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theodorenghiem
Post  Post subject: The relationships between Prime number and Fibonacci number  |  Posted: Thu Nov 17, 2016 1:07 am

Joined: Mon Nov 14, 2016 1:06 am
Posts: 3

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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.

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.

Since I am not allowed to attach my result here, I will share the link in my next post

Thinh Nghiem


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Dywyddyr
Post  Post subject: Re: The relationships between Prime number and Fibonacci num  |  Posted: Fri Nov 18, 2016 3:54 am
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Joined: Sat Sep 26, 2015 1:53 pm
Posts: 84

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http://www.scienceforums.com/topic/2957 ... ci-number/
'nuff said.


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Olinguito
Post  Post subject: Re: The relationships between Prime number and Fibonacci num  |  Posted: Sun Jan 01, 2017 2:43 pm
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Joined: Mon Aug 19, 2013 3:56 pm
Posts: 136

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http://math.stackexchange.com/questions ... cci-number
’Nuff said.

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