Fibonacci Numbers

Fibonacci Numbers were originally defined by the Italian Mathematician Fibonacci.
He defined Fibonacci Numbers in the thirteenth century in order to model the growth rate of the rabbit population.
The way in which he figure this out was that the number of pairs of rabbits born in a given year is equal to the number of pairs of rabbits born in each of the previous two years.
That is where the equation Fn=Fn-1+Fn-2 came from.
This equation works when you have the base cases F0=0 and F1=1.
Thus F2=1, F3=2, and the series continues {3,5,8,13,21,34, 55, 89, 144,...}
In the long run Fibonacci equation didn't do a very good job of counting rabbits.

First 100 Fibonacci Numbers Factorized

http://www.ee.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibtable.html

n F(n)=factorization

1 : 1 = 1
2 : 1 = 1
3 : 2 = 2 Prime
4 : 3 = 3 Prime
5 : 5 = 5 Prime
6 : 8 = 2^3
7 : 13 = 13 Prime
8 : 21 = 3*7
9 : 34 = 2*17
10 : 55 = 5*11
11 : 89 = 89 Prime
12 : 144 = 2^4*3^2
13 : 233 = 233 Prime
14 : 377 = 13*29
15 : 610 = 2*5*61
16 : 987 = 3*7*47
17 : 1597 = 1597 Prime
18 : 2584 = 2^3*17*19
19 : 4181 = 37*113
20 : 6765 = 3*5*11*41
21 : 10946 = 2*13*421
22 : 17711 = 89*199
23 : 28657 = 28657 Prime
24 : 46368 = 2^5*3^2*7*23
25 : 75025 = 5^2*3001
26 : 121393 = 233*521
27 : 196418 = 2*17*53*109
28 : 317811 = 3*13*29*281
29 : 514229 = 514229 Prime
30 : 832040 = 2^3*5*11*31*61
31 : 1346269 = 557*2417
32 : 2178309 = 3*7*47*2207
33 : 3524578 = 2*89*19801
34 : 5702887 = 1597*3571
35 : 9227465 = 5*13*141961
36 : 14930352 = 2^4*3^3*17*19*107
37 : 24157817 = 73*149*2221
38 : 39088169 = 37*113*9349
39 : 63245986 = 2*233*135721
40 : 102334155 = 3*5*7*11*41*2161
41 : 165580141 = 59369*2789
42 : 267914296 = 2^3*13*29*211*421
43 : 433494437 = 433494437 Prime
44 : 701408733 = 3*43*89*199*307
45 : 1134903170 = 2*5*17*61*109441
46 : 1836311903 = 139*461*28657
47 : 2971215073 = 2971215073 Prime
48 : 4807526976 = 2^6*3^2*7*23*47*1103
49 : 7778742049 = 13*97*6168709
50 : 12586269025 = 5^2*11*101*151*3001
51 : 20365011074 = 2*1597*6376021
52 : 32951280099 = 3*233*521*90481
53 : 53316291173 = 953*55945741
54 : 86267571272 = 2^3*17*19*53*109*5779
55 : 139583862445 = 5*89*661*474541
56 : 225851433717 = 3*7^2*13*29*281*14503
57 : 365435296162 = 2*37*113*797*54833
58 : 591286729879 = 59*514229*19489
59 : 956722026041 = 353*2710260697
60 : 1548008755920 = 2^4*3^2*5*11*31*41*61*2521
61 : 2504730781961 = 555003497*4513
62 : 4052739537881 = 557*3010349*2417
63 : 6557470319842 = 2*13*17*421*35239681
64 : 10610209857723 = 3*7*47*1087*2207*4481
65 : 17167680177565 = 5*233*14736206161
66 : 27777890035288 = 2^3*89*199*19801*9901
67 : 44945570212853 = 269*1429913*116849
68 : 72723460248141 = 3*67*1597*63443*3571
69 : 117669030460994 = 2*137*829*18077*28657
70 : 190392490709135 = 5*11*13*29*71*911*141961
71 : 308061521170129 = 46165371073*6673
72 : 498454011879264 = 2^5*3^3*7*17*19*23*107*103681
73 : 806515533049393 = 86020717*9375829
74 : 1304969544928657 = 73*149*54018521*2221
75 : 2111485077978050 = 2*5^2*61*230686501*3001
76 : 3416454622906707 = 3*37*113*29134601*9349
77 : 5527939700884757 = 13*89*4832521*988681
78 : 8944394323791464 = 2^3*79*233*521*859*135721
79 : 14472334024676221 = 157*92180471494753
80 : 23416728348467685 = 3*5*7*11*41*47*1601*3041*2161
81 : 37889062373143906 = 2*17*53*109*4373*19441*2269
82 : 61305790721611591 = 370248451*59369*2789
83 : 99194853094755497 = 99194853094755497 Prime
84 : 160500643816367088 = 2^4*3^2*13*29*83*211*281*421*1427
85 : 259695496911122585 = 5*1597*3415914041*9521
86 : 420196140727489673 = 433494437*6709*144481
87 : 679891637638612258 = 2*173*3821263937*514229
88 : 1100087778366101931 = 3*7*43*89*199*263*307*881*967
89 : 1779979416004714189 = 1069*1665088321800481
90 : 2880067194370816120 = 2^3*5*11*17*19*31*61*181*541*109441
91 : 4660046610375530309 = 13^2*233*159607993*741469
92 : 7540113804746346429 = 3*139*461*275449*28657*4969
93 : 12200160415121876738 = 2*557*4531100550901*2417
94 : 19740274219868223167 = 6643838879*2971215073
95 : 31940434634990099905 = 5*37*113*761*6773500*29641
96 : 51680708854858323072 = 2^7*3^2*7*23*47*7691103*3167*2207
97 : 83621143489848422977 = 193*389*3084989*361040209
98 : 135301852344706746049 = 13*29*97*599786069*6168709
99 : 218922995834555169026 = 2*17*89*197*18546805133*19801
100: 354224848179261915075 = 3*5^2*11*41*101*151*401*570601*3001