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Join this group to post and comment. Thinh Nghiem • Dec 21, 2016

# The relationships between Prime number and Fibonacci number

Hello all,
Recently when learning programming language, I accidentally found out an interesting relationship between prime number and Fibonacci number.
That is, a positive integer number can be analyzed as one of three following rules
- the sum of a prime number and a Fibonacci number
For example
16 = 11 (prime) + 5 (Fibonnaci)
61 = 59 (prime) + 2 (Fibonacci)
- or a prime number minus a Fibonacci number
For example
59 = 61 (prime) – 2 (Fibonacci)
83 = 227 (prime) – 144 (Fibonacci)
- or a Fibonacci number minus a prime number
For example
1651=196418 (Fibonacci) – 194767 (Prime)
1759=10946 (Fibonacci) – 9187 (Prime)

By using programming, I have tried to proof my finding up to 10,000,000 (10 million). Among them, there are 96,634 records ~ 0.97% failed due to the limitation of great number processing of my programming language (C and Java)

I put all of my 10,000,000 output records in a microsoft access file Data.accdb, and share it in google drive with link
Data - Google Drive

where I shared full access for everyone. You can come there, open this file and see table data1.
The 4th column in the data file expresses the format of the whole number (Fibonacci-Prime, Prime+Fibonacci, Prime-Fibonacci, or fail)
I welcome for feedbacks from you
Regards,

Thinh Nghiem