Related papers: On Excess of the Odious Primes

The main results extend to sums over primes in a short interval earlier estimates by the author for "long" Weyl sums over primes.

We verify the Hardy-Littlewood conjecture on primes in quadratic progressions on average. The results in the present paper significantly improve those of a previous paper of the authors(arXiv:math.NT/0605563).

We present a new topological proof of the infinitude of prime numbers with a new topology. Furthermore, in this topology, we characterize the infinitude of any non-empty subset of prime numbers.

We speculate on the distribution of primes in exponentially growing, linear recurrence sequences $(u_n)_{n\geq 0}$ in the integers. By tweaking a heuristic which is successfully used to predict the number of prime values of polynomials, we…

We introduce extremely symmetric primes and provide some elementary properties of these.

The predicate complementary to the well-known Godel's provability predicate is defined. From its recursiveness new consequences concerning the incompleteness argumentation are drawn and extended to new results of consistency, completeness…

We present a new, elementary, dynamical proof of the prime number theorem.

Let $\mathcal{P}$ denote the set of all primes. In 1950, P. Erd\H{o}s conjectured that if $c$ is an arbitrarily given constant, $x$ is sufficiently large and $a_1,\dots , a_t$ are positive integers with $a_1<a_2<\cdot\cdot\cdot<a_t\leqslant…

On the assumption of the Riemann hypothesis, we give explicit upper bounds on the difference between consecutive prime numbers.

The twin prime conjecture asserts that there are infinitely many pairs of primes that differ by two. While recent advances have improved our understanding of bounded prime gaps, the conjecture remains unresolved. This paper refines the…

In this article we present method of solving some additive problems with primes. The method may be employed to the Goldbach-Euler conjecture and the twin primes conjecture. The presented method also makes it possible to obtain some…

We present a proof system that extends action logic by omega iteration, which is viewed as infinitary multiplicative conjunction. We prove cut admissibility and establish complexity bounds for the provability predicate.

Let $p$ be a prime. For $p=2$, the fields of values of the complex irreducible characters of finite groups whose degrees are not divisible by $p$ have been classified; for odd primes $p$, a conjectural classification has been proposed. In…

An technically interesting proof of a known theorem.

We introduce a heuristic prediction for the distribution of the isomorphism class of the Galois group of the maximal pro-p extension of Q unramified outside a "random" set of primes. This is guided by reasoning similar to that governing the…

In this article, we prove a weighted version of Saitoh's conjecture. As an application, we prove a weighted version of Saitoh's conjecture for higher derivatives.

We define a reasonably well-behaved class of ultraimaginaries, i.e.\ classes modulo invariant equivalence relations, called {\em tame}, and establish some basic simplicity-theoretic facts. We also show feeble elimination of supersimple…

We provide a proof of a variant of the Landau-Siegel Zeros conjecture.

In this note we prove an inequality involving primes and the product of consecutive primes.

In this paper, we formulate and prove several variants of the Erd\H{o}s-Tur\'{a}n additive bases conjecture.