Primes of the Form [nc]

PRIMES OF THE FORM p +Ny

PRIMES IN THE FORM [αp + β]

Recently Jia [4] solved a conjecture of Long and showed that for any irrational number α > 0, there exist infinitely many primes not in the form 2n + 2[αn] + 1, where [x] denotes the largest integer not exceeding x. Subsequently, in [2] Banks and Shparlinski investigated the primes in the sequence {[αn + β] : n ≥ 1}. Motivated by the binary Goldbach conjecture and the twin primes conjecture, we...

The nc-supplemented subgroups of finite groups

A subgroup $H$ is said to be $nc$-supplemented in a group $G$ if there exists a subgroup $Kleq G$ such that $HKlhd G$ and $Hcap K$ is contained in $H_{G}$, the core of $H$ in $G$. We characterize the supersolubility of finite groups $G$ with that every maximal subgroup of the Sylow subgroups is $nc$-supplemented in $G$.

Curves, Cryptography, and Primes of the Form x + yD

An ongoing challenge in cryptography is to find groups in which the discrete log problem “hard”, or computationally infeasible. Such a group can be used as the setting for many cryptographic protocols, from DiffieHellman key exchange to El Gamal encryption. As the group of points of an elliptic curve over a finite field is one of the few known examples, it is important to be able to efficiently...

Search for primes of the form m 2 + 1

The results of the computer hunt for the primes of the form q = m + 1 up to 10 are reported. The number of sign changes of the difference πq(x) − Cq 2 ∫ x 2 du √ u log(u) and the error term for this difference is investigated. The analogs of the Brun’s constant and the Skewes number are calculated. An analog of the B conjecture of Hardy–Littlewood is formulated. It is argued that there is no Ch...