage
• 27. An average Brun–Titchmarsh theorem and shifted primes with a large prime factor. Preprint. Download. arXiv
• 26. On the weighted AM-GM inequality and refined inequalities between arithmetic functions. Preprint. Download. Preprints
• 25. On the exceptional set in the $abc$ conjecture. Preprint. Download. arXiv
• 24. On the largest prime factor of integers in short intervals II. Preprint. Download. Cambridge Open Engage
• 23. On Chen's theorem, Goldbach's conjecture and almost prime twins II. Mathematical Reports, 28(1–2): 39–61, 2026. Download. Link to the publisher. arXiv
• 22. On the largest prime factor of quadratic polynomials. Preprint. Download. arXiv
• 21. A remark on the distribution of $\sqrt{p}$ modulo one involving primes of special type II. European Journal of Mathematics, 11:85, 2025. Download. Link to the publisher. arXiv
• 20. Largest square divisors of shifted primes. Preprint. Download. arXiv
• 19. On the generalized Dirichlet divisor problem. Preprint. Download. Preprints
• 18. On almost primes in Piatetski-Shapiro sequences. Preprint. Download. arXiv
• 17. Primes in arithmetic progressions to smooth moduli: A minorant version. Preprint. Download. arXiv
• 16. On prime-producing sieves and distribution of $\alpha p - \beta$ mod $1$. Preprint. Download. arXiv
• 15. A note on variants of Buchstab's identity. Bulletin of the Belgian Mathematical Society – Simon Stevin, to appear. Download. arXiv
• 14. The number of primes in short intervals and numerical calculations for Harman's sieve. Preprint. Download. arXiv
• 13. On the Piatetski-Shapiro Prime Number Theorem II. Preprint. Download. Preprints
• 12. On the Piatetski-Shapiro Prime Number Theorem. Preprint. Download. Preprints
• 11. On the largest prime factor of integers in short intervals. Cambridge Journal for Junior Scientists, 3(1): 1–16, 2026. Download. Link to the publisher. Preprints
• 10. Primes in almost all short intervals. Preprint. Download. arXiv
• 9. On the primitive divisors of quadratic polynomials. Preprint. Download. arXiv
• 8. On Chen's theorem, Goldbach's conjecture and almost prime twins. Preprint. Download. arXiv
• 7. On a conjecture involving twin practical numbers. Preprint. Download. Preprints
• 6. A remark on large even integers of the form $p + P_3$. Preprint. Download. arXiv
• 5. Hybrid estimation of single exponential sums, exceptional characters and primes in short intervals. Preprint. Download. arXiv
• 4. Remarks on additive representations of natural numbers. Preprint. Download. arXiv
• 3. A remark on the distribution of $\sqrt{p}$ modulo one involving primes of special type. Hiroshima Mathematical Journal, 56(1): 57–60, 2026. Download. Link to the publisher. arXiv
• 2. On the upper and lower bound orders of almost prime triples. Preprint. Download. arXiv
• 1. On some problems of primes with the floor function. Preprint. Download. arXiv

Manuscripts and Notes

• Note on variable role-reversals. Download
• Waring–Goldbach Problem: One square, four fifth powers and twenty-two seventh powers. Download
• Waring–Goldbach Problem: One square, four fifth powers and fifteen sixth powers. Download
• An average upper bound for a divisibility set. Download
• The explicit expressions for the Buchstab function $\omega(u)$ ($3 \leqslant u < 4$). Download
• Proof of a weighted sieve inequality. Download
• Primes in almost all short intervals III. Download
• A refinement of IMO 2020 Problem 2. Download

Presentations

• 6. Primes in arithmetic progressions to large moduli. The 4th Workshop on Cute Mathematics. 26 July 2026. Download
• 5. Primes in short intervals. Nankai University Additive Number Theory Seminar. Online. 4 December 2025. Download
• 4. On Bertrand's Postulate (in Chinese). Tianjin Nankai High School: Student Research Experience Sharing and Shiing-Shen Chern Class Research Group Launch Meeting. Online. 21 November 2025. Download
• 3. Primes in short intervals. The 3rd Workshop on Cute Mathematics. 21 July 2025. Download
• 2. On the Goldbach's conjecture (in Chinese). 2025 'Haidian $\pi$ Mathematics Festival' Closing Ceremony Research Presentation. The High School Affiliated to Beijing Institute of Technology. 4 July 2025. Download
• 1. On Chen's theorem, Goldbach's conjecture and applications of sieve methods. S.-T. Yau High School Science Award (Mathematics) Global Final Research Report. Tsinghua University. 7 December 2024. Download