Let $\alpha>1$ be irrational and of finite type, $\beta\in\mathbb{R}$. In this paper, it is proved that for $R\geqslant13$ any fixed $c\in(1,c_R)$, there exist infinitely many primes in the intersection Beatty sequence $\mathcal{B}_{\alpha,\beta}$ $\lfloor n^c\rfloor$, where $c_R$ an explicit constant depending on $R$ herein, $n$ a natural number with at most prime factors, counted multiplicity.

Let $E$ be an elliptic curve over $Bbb{Q}$ with the given Weierstrass equation $ y^2=x^3+ax+b$. If $D$ is a squarefree integer, then let $E^{(D)}$ denote the $D$-quadratic twist of $E$ that is given by $E^{(D)}: y^2=x^3+aD^2x+bD^3$. Let $E^{(D)}(Bbb{Q})$ be the group of $Bbb{Q}$-rational points of $E^{(D)}$. It is conjectured by J. Silverman that there are infinitely many primes $p$ for which $...

let $e$ be an elliptic curve over $bbb{q}$ with the given weierstrass equation $ y^2=x^3+ax+b$. if $d$ is a squarefree integer, then let $e^{(d)}$ denote the $d$-quadratic twist of $e$ that is given by $e^{(d)}: y^2=x^3+ad^2x+bd^3$. let $e^{(d)}(bbb{q})$ be the group of $bbb{q}$-rational points of $e^{(d)}$. it is conjectured by j. silverman that there are infinitely many primes $p$ for which $...

Let $G$ be a group and $pi(G)$ be the set of primes $p$ such that $G$ contains an element of order $p$. Let $nse(G)$ be the set of the number of elements of the same order in $G$. In this paper, we prove that the simple group $L_2(p^2)$ is uniquely determined by $nse(L_2(p^2))$, where $pin{11,13}$‎.‎

Effects of morphologically related primes were examined in two masked prime experiments. Responses to both free root and derived suffixed word targets were facilitated when primes were derived suffixed words containing the target's root, and this facilitation effect showed a time course similar to that for the facilitation effect of repetition primes (though systematically smaller in magnitude)...

Germain Grisez, associate professor of philosophy at Georgetown, married and father of four, has published an extraordinarily important philosophical study of the moral evil of contraception. It is not the topics treated that would distinguish the study from others on the same subject. In the Introduction, Grisez criticizes the increasingly popular attitude among Catholics that appealing to exp...

The transference principle of Green and Tao enabled various authors to transfer Szemer\'edi's theorem on long arithmetic progressions in dense sets sparse integers, mostly primes. In this paper, we provide a which applies general affine-linear configurations finite complexity. We illustrate the broad applicability our with case almost twin primes, by mean either Chen primes or "bounded gap prim...