BMS1988  Fibonacci factorization
The Mysterious Affair at Byte Court
Hercule was quietly on hollydays (Noël) at Byte Court when Fibonacci and Lucas (welldressed) knocked at his door.
They came in, and the first one said : "Monsieur, can you factorise my first 1001 terms, please?".
Hercule said : "It was useless to come in to ask that, but since you are here, I'll do that very quickly."
Then Lucas said : "It's not a speed challenge, we like Styles too, the shorter your code is, the best your score is."
Output
You have to output 1001 lines, the factorization of the 1001 first terms of the Fibonacci sequence.
See sample for output details.
Example
F(0)= 0 F(1)= 1 F(2)= 1 F(3)= 2 F(4)= 3 F(5)= 5 F(6)= 2^3 F(7)= 13 F(8)= 3 * 7 F(9)= 2 * 17 F(10)= 5 * 11 F(11)= 89 F(12)= 2^4 * 3^2 [...] F(1000)= 3 * 5^3 * 7 * 11 [...]
hide comments
mehmetin:
20200209 16:14:57
Do we need an advanced factorization algorithm like "quadratic sieve" to solve this problem?


Alessandro Amici:
20180311 15:44:17
Yessss!! 360 characters! I wrote this solution three years ago but it was getting TLE by a tiny fraction of a second. Now with new hardware or with the new interpreter it gets AC. I don't even know what it does anymore :D :D :D


knowcode:
20150726 17:39:15
is it okay if giving output of factors F(0) and F(1) are not a part of factorization algorithm?


Alessandro Amici:
20150111 15:28:19
Francky, this is one of the problems I enjoyed the most in SPOJ on so many levels, second only to SIZECON. Compliments and thank you!


Alessandro Amici:
20150103 13:08:44
Got it :) Now let's golf.


Alessandro Amici:
20150103 11:24:00
@Francky great problem! Can you please check my submissions 13335447 and 13335452? I can get AC in the second one by putting a lot of precomputed values, but I don't understand how the first one is getting NZEC. In order not to give up any spoiler I put my specific questions in comments inside the submissions. Thanks!


ruslion:
20130130 03:09:53
if I factorize every sequence member as


Francky:
20130123 15:57:37
@pinco : we can't neither read psetter files, it would too easy to solve any problem. The problem code is BMS1988, it's not for nothing !!! stdin can't be anything else than that it is to make a good challenge. 

Francky:
20130122 10:02:29
Spoil : within a spoj submission, it's impossible to download the solution from Internet at http://mersennus.net/fibonacci/, but Hercule is a stdin detective... Everybody can solve the task without being a detective, and it's recommended to do so at first attempts. Enjoy ;)


(Tjandra Satria Gunawan)(æ›¾æ¯…æ˜†):
20130121 20:17:04
Uwah... only ~760 bytes to solve this problem :O 
Added by:  Francky 
Date:  20130120 
Time limit:  1s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ASM64 
Resource:  Own problem 