The (recurrence) formula for these Fibonacci numbers is:
The first 100 Fibonacci numbers, completely factorised
If a number has no factors except 1 and itself, then it is called a prime number.The factorizations here are produced by Maple with the command
with(combinat); seq(lprint(n,`:`,fibonacci(n),`=`,ifactor(fibonacci(n))),n=1..100);and then reformatted slightly:
The first 100 Fibonacci numbers n F(n)=factorization 1 : 1 = 1 2 : 1 = 1 3 : 2 = 2 Prime 4 : 3 = 3 Prime 5 : 5 = 5 Prime 6 : 8 = 23 7 : 13 = 13 Prime 8 : 21 = 3 x 7 9 : 34 = 2 x 17 10 : 55 = 5 x 11 11 : 89 = 89 Prime 12 : 144 = 24 x 32 13 : 233 = 233 Prime 14 : 377 = 13 x 29 15 : 610 = 2 x 5 x 61 16 : 987 = 3 x 7 x 47 17 : 1597 = 1597 Prime 18 : 2584 = 23 x 17 x 19 19 : 4181 = 37 x 113 20 : 6765 = 3 x 5 x 11 x 41 21 : 10946 = 2 x 13 x 421 22 : 17711 = 89 x 199 23 : 28657 = 28657 Prime 24 : 46368 = 25 x 32 x 7 x 23 25 : 75025 = 52 x 3001 26 : 121393 = 233 x 521 27 : 196418 = 2 x 17 x 53 x 109 28 : 317811 = 3 x 13 x 29 x 281 29 : 514229 = 514229 Prime 30 : 832040 = 23 x 5 x 11 x 31 x 61 31 : 1346269 = 557 x 2417 32 : 2178309 = 3 x 7 x 47 x 2207 33 : 3524578 = 2 x 89 x 19801 34 : 5702887 = 1597 x 3571 35 : 9227465 = 5 x 13 x 141961 36 : 14930352 = 24 x 33 x 17 x 19 x 107 37 : 24157817 = 73 x 149 x 2221 38 : 39088169 = 37 x 113 x 9349 39 : 63245986 = 2 x 233 x 135721 40 : 102334155 = 3 x 5 x 7 x 11 x 41 x 2161 41 : 165580141 = 59369 x 2789 42 : 267914296 = 23 x 13 x 29 x 211 x 421 43 : 433494437 = 433494437 Prime 44 : 701408733 = 3 x 43 x 89 x 199 x 307 45 : 1134903170 = 2 x 5 x 17 x 61 x 109441 46 : 1836311903 = 139 x 461 x 28657 47 : 2971215073 = 2971215073 Prime 48 : 4807526976 = 26 x 32 x 7 x 23 x 47 x 1103 49 : 7778742049 = 13 x 97 x 6168709 50 : 12586269025 = 52 x 11 x 101 x 151 x 3001 51 : 20365011074 = 2 x 1597 x 6376021 52 : 32951280099 = 3 x 233 x 521 x 90481 53 : 53316291173 = 953 x 55945741 54 : 86267571272 = 23 x 17 x 19 x 53 x 109 x 5779 55 : 139583862445 = 5 x 89 x 661 x 474541 56 : 225851433717 = 3 x 72 x 13 x 29 x 281 x 14503 57 : 365435296162 = 2 x 37 x 113 x 797 x 54833 58 : 591286729879 = 59 x 514229 x 19489 59 : 956722026041 = 353 x 2710260697 60 : 1548008755920 = 24 x 32 x 5 x 11 x 31 x 41 x 61 x 2521 61 : 2504730781961 = 555003497 x 4513 62 : 4052739537881 = 557 x 3010349 x 2417 63 : 6557470319842 = 2 x 13 x 17 x 421 x 35239681 64 : 10610209857723 = 3 x 7 x 47 x 1087 x 2207 x 4481 65 : 17167680177565 = 5 x 233 x 14736206161 66 : 27777890035288 = 23 x 89 x 199 x 19801 x 9901 67 : 44945570212853 = 269 x 1429913 x 116849 68 : 72723460248141 = 3 x 67 x 1597 x 63443 x 3571 69 : 117669030460994 = 2 x 137 x 829 x 18077 x 28657 70 : 190392490709135 = 5 x 11 x 13 x 29 x 71 x 911 x 141961 71 : 308061521170129 = 46165371073 x 6673 72 : 498454011879264 = 25 x 33 x 7 x 17 x 19 x 23 x 107 x 103681 73 : 806515533049393 = 86020717 x 9375829 74 : 1304969544928657 = 73 x 149 x 54018521 x 2221 75 : 2111485077978050 = 2 x 52 x 61 x 230686501 x 3001 76 : 3416454622906707 = 3 x 37 x 113 x 29134601 x 9349 77 : 5527939700884757 = 13 x 89 x 4832521 x 988681 78 : 8944394323791464 = 23 x 79 x 233 x 521 x 859 x 135721 79 : 14472334024676221 = 157 x 92180471494753 80 : 23416728348467685 = 3 x 5 x 7 x 11 x 41 x 47 x 1601 x 3041 x 2161 81 : 37889062373143906 = 2 x 17 x 53 x 109 x 4373 x 19441 x 2269 82 : 61305790721611591 = 370248451 x 59369 x 2789 83 : 99194853094755497 = 99194853094755497 Prime 84 : 160500643816367088 = 24 x 32 x 13 x 29 x 83 x 211 x 281 x 421 x 1427 85 : 259695496911122585 = 5 x 1597 x 3415914041 x 9521 86 : 420196140727489673 = 433494437 x 6709 x 144481 87 : 679891637638612258 = 2 x 173 x 3821263937 x 514229 88 : 1100087778366101931 = 3 x 7 x 43 x 89 x 199 x 263 x 307 x 881 x 967 89 : 1779979416004714189 = 1069 x 1665088321800481 90 : 2880067194370816120 = 23 x 5 x 11 x 17 x 19 x 31 x 61 x 181 x 541 x 109441 91 : 4660046610375530309 = 132 x 233 x 159607993 x 741469 92 : 7540113804746346429 = 3 x 139 x 461 x 275449 x 28657 x 4969 93 : 12200160415121876738 = 2 x 557 x 4531100550901 x 2417 94 : 19740274219868223167 = 6643838879 x 2971215073 95 : 31940434634990099905 = 5 x 37 x 113 x 761 x 67735001 x 29641 96 : 51680708854858323072 = 27 x 32 x 7 x 23 x 47 x 769 x 1103 x 3167 x 2207 97 : 83621143489848422977 = 193 x 389 x 3084989 x 361040209 98 : 135301852344706746049 = 13 x 29 x 97 x 599786069 x 6168709 99 : 218922995834555169026 = 2 x 17 x 89 x 197 x 18546805133 x 19801 100: 354224848179261915075 = 3 x 52 x 11 x 41 x 101 x 151 x 401 x 570601 x 3001[There is a complete list of all Fibonacci numbers and their factors up to the 1000-th Fibonacci and 1000-th Lucas numbers and partial results beyond that on Blair Kelly's site.]
