MAA Writing Awards
A Pascal-Type Triangle Characterizing Twin Primes
Year of Award: 2006
Award: Lester R. Ford
Publication Information: The American Mathematical Monthly, vol. 112, (2005), pp. 673-681
Summary: (From MAA Online) It is a well-known property of Pascal's triangle that the entries of the kth row, without the initial and final entries 1, are all divisible by k if and only if k is prime. This paper presents a triangular array, analogous to Pascal's, that characterizes twin prime pairs in a similar fashion. The proof involves generating function techniques. Connections with orthogonal polynomials, in particular Chebyshev and ultraspherical polynomials, are also discussed.
Kenneth B. Stolarsky received his undergraduate education at Caltech and obtained a Ph.D.from the University of Wisconsin (Madison) in 1968 under the supervision of Marvin I. Knopp. He did one year of postdoctoral work at the Institute for Advanced Study (Princeton) and has been (aside from sabbaticals at the University of Colorado (Boulder) and Yale University (New Haven)) at the University of Illinois (Urbana- Champaign) since then, where he is presently professor of mathematics. His research interests include number theory, extremal problems of geometry, and classical analysis.