S_{0,4}

[koh]

    Max wrote : 

>On 2/21/06, Joerg Arndt <arndt at jjj.de> wrote:
>
>> > Starting with 5500000011111 I was able to complete 3680 iterations
>> > until I came up to the need of factorization of 345-bit number:
>> >
>> > 53745739035525498795880532110461237696331778423865306564243673498785024002833035483307382497112648461303
>> >
>> > I'm going to factor it with NFS later and continue.
>> >
>>
>> Let me know what it takes (and what software you are using).
>
>I cannot give you exact timing but it was factored within a day with
>the help of ggnfs:
>http://sourceforge.net/projects/ggnfs
>
>That number happened to be the product of two primes:
>
>18223164902649732703974292810329988561
>and
>2949308713532555425842465546059346081104682577291637010561295300423
>
>
>
>On 2/22/06, Ralf Stephan <ralf at ark.in-berlin.de> wrote:
>
>> How do you folks know there is a 40-50 digit factor?
>> Everything else is certainly out of the question.
>
>I did not know anything about that number except that PARI and ECM
>applet could not factor it in reasonable amount of time.
>
>
>Max
>

    It is nice.

    Have you continued after 3680th term?

    By the way.

    What of the form was the number?

    I suppose that it is of the form p^k-1, becaues Sigma(n)=Product (p_i^(e_i+1)-1)/(p_i-1).
    
    If so, and p is small, then see site of "Cunningham project".

         

    There are many factorizations for p^n-1.

    Yasutoshi