A Pascal-Type Triangle Characterizing Twin Primes

摘要: 1. INTRODUCTION. Two of the most ubiquitous objects in mathematics are sequence prime numbers and binomial coefficients (and thus Pascal’s triangle). A connection between two is given by a well-known characterization numbers: Consider entries kth row triangle, without initial final entries. They all divisible k if only prime. It purpose this article to present triangular array similar triangle prove corresponding criterion for twin pairs .A further goal place context some classical orthogonal polynomials relate it recent work John D’Angelo. To begin, sake completeness, we short proof Pascal criterion. First suppose that = p Then see j p! j! ( − j)! (1 ≤ 1)