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11-17-2016, 03:08 AM #1
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- Nov 2016
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The relationships between Prime number and Fibonacci number
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
16 = 11 (prime) + 5 (Fibonnaci)
61 = 59 (prime) + 2 (Fibonacci)
- or a prime number minus a Fibonacci number
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
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 email@example.com