There are Infinitely Many Fibonacci Primes

There are Infinitely Many Fibonacci Primes

Fengsui Liu

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There are Infinitely Many Fibonacci Primes

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Abstract

We invent a novel algorithm and solve the Fibonacci prime conjecture by an interaction between proof and algorithm. 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, a modulo algorithm on finite sets of natural numbers, for indices of Fibonacci primes. The sifting process mechanically yields a sequence of sets of natural numbers, which converges to the index set of all Fibonacci primes. The corresponding cardinal sequence is strictly increasing. The algorithm reveals a structure of particular order topology of the index set of all Fibonacci primes, then we readily prove that the index set of all Fibonacci primes is an infinite set based on the existing theory of the structure. Some mysteries of primes are hidden in second order arithmetics.

References

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Funding

No external funding was declared for this work.

Conflict of Interest

The authors declare no conflict of interest.

Ethical Approval

No ethics committee approval was required for this article type.

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Not applicable for this article.

How to Cite This Article

Fengsui Liu. 2020. \u201cThere are Infinitely Many Fibonacci Primes\u201d. Global Journal of Science Frontier Research - F: Mathematics & Decision GJSFR-F Volume 20 (GJSFR Volume 20 Issue F5).

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GJSFR Volume 20 Issue F5

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Journal Specifications

Crossref Journal DOI 10.17406/GJSFR

Print ISSN 0975-5896

e-ISSN 2249-4626

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Classification

GJSFR-F Classification MSC 2010: 11N35

11N32

11U09

11Y16

11B37

11B50

Submission ReceivedMay 26, 2020
Peer Review Double Blind
Handling Editor
Accepted June 22, 2020
Published July 3, 2020

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v1.2

Issue date

August 22, 2020

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