Sorry
Ernst, but you're being misled by the success of the SPECIAL Number Field
Seive.
Indeed, we
can factor some fairly hard integers with over 200 digits, such as M727, R211
and (in progress right now) M751 but we can factor some easy integers with
millions of digits via trial division!
State of the
art with hard integers (i.e. those with no known special form and with no small
factors) is still 155 digits, or 512 bits. That limit will rise and and I
expect it to reach 576 bits in the next year, but we're
probably still quite a way from seeing a general 665-bit
factorization.
Paul
-----Original Message-----Luke Welsh wrote:
From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED]]
Sent: 20 December 2001 22:50
To: [EMAIL PROTECTED]
Subject: Mersenne: Re: 2^4-1 Factored!
>http://www.research.ibm.com/resources/news/20011219_quantum.shtml
Interesting...but the QC folks apprently seem to think classical factoring
work is frozen in time, viz. their comment about the supposed unfactorizability
of 200-digit composites. M727 is larger than 200 digits, and has a smallest
prime factor of 98 digits. Of course when QC comes into its own, 200-digit
numbers will be factored almost instantly. But we aren't there yet.
-Ernst
