No_25:1000-digit Fibonacci number

The Fibonacci sequence is defined by the recurrence relation:
Fn = Fn

1 +
Fn

2, where F1 = 1 and F2 = 1.
Hence the first 12 terms will be:
F1 = 1

F2 = 1

F3 = 2

F4 = 3

F5 = 5

F6 = 8

F7 = 13

F8 = 21

F9 = 34

F10 = 55

F11 = 89

F12 = 144
The 12th term, F12, is the first term to contain three digits.
What is the first term in the Fibonacci sequence to contain 1000 digits?
解题思路：

死办法，对每一个求得位数是否是1000位

import datetime
start_time=datetime.datetime.now()
a,b,index=1,1,2
while 1:
a,b,index=a+b,a,index+1
if len(str(a))==1000:
print a
print index
break
end_time=datetime.datetime.now()
print end_time-start_time

结果为：

1070066266382758936764980584457396885083683896632151665013235203375314520604694040621889147582489792657804694888177591957484336466672569959512996030461262748092482186144069433051234774442750273781753087579391666192149259186759553966422837148943113074699503439547001985432609723067290192870526447243726117715821825548491120525013201478612965931381792235559657452039506137551467837543229119602129934048260706175397706847068202895486902666185435124521900369480641357447470911707619766945691070098024393439617474103736912503231365532164773697023167755051595173518460579954919410967778373229665796581646513903488154256310184224190259846088000110186255550245493937113651657039447629584714548523425950428582425306083544435428212611008992863795048006894330309773217834864543113205765659868456288616808718693835297350643986297640660000723562917905207051164077614812491885830945940566688339109350944456576357666151619317753792891661581327159616877487983821820492520348473874384736771934512787029218636250627816

4782

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