Related papers: Some history about Twin Prime Conjecture
This paper examines the concept of a combination rule for belief functions. It is shown that two fairly simple and apparently reasonable assumptions determine Dempster's rule, giving a new justification for it.
This short paper presents an exact formula for counting twin prime pairs less than or equal to x in terms of the classical Smarandache Function. An extension of the formula to count prime pairs (p, p+2n), n > 1, is also given.
It is known that the sum of the reciprocal of integers, $\sum_n (1/n)$, and the sum of the reciprocal of primes, $\sum_n (1/p_n)$, both diverge. Here, we study a series made from primes that sums exactly to 1. We also show this sum is…
In this paper, we give a simple counter example to the famous Hodge conjecture.
We survey the impact of Lieb's influential paper "Proofs of some conjectures on permanents" [J. Math. Mech. 16 1966, 127-134], which introduced the famous permanental dominance conjecture. This conjecture has defied all attacks for over…
We present two related conjectures, arising in work on i-matchings in random r-regular bipartite graphs. The conjectures themselves are easily stated and involve only basic properties of convergent power series. One formulation involves…
In this note, we propose simple summations for primes, which involve two finite nested sums and Bernoulli numbers. The summations can also be expressed in terms of Bernoulli polynomials.
We study the distribution of primes from a topological viewpoint. Certain conjecture is introduced, and we show that it is equivalent to the Riemann Hypothesis.
We present a proof of a combinatorial conjecture from the second author's Ph.D. thesis. The proof relies on binomial and multinomial sums identities. We also discuss the relevance of the conjecture in the context of PAC-Bayesian machine…
In this paper we give an elementary proof of the local sum conjecture in two dimensions. In a remarkable paper [CMN, arXiv:1810.11340], this conjecture has been established in all dimensions using sophisticated, powerful techniques from a…
Discussion of "On the Birnbaum Argument for the Strong Likelihood Principle" by Deborah G. Mayo [arXiv:1302.7021].
This paper presents the best known bounds for a conjecture of Gluck and a conjecture of Navarro.
We present an algorithm analogous to the sieve of Eratosthenes that produces the list of twin primes. Next, we count the number of twin primes resulting from the construction with two different heuristic arguments. The first method is…
We present the proofs of the conjectures mentioned in the paper published in the proceedings of the 2024 AAAI conference [1], and discovered by the decomposition methods presented in the same paper.
A conjecture concerning some pairs of interfering estimates for some integrals is formulated in three equivalent versions. Its importance for the the Paley problem for plurisubharmonic functions and for certain classes of extremal problems…
In this paper we introduce a simple method of searching for the prime pairs in the famous Goldbach Conjecture. The method, which is based on certain integer identities as well as an observation related to the remainder property, enables us…
This paper had been withdrawn because the prime reported effect had not been confirmed in further investigations (see arXiv:0812.4488 [hep-lat]).
This is a typeset version of Alan Turing's declassified Second World War paper \textit{Paper on Statistics of Repetitions}. See the companion paper, \textit{The Applications of Probability to Cryptography}, also available from arXiv at…
In this paper, we prove certain theorems about three consecutive primes.
In this note we put forward a conjecture on the average optimal length for bipartite matching with a finite number of elements where the different lengths are independent one from the others and have an exponential distribution.