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The relationships between Prime number and Fibonacci number


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#1 theodorenghiem

theodorenghiem

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Posted 16 November 2016 - 09:04 PM

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/0BzAetX6K_uyAUXZHQTd5V3ZIa2c/view?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 [/size]format.
 
It is perfect if anyone can help me to develop a program to verify this rule with greater number, like 5,000, 10,000 etc.
 
Mod Edit remove email address
 
Regards,
 
Thinh Nghiem
 
Mod Edit:  Moved from All Other Apps to Programming - Hamluis.

Edited by Al1000, 19 November 2016 - 02:02 AM.
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#2 KingDavidlll

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Posted 04 December 2016 - 04:57 AM

May I ask what this is for?






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