There are Infinitely Many Fibonacci Primes

Fengsui Liu

There are Infinitely Many Fibonacci Primes

Fengsui Liu *

Contact

There are Infinitely Many Fibonacci Primes

Article Fingerprint

ReserarchID

0F8KE

There are Infinitely Many Fibonacci Primes Banner

AI TAKEAWAY

Connecting with the Eternal Ground

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

17 Cites in Article

Reference Format

Chris Caldwell The Top Twenty: Fibonacci Number from the Prime Pages.
K Kuratowsky,A Mostowsky (1976). Introduction to Descriptive Set Theory.
L Kudryavtsev Encyclopaedia of Mathematics.
M Jesper,Ller (2005). General Topology web.
Marc Renault The Fibonacci Sequence Modulo m.
J Munkres (2000). Topology.
Fengsui Liu (2011). On the Sophie Germain Prime Conjecture.
Fengsui Liu (2018). Which polynomials represent infinitely many primes.
Fengsui Liu (2018). There Are Infinitely Many Mersnne Composite Numbers with Prime Exponents.
Fengsui Liu (2018). There Are Infinitely Many Mersnne Composite Numbers with Prime Exponents.
Franz Lemmermeyer (2000). Reciprocity Laws.
J Littlewood (1953). Pathology and Identity. By R. Littlewood. (Pp. 322; illustrated; £40.00.) Cambridge University Press: Cambridge. 1993..
M Sautoy (2003). The Music of the Primes.
S Ross (1988). A First Course in Probability.
Steven Vajda Fibonacci and Lucas Numbers, and the Golden Section: Theory and Applications.
Paulo Ribenboim (2000). My Numbers, My Friends.
Vladimir Drobot (1998). On Primes in the Fibonacci Sequence.

Download References

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.

Data Availability

Not applicable for this article.

How to Cite This Article

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

More Citation Formats

Select Citation Style:

Download Citation

GJSFR Volume 20 Issue F5

Explore Journals Explore Volume Read This Issue

Journal Specifications

Crossref Journal DOI 10.17406/GJSFR

Print ISSN 0975-5896

e-ISSN 2249-4626

Keywords

Not Found

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

Version of record

v1.2

Issue date

August 22, 2020

Language

English

Experiance in AR

Explore published articles in an immersive Augmented Reality environment. Our platform converts research papers into interactive 3D books, allowing readers to view and interact with content using AR and VR compatible devices.

View in VR

Read in 3D

Your published article is automatically converted into a realistic 3D book. Flip through pages and read research papers in a more engaging and interactive format.

View in 3D

Article Matrices

Total Views: 859

Total Downloads: 52

All Trends