Congruence Properties of Mersenne Primes
  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. 
M. S. Srinath, Garimella Rama Murthy, V. Chandrasekharan
math.NT