IntelliPaper
Abstract
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 infnite set .
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Conflict of Interest
The authors declare no conflict of interest.
Ethical Approval
Not applicable
Data Availability
The datasets used in this study are openly available at [repository link] and the source code is available on GitHub at [GitHub link].
Funding
This work did not receive any external funding.
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