Dears,
Recently when learning Java 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 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)

I have tried with the first 1,000 positive integer number from 1 to 1,000 MANUALLY and ensured that all of them matched with one of the two above rules.

I shared my analyzing here in the excel file with 1,000 positive integer number from 1 to 1,000 with the link
https://drive.google.com/file/d/0BzA...ew?usp=sharing

The majority of them belong to the first case are formatted with normal writing. I set the minority cases (the second one where result equals to prime minus Fibonacci) with red and bold format.

It is perfect if anyone can help me to develop a program in JAVA to verify this rule with greater number, like 5,000, 10,000 etc.

You can discuss here or email me at theodorenghiem@yahoo.co.nz

Regards,

Thinh Nghiem