Following footsteps of Gauss, Euler, Riemann, Hurwitz, Smith, Hardy, Littlewood, Hedlund, Khinchin and Chebyshev, we visit some topics in elementary number theory. For matrices defined by Gaussian primes we observe a circular spectral law for the eigenvalues. We experiment then with various Goldbach conjectures for Gaussian primes, Eisenstein primes, Hurwitz primes or Octavian primes. These con...

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 ...

transfusion of blood products from an infected person with aids, is meant to infect recipient. blood products such as whole blood, red blood cells, platelets, plasma, frozen blood precipitate, factor viii, factor ix, can be infected with hiv. transmissions from blood factors can be seen in plasma from thousands of donors that were collected in a container and were used to treat hemophilia. bloo...

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.

Associative priming effects can be obtained with masked nonword primes or with masked pseudohomophone primes (e.g., judpe-COURT, tode-FROG), but not with visible primes. The usual explanation is that when the prime is visible, these stimuli no longer activate the semantic representations of their base words. Given the important role of transposed-letter stimuli (e.g., jugde) in visual word reco...

Listeners require context to understand the highly reduced words that occur in casual speech. The present study reports four auditory lexical decision experiments in which the role of semantic context in the comprehension of reduced versus unreduced speech was investigated. Experiments 1 and 2 showed semantic priming for combinations of unreduced, but not reduced, primes and low-frequency targe...

A recent study of the affect misattribution procedure (AMP) found that participants who retrospectively reported that they intentionally rated the primes showed larger effect sizes and higher reliability. The study concluded that the AMP's validity depends on intentionally rating the primes. We evaluated this conclusion in three experiments. First, larger effect sizes and higher reliability wer...