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Goldston, D.A., Pintz, J. and Yildirin, C.Y. (2005) Primes in Tuples I. arXiv:math\0508185v1 [math.NT] 10 Aug.

has been cited by the following article:

• TITLE: Mersenne Numbers, Recursive Generation of Natural Numbers, and Counting the Number of Prime Numbers

  AUTHORS: Ramon Carbó-Dorca

  KEYWORDS: Mersenne Numbers, Recursive Generation of Natural Numbers, Mersenne Natural Number Intervals, Counting the Number of Prime Numbers in Mersenne Natural Intervals, Correlation between Prime Number Set Cardinalities and Mersenne Numbers, Extended Twin Prime Number Conjecture

  JOURNAL NAME: Applied Mathematics, Vol.13 No.6, June 22, 2022

  ABSTRACT: A simple recursive algorithm to generate the set of natural numbers, based on Mersenne numbers: MN = 2N – 1, is used to count the number of prime numbers within the precise Mersenne natural number intervals: [0; MN]. This permits the formulation of an extended twin prime conjecture. Moreover, it is found that the prime numbers subsets contained in Mersenne intervals have cardinalities strongly correlated with the corresponding Mersenne numbers.