Fibonacci Numbers And Prime Factorization

Fibonacci   N umbers   a nd   P rime   F actorization  

 

1.     T he   s tart   o f   t he   F ibonacci   s equence   i s   l isted   i n   t he   f irst   r ow   o f   t he   t able   b elow.            

            W hat   r ule   i s   u sed   t o   d etermine   t he   n ext   n umber?  

 

 

 

2.     I n   t he   s econd   r ow   o f   t he   t able   f ill   i n   t he   m issing   p rime   f actorization.  

 

Fibon.  

1  

1  

2   3   5   8  

13   21  

34  

55  

89   144  

 

#

Prime  

n/a   n/a  

2   3   5    

13    

 

 

89    

factors  

 

 

 

3.     W hy   i s   n /a   w ritten   u nder   t he   o nes   i n   t he   s equence?  

 

4.     L ook   a t   a ny   t wo   c onsecutive   F ibonacci   n umbers.    

            W hat   c an   y ou   n otice   a bout   t heir   p rime   f actors?  

 

 

 

 

5.   T he   n ext   F ibonacci   N umbers   i n   t he   s equence   a re   l isted   b elow.     P ick   a ny   t wo   c onsecutive  

Fibonacci   n umbers   a nd   s ee   i f   t he   p attern   h olds.     I f   i t   d oes   n ot,   m ake   a nother   c onjecture.    

(it   m ay   b e   h elpful   t o   k now   t hat   :     2 9,   3 7,   4 1,   4 7,   6 1,   1 13,   2 33,   a nd   1 597are   p rime   n umbers)  

 

                              .   .   .   2 33,   3 77,   6 10,   9 87,   1 597,   2 584,   4 181,   6 765,     .   .   .  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Fibonacci   P rime   M ystery:     I t   h as   b een   p roven   t hat   t here   i s   o nly   o ne   s quare   n umber   a nd   o nly  

one   c ubed   n umber,   b ut   i s   t here   a   g reatest   P rime   F ibonacci   n umber?     N o   o ne   k nows.     T he  

largest   k nown   F ibonacci   p rime   w as   f ound   i n   2 015.     I t   i s   t he   8 1,839

    n umber   i n   t he   s equence  

th

and   h as   1 7,103   d igits.