Gaps entre primos indexados em 2n

Abstract

Although infinite series and sequences of real numbers form an introductory topic in Calculus and Analysis, they have wide use in Mathematics and Physics due to its aplications. In this work, our goal is to study the behaviour of the subsequence {p2n} of the sequence {pn} of prime numbers through the theory of series of positive numbers. Our approach uses a combination between the important Kummer’s Test which furnishes necessary and sufficient conditions for the convergence or divergence of a positive terms series and the remarkable Cauchy condensation test which characterizes the convergence or divergence of decreasing positive terms series.