>From: Stefan Struiker <[EMAIL PROTECTED]>
>To: George Woltman <[EMAIL PROTECTED]>, [EMAIL PROTECTED]
>Subject: Re: Mersenne: M#36 & M#37
>Date: Fri, 19 May 2000 21:01:55 -0700
>
>
>
>George Woltman wrote:
>
> > Hi all,
> >
> > Congratulations to all GIMPS members on achieving another
> > milestone! Today, double-checking has proved that M(2976221)
> > and M(3021377) are the 36th and 37th Mersenne primes.
> >
> > Keep up the good work!
> > George
>
>How many DDs does it take to "reasonably establish" primality, given the
>apparent slight
>error in the L-L test? Is there an extra-precision version of the test to
>nail things down?
>
>Just Curious,
>Stefanovic
IIRC, there is no real difference in the double-check and the first-time
test. However, double, triple and if need be quadruple checks are run until
the residues - the last 64 bits in the LL sequence - match. The chances of
this happening accidentally are one in 2^64 or, in US reckoning, 1 in a
number that is well over 17 quintillion. I don't know what the equivalent
number in European reckoning would be.
Deliberate attacks, e.g. sending false residues for a double-check with a
match in the public 56 bits of the residue and a guess for the other 8 bits,
is unlikely to succeed (1 chance in 256). If someone did this to gain
credit, they would most likely be tempted into doing it for a large number
of exponents. When they did this, the public-section-only matches that
would be almost certain to result would be a definate 'red flag' to George.
Nathan
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