On Thursday, January 30, 2014 7:54:45 PM UTC+1, Jean-Pierre Flori wrote:

> On Thursday, January 30, 2014 7:35:46 PM UTC+1, Ondřej Čertík wrote:
>>
>> Hi, 
>>
>> What is the state of the art library for factoring integers? 
>> I was under the impression, that it is the GCM-ECM library 
>> (http://ecm.gforge.inria.fr/). 
>>
>> I've been trying to use ECM and I noticed the following behavior: 
>>
>> sage: from sage.libs.libecm import ecmfactor 
>> sage: N = 121 
>> sage: factor(N) 
>> 11^2 
>> sage: ecmfactor(N, 1) 
>> (True, 121) 
>> sage: ecmfactor(N, 100) 
>> (True, 121) 
>> sage: ecmfactor(N, 200) 
>> (True, 121) 
>> sage: ecmfactor(N, 0) 
>> (True, 121) 
>> sage: ecmfactor(N, 0.) 
>> (True, 11) 
>>
>> And I guess your problem here is also that 121 is a perfect power of a 
prime number, whence the discrepancy with 120.
FYI its really easy and cheap to detect such perfect powers without using 
factorization of any kind.

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