Recently when learning programming language, I accidentally found out an interesting relationship between prime number and Fibonacci number. There are 3 rules at all for them.
That is, a positive integer number can be analyzed as either:
- the sum of a prime number and a Fibonacci number
16 = 11 (prime) + 5 (Fibonnaci)
61 = 59 (prime) + 2 (Fibonacci)
- or a prime number minus a Fibonacci number
59 = 61 (prime) – 2 (Fibonacci)
83 = 227 (prime) – 144 (Fibonacci)
- or a Fibonacci number minus a prime number
1651=196418 (Fibonacci) – 194767 (Prime)
1759=10946 (Fibonacci) – 9187 (Prime)
By using programming in C and Java, I have tried to prove 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, share it with full access in google drive with link
There we can 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 post my finding here so that researcher can verify if it can be applied into development of encryption, security, or any technical aspect.
All feedbacks are welcomed.