Runbo Li

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20232026

most citedPrimes in almost all short intervals

2 citations · 4 across the 17 of their papers we have counts for

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math.NT2024★ 2 cited

Primes in almost all short intervals

Runbo Li

The author sharpens a result of Jia (1996), showing that the interval $[n, n + n^{\frac{1}{21.5} + ε}]$ contains prime numbers for almost all $n$ . Watt's mean value bound, a…

math.NT2024

On the largest prime factor of quadratic polynomials

Runbo Li

Let $x$ denote a sufficiently large integer. We show that the recent result of Grimmelt and Merikoski actually yields the largest prime factor of $n^{2} + 1$ is greater than $x^{1.317…

math.NT2024

On Chen's theorem, Goldbach's conjecture and almost prime twins II

Runbo Li

Let $N$ denote a sufficiently large even integer and $x$ denote a sufficiently large integer, we define $D_{1, 2} (N)$ as the number of primes $p$ that such that $N - p$ has at most…

math.GM2024

A remark on large even integers of the form $p + P_{3}$

Runbo Li

Let $N$ denotes a sufficiently large even integer, $p$ denotes a prime and $P_{r}$ denotes an integer with at most $r$ prime factors. In this paper, we study the solutions of the e…

math.NT2024

Hybrid estimation of single exponential sums, exceptional characters and primes in short intervals

Runbo Li

We provide a new hybrid estimation of single exponential sums, combining Van der Corput, Huxley and Bourgain's result. We also focus on primes in short intervals $(x - x^{α}, x]$ under…

math.NT2024

A remark on the distribution of $p$ modulo one involving primes of special type II

Runbo Li

Let $P_{r}$ denote an integer with at most $r$ prime factors counted with multiplicity. In this paper we prove that for some $λ < \frac{1}{12}$ , the inequality ${p} < p^{- λ}$ …

math.NT2024

On the upper and lower bound orders of almost prime triples

Runbo Li

A Hardy-Littlewood triple is a 3-tuple of integers with the form $(n, n + 2, n + 6)$ . In this paper, we study Hardy-Littlewood triples of the form $(p, P_{a}, P_{b})$ and improve the u…

Primes in almost all short intervals

On the largest prime factor of quadratic polynomials

On Chen's theorem, Goldbach's conjecture and almost prime twins II

A remark on large even integers of the form p+P3​

Hybrid estimation of single exponential sums, exceptional characters and primes in short intervals

A remark on the distribution of p​ modulo one involving primes of special type II

On the upper and lower bound orders of almost prime triples

A remark on large even integers of the form $p + P_{3}$

A remark on the distribution of $p$ modulo one involving primes of special type II