Congruence Properties of Mersenne Primes

2011/12/11 by M. S. Srinath, Srinath, M. S., Garimella Rama Murthy +3
Mathematics · #Advanced Mathematical Theories #Analytic Number Theory Research #FOS: Mathematics #History and Theory of Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1112.2348

openalex publication_date 2011/12/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this research paper, relationship between every Mersenne prime and certain Natural numbers is explored. We begin by proving that every Mersenne prime is of the form 4n + 3,for some integer 'n' and generalize the result to all powers of 2. We also tabulate and show their relationship with other whole numbers up to 10. A number of minor results are also proved. Based on these results, approaches to determine the cardinality of Mersenne primes are discussed.

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