Although there are an infinite amount of prime numbers, the hunt for the largest has in recent years centred on rare Mersenne primes
, named after Marin Mersenne, a 17th-century French monk and mathematician.
i) If [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], then there are infinitely many Mersenne primes
In this paper, using only the immediate part of the generalized Fermat induction, simple definitions, elementary arithmetic congruences, elementary arithmetic calculus, elementary complex analysis, reasoning by reduction to absurd and two elementary properties of a simple Remark, we prove a Theorem which implies the Mersenne primes
conjecture; moreover, our Theorem clearly implies that the Mersenne primes
conjecture that we solved, was only an elementary consequence of the Goldbach conjecture.
mersenne org GIMPS was formed in 1996 and harnesses the power of hundreds of thousands of small home, school and business computers to search for more Mersenne primes
His exploration of elementary and advanced topics in classical number theory covers a range of numbers, including Fermat numbers, Mersenne primes
, powerful numbers, sublime numbers, Wieferich primes, insolite numbers, Sastry numbers, and voracious numbers.
Record numbers Computers at Central Missouri State University identified the 43rd and 44th Mersenne primes
In the conclusion we discuss briefly other approaches to the determination of the physical constants, in particular, a program based on the Mersenne primes
Six of the last seven Mersenne primes
were discovered on Cray Research supercomputers.
are most relevant to number theory and have practical implications for encryption and computational benchmarking.
Abstract In this paper, I present some problems involving Mersenne primes
for Scientia Magna.
This is because prime numbers are the building blocks of our system of integers, and Mersenne primes
give an entry into our understanding of primes in general.
themselves are of interest to computational number theorists, who pursue such basic questions as the distribution of primes among all whole numbers.