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.