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From: [email protected] (Bill Stewart)
Subject: 167-digit number factored
X-Mailer: Mozilla/2.1 (compatible; Opera/2.1; Windows 95)
The article's gotten a bit garbled through replies, but this was on sci.crypt.
> In article <[email protected]> [email protected] (Paul Rubin) writes:
> >In article <[email protected]>,
> >Samuel S Wagstaff <[email protected]> wrote:
>
> >>On Tuesday, 4 February 1997, we completed the factorization of a
> >>composite number of 167 digits, one of the `More Wanted' factorizations
> >>of the Cunningham Project. It is:
> >>
> >>3,349- = (3^349 - 1)/2 = c167 = p80 * p87
> >>
>
> >Congratulations.... was this factorization much easier than
> >factoring a general 167 (or 160) digit number?
>
> Yes, this c167 is much easier. I just finished the 136-digit number
>
> n = (2^454 - 2^341 + 2^227 - 2^114 + 1)/13
>
> (a divisor of (2^1362 + 1)/(2^454 + 1)). The sieving took
> 85 machine-days (about two weeknights) on a network of 60 SGI machines,
> and took advantage of n's representation as a polynomial in 2^113.
> Last year's factorization of RSA130 (130 digits) took 6 calendar-months
> to sieve, at multiple sites. By the way, the new factorization is
> n = p49 * p88, where
>
> p49 = 2393102462756185953833037662530180237989024296581
> p88 = 14952485345141425227257136559467580083134337 \
> 51379919088823926933276083374444560702796609
>
> The c167 factorization of (3^349 - 1)/2 was about as hard
> as doing a general number around 115-120 digits.
> --
> Peter L. Montgomery [email protected] San Rafael, California
>
> A mathematician whose age has doubled since he last drove an automobile.
>