Related papers: Some history about Twin Prime Conjecture
We give a more comrehensive treatment of Chen's double sieve and improve related constants in Goldbach's conjecture and the twin prime problem.
Presented here are over one hundred conjectures ranging from easy to difficult, from many mathematical fields. I also summarize briefly methods and tools that have led to this collection.
In this paper, we consider pairs of a prime and a prime power with a fixed difference. We prove an average result on the distribution of such pairs. This is a partial improvement of the result of Bauer (1998).
In this short note we present a family of counterexamples to the King's conjecture.
This is a survey on Sarnak's Conjecture
In this article, we derive a congruence property of particular sum rules involving prime numbers. The resulting expression involves Bernoulli numbers and polynomials, for which we obtain, as a consequence, a general congruence relation as…
In this paper, a simple explanation for the Goldbach Conjecture is given. We have shown that the probability of violating the conjecture not only for the prime numbers, but also for any subset of natural numbers whose distribution is…
We survey some past conditional results on the distribution of large differences between consecutive primes and examine how the Hardy-Littlewood prime k-tuples conjecture can be applied to this question.
In this note we show that the known relation between double groupoids and matched pairs of groups may be extended, or seems to extend, to the triple case. The references give some other occurrences of double groupoids.
This paper presents some considerations about the Goldbach's conjecture (GC). The work is based on elementary results of the number theory and it provides a constructive method that permits, given an even integer, to find at least a pair of…
This paper has been withdrawn by the authors due to the fact that the conjecture has indeed already long been established.
This is a detailed survey on the QWEP conjecture and Connes' embedding problem. Most of contents are taken from Kirchberg's paper [Invent. Math. 112 (1993)].
Selected examples of possible origins of power-law distributions are presented.
This note considers reciprocal of primes in binary representation and shows that the conjecture that 0s exceed 1s in most cases continues to hold for primes less one million. The conjecture has also been tested for ternary representation…
Several examples of generalized number systems are constructed to compare various conditions occurring in the literature for the prime number theorem in the context of Beurling generalized primes.
Following an idea of Rowland we give a conjectural way to generate increasing sequences of primes using algorithms involving the gcd. These algorithms seem not so useless for searching primes since it appears we found sometime primes much…
The contents are divided into two papers "The Monotone Cumulants" (arXiv:0907.4896) and "Conditionally monotone independence" (arXiv:0907.5473).
We resolve the function field analogue of the conjecture concerning distribution of twin primes in arithmetic progression.
A family of congruences interpolating between those of Wilson and Giuga is constructed. Several elementary results are established, in order to present a possible approach to establishing Giuga's conjecture.
This article covers three topics. (1) It establishes links between the density of certain subsets of the set of primes and related subsets of the set of natural numbers. (2) It extends previous results on a conjecture of Bruinier and Kohnen…