There are Infinitely Many Mersenne Primes

London Journal of Research in Science: Natural and Formal
Volume | Issue | Compilation
Authored by FENGSUI LIU , NA
Classification: NA
Keywords: NA
Language: English

From the entire set of natural numbers successively deleting the residue class 0 mod a prime, we retain this prime and possibly delete another one prime retained. Then we invent a recursive sieve method for exponents of Mersenne primes. This is a novel algorithm on sets of natural numbers. The algorithm mechanically yields a sequence of sets of exponents of almost Mersenne primes, which converge to the set of exponents of all Mersenne primes. The corresponding cardinal sequence is strictly increasing. We capture a particular order topological structure of the set of exponents of all Mersenne primes. The existing theory of this structure allows us to prove that the set of exponents of all Mersenne primes is an infinite set. There are Infinitely Many Mersenne Primes

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