Les primes relascopiques

Small Gaps between Primes or Almost Primes

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 ...

Catalan Numbers, Primes and Twin Primes

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 ...

Les maladies causées par les anaérobies pathogènes sporulés chez les animaux domestiques

Recognizing Primes

This is a survey article on primality testing and general methods for recognizing primes. We also look at methods for generating random primes since this is valuable in cryptographic methods such as the RSA cipher. Mathematics Subject Classification: Primary: 11A41; Secondary: 11A51

Les Rotations Et Les Quaternions

La construction du corps non commutatif H de quaternions est une variante plus compliquée de la construction du corps commutatif C de nombres complexes. Donc on commence en rappelant la construction de C à partir de R. Les nombres complexes s’écrivent a+ bi avec a, b ∈ R. Donc C est un espace vectoriel sur R de dimension 2 avec base {1, i}. La loi d’addition de C est celle que C possède en tant...