November 16th, 2016, 05:17 PM  #1 
Newbie Joined: Aug 2016 From: Auckland Posts: 10 Thanks: 1  The relationships between Prime number and Fibonacci number
Dears, 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 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. So prime number and Fibonacci number are in actual not completely independent with each other. It is perfect if anyone can prove this rule in general case, or explain its reason. I do not think that this is only an accidental effect. You can discuss here or email me at theodorenghiem@yahoo.co.nz Regards, Thinh Nghiem 
November 17th, 2016, 05:11 AM  #2 
Senior Member Joined: Mar 2015 From: England Posts: 184 Thanks: 5 
Woah!

November 17th, 2016, 05:52 PM  #3 
Newbie Joined: Aug 2016 From: Auckland Posts: 10 Thanks: 1 
Thank you Hawki. Somebody else found that this rule may not be right for greater integer. I am checking

November 17th, 2016, 06:16 PM  #4 
Senior Member Joined: Sep 2016 From: USA Posts: 114 Thanks: 45 Math Focus: Dynamical systems, analytic function theory, numerics 
sigh

November 17th, 2016, 07:28 PM  #5  
Math Team Joined: May 2013 From: The Astral plane Posts: 1,570 Thanks: 613 Math Focus: Wibbly wobbly timeywimey stuff.  Quote:
Dan Addendum: It is generally not a good habit, even on this site, to share your email address openly like this. This is not a criticism, just experience.  
November 20th, 2016, 06:51 PM  #6 
Newbie Joined: Aug 2016 From: Auckland Posts: 10 Thanks: 1 
Dear Topsquark, I also sent my finding to professors in university. They confirmed that it is new. However the problem is nobody can be sure if it is matched for greater values or not. A program running is better than doing manually like me. Also they recommend me that this falls into the very hard to prove or disprove case. Anybody have idea how to check more? I am very appreciate to welcome your feedback 
November 29th, 2016, 03:17 AM  #7  
Member Joined: Oct 2016 From: labenon Posts: 33 Thanks: 4  Quote:
 
November 30th, 2016, 01:36 PM  #8  
Newbie Joined: Aug 2016 From: Auckland Posts: 10 Thanks: 1  Quote:
We are sharing our learning to grow up with each other. Do you have coding skills? If yes, it is nice that you can help me in checking with greater number, like 10,000 or 100,000 1,000 is too small to give any conclusion. This is the feedback from other members in community  
November 30th, 2016, 02:02 PM  #9 
Math Team Joined: May 2013 From: The Astral plane Posts: 1,570 Thanks: 613 Math Focus: Wibbly wobbly timeywimey stuff.  
November 30th, 2016, 06:45 PM  #10 
Senior Member Joined: Sep 2007 From: USA Posts: 349 Thanks: 67 Math Focus: Calculus  

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fibonacci, number, prime, relationships 
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