thinhnghiem

Mathematics discovery applied in Security and algorithms

Discussion created by thinhnghiem on Dec 28, 2016

Dears,

 

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

 

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 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

 

https://drive.google.com/drive/u/0/folders/0BzAetX6K_uyALUc2ZnkzV2xaTkE

 

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.

 

Regards,

 

Thinh Nghiem

 

 

 

 

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