We review the arguments in favor of using so called strong primes in the RSA public key cryptosystem There are two types of such arguments those that say that strong primes are needed to protect against factoring attacks and those that say that strong primes are needed to protect against cycling attacks based on repeated encryption We argue that contrary to common belief it is unnecessary to us...

People have a tendency to unconsciously mimic other's actions. This mimicry has been regarded as a prosocial response which increases social affiliation. Previous research on social priming of mimicry demonstrated an assimilative relationship between mimicry and prosociality of the primed construct: prosocial primes elicit stronger mimicry whereas antisocial primes decrease mimicry. The present...

There are a number of subsets of primes with a conjectured density of a constant times x/ log x. These include the primes separated by a fixed even integer, Sophie Germain primes and the so-called “thin primes”, i.e. primes of the form 2q − 1 where q is prime [3]. In order to gain some familiarity with sequences of this density we undertook an investigation of the set of primes of prime order, ...

Let pn denote the nth prime. Goldston, Pintz, and Yıldırım recently proved that lim inf n→∞ (pn+1 − pn) log pn = 0. We give an alternative proof of this result. We also prove some corresponding results for numbers with two prime factors. Let qn denote the nth number that is a product of exactly two distinct primes. We prove that lim inf n→∞ (qn+1 − qn) ≤ 26. If an appropriate generalization of ...

Huber, Shriffrin, Lyle, and Ruys (2001) measured short-term repetition priming effects in perceptual identification with two-alternative forced-choice testing. There was a preference to choose repeated words following passive viewing of primes and a preference against choosing repeated words following active responding to primes. In this present study, we explored conditions of prime processing...

Many contemporary texts include shortcuts, such as cu or phones4u. The aim of this study was to investigate how the meanings of shortcuts are retrieved. A primed lexical decision paradigm was used with shortcuts and the corresponding words as primes. The target word was associatively related to the meaning of the whole prime (cu/see you - goodbye), to a component of the prime (cu/see you - look...

A number of cryptographic standards currently under development call for the use of strong primes in the generation of an RSA key. This paper suggests a fast way of generating random strong primes that also satisfy a number of other cryptographic requirements. The method requires no more time to generate strong primes than it takes to generate random primes.

We study the parallel properties of the Ramanujan primes and a symmetric counterpart, the Labos primes. Further, we study all primes with these properties (generalized Ramanujan and Labos primes) and construct two kinds of sieves for them. Finally, we give a further natural generalization of these constructions and pose some conjectures and open problems.

with C0 = 1. Their appearances occur in a dazzling variety of combinatorial settings where they are used to enumerate all manner of geometric and algebraic objects (see Richard Stanley’s collection [28, Chap. 6]; an online Addendum is continuously updated). Quite a lot is known about the divisibility of the Catalan numbers; see [2, 10]. They are obviously closely related to the middle binomial ...

Modular arithmetic with prime moduli has been crucial in present day cryptography. The primes of Mersenne, Solinas, Crandall and the so called IKE-MODP primes have been widely used in efficient implementations. In this paper we study the density of primes with binary signed representation involving a small number of non-zero ±1-digits, and its repercussion in the generation of those primes.