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− | {{Types of Primes Infobox|title=Fibonacci Primes|discov=Leonardo Fibonacci|amount=Unknown|expression=A prime which is also a term in the Fibonacci sequence|1st=[[2]], [[3]], [[5]], [[13]], [[89]], [[233]], [[1597]], [[28657]], [[514229]], [[433494437]], [[2971215073]], [[99194853094755497]], [[1066340417491710595814572169]], [[19134702400093278081449423917]], |
+ | {{Types of Primes Infobox|title=Fibonacci Primes|discov=Leonardo Fibonacci|amount=Unknown|expression=A prime which is also a term in the Fibonacci sequence|1st=[[2]], [[3]], [[5]], [[13]], [[89]], [[233]], [[1597]], [[28657]], [[514229]], [[433494437]], [[2971215073]], [[99194853094755497]], [[1066340417491710595814572169]], [[19134702400093278081449423917]], }} |
Fibonacci Primes are prime numbers that are also of the Fibonacci Sequence. The Fibonacci Sequence is formed by adding the two preceding numbers to form a third, for example 1, 1, 2, 3, 5, 8, 13... |
Fibonacci Primes are prime numbers that are also of the Fibonacci Sequence. The Fibonacci Sequence is formed by adding the two preceding numbers to form a third, for example 1, 1, 2, 3, 5, 8, 13... |
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Revision as of 04:39, 11 December 2016
Fibonacci Primes
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Basic Info
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Discovered by | Leonardo Fibonacci |
Number of | Unknown |
Description | A prime which is also a term in the Fibonacci sequence |
First Few | 2, 3, 5, 13, 89, 233, 1597, 28657, 514229, 433494437, 2971215073, 99194853094755497, 1066340417491710595814572169, 19134702400093278081449423917, |
Fibonacci Primes are prime numbers that are also of the Fibonacci Sequence. The Fibonacci Sequence is formed by adding the two preceding numbers to form a third, for example 1, 1, 2, 3, 5, 8, 13...
In the Fibonacci series, any number which appears as a position n is the sequence divides the number at position 2n, 3n, 4n, etc. in the sequence. For example, the fourth Fibonacci number, F4 = 3, divides F8 (21), F12 (144) and F16 (987), and all further Fibonacci numbers at a position that is a multiple of 4. As a result, a Fibonacci Prime can only appear at a prime valued position in the Fibonacci series, with the exception of F4 = 3 (which is a multiple of F2 = 1). The converse is not true, however, as the 19th Fibonacci number (4181), for example, is a composite number.