Related papers: Extremely symmetric primes
Noncommutative geometry has seen remarkable applications for high energy physics, viz. the geometrical interpretation of the Standard Model. The question whether it also allows for supersymmetric theories has so far not been answered in a…
By establishing an improved level of distribution we study almost primes of the form $f(p,n)$ where $f$ is an irreducible binary form over $\mathbb Z$.
We give a more strong heuristic justification of our conjecture on the excess of the odious primes.
It is known that the polyomino ideal of a simple polyomino is a prime ideal. A new class of nonsimple polyominoes $\Pc$ for which the polyomino ideal $I_{\Pc}$ is a prime ideal will be presented.
Some symmetry problems are formulated and solved. New simple proofs are given for the earlier studied symmetry problems.
The primitive elements of the supersymmetry algebra cohomology as defined in a previous paper are computed for standard supersymmetry algebras in four and five dimensions, for all signatures of the metric and any number of supersymmetries.
We characterize completey (give a necessary and suffcient condition using special neat embeddings)for a relation algebra to belong to the amalgamation, strong amalgamation, and superamalgamation base of the class of representable algebras.…
Dickson conjectured that a set of polynomials will take on infinitely many simultaneous prime values. Later others, such as Hardy and Littlewood, gave estimates for the number of these primes. In this article we look at this conjecture,…
The class of the hypercomplex pseudo-Hermitian manifolds is considered. The flatness of the considered manifolds with the 3 parallel complex structures is proved. Conformal transformations of the metrics are introduced. The conformal…
Using the Rowland idea, we find two infinite sets of generators of primes. We also pose some conjectures concerning twin primes.
Under the prime-tuple hypothesis, the set of signed primes is a sumset.
We provide a framework for using elliptic curves with complex multiplication to determine the primality or compositeness of integers that lie in special sequences, in deterministic quasi-quadratic time. We use this to find large primes,…
We completely describe inhomogeneous properly embedded almost symmetric submanifolds of Euclidean space as certain unions of parallel symmetric submanifolds of the ambient Euclidean space.
In this paper, we present several explicit formulas of the sums and hyper-sums of the powers of the first (n+1)-terms of a general arithmetic sequence in terms of Stirling numbers and generalized Bernoulli polynomials.
Primes in the two complete associative normed division algebras C and H have affinities with structures seen in the standard model of particle physics. On the integers in the two algebras, there are two equivalence relations: a strong one,…
The thesis is devoted to abstract, geometric and symmetric aspects of modern elementary particle theories. A new direction in constructing supersymmetric and superstring models based on consequent and strong consideration and inclusion of…
Let R be a multiplicative hyperring with identity. In this paper, we define the concept of J-prime hyperideals which is a generalization of n-hyperideals and we will show some properties of them. Then we extend the notion of J-prime to…
We show that for every positive integer $k$, there exist $k$ consecutive primes having the property that if any digit of any one of the primes, including any of the infinitely many leading zero digits, is changed, then that prime becomes…
We study odd numbers through a straightforward indexing. We focus in particular on odd prime and composite numbers and their distribution. With a counting argument, we calculate the limit of two sums and compare their convergence rate.
The group gradings on the symmetric composition algebras over arbitrary fields are classified. Applications of this result to gradings on the exceptional simple Lie algebras are considered too.