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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