Re: 42nd Known Mersenne Prime Found == 2^25,964,951-1 == The number has 7,816,230 digits

tomstdenis_at_gmail.com
Date: 02/28/05 

Date: 27 Feb 2005 16:44:41 -0800

John E. Hadstate wrote:
> "superuser" <superuser@domain.com> wrote in message
> news:v7j421137m3jshqjealadgtl61b80m04es@4ax.com...
> > I didn't see another post on this subject, but if the post
> is
> > redundant, my appologies.
> >
> > On February 18, 2005 the 42nd known Mersenne Prime was
> found.
> >
> > http://www.mersenne.org/
> >
>
> We were too busy arguing about whether old people should be
> allowed to write computer programs and whether computers
> (especially those programmed by old people) should be
> allowed to address more than 4 gigabytes to pay any serious
> attention to a crypto-related topic.
>
> It was an eye-opening article from a number of perspectives.

Where did the 4G limit come from? The test for whether a 25Mbit
mersenne number is prime simply requires the squaring/reduction
[Lucas-Lehmer] test 25 million times of a 25Mbit number.

25Mbit is about 927,319 "28-bit" digits which with LTM would take
roughly 2^54 single precision multiplications [with Toom-Cook roughly
speaking about 500-1000 days or about 3 years]. [6 cycle 32x32=>64].
Memory required would be definitely less than 32MiB.

The Prime95 takes it further and does a general FFT which is why it's
faster. But the ram requirement is far less than 4GiB in any case.

Tom