>From: "Dave Mullen" <[EMAIL PROTECTED]>
>To: <[EMAIL PROTECTED]>
>Subject: Mersenne: Re: How much are the 10 M gamblers contributing?
>Date: Fri, 3 Mar 2000 17:42:02 +0800
>
>Perhaps I'm a little under-speed here ...
>
>I understood that the $100,000 award was for the first 10 million digit
>(that is to say 10 million decimal digit Mersenne Prime).
Well, it doesn't have to be a Mersenne prime, but checking an arbitrary
prime in a range in which probable primes haven't been shown (by
elimination) to all prime inbvolves locating a strong candidate with
probable primes and then trying all prime factors up to its square root.
For a 10 million digit number, that would be all prime factors up to those
of something like 5.1 M digits, which is to say a HUGE number of factors.
Thus, the winner will almost certainly be a Mersenne prime, unless the
Mersenne primes are shown to be finite in number, in which case we will have
to wait until there are computers strong enough to factor arbitrary primes
in that size range. I am not sure that factors such as the speed of light
and the Hesieberg principal will even permit that in any reasonable length
of time.
>
>Now a number of 10 million decimals is approx. 33 million bits long i.e.
>the Prime Exponent would be approx. 33 million.
>
>And I'm sure some of you have read the theories about the "missing
>Mersenne", and the analysis done on the sequence of known Mersenne Primes.
>If they turn out to be accurate, then we might be better looking at the 47
>- 49 million Prime Exponent range.
Well, that might be a good idea, but don't higher exponents take longer to
test in a manner that is slightly more than linear?
>
>For interest, has anyone calculated benchmarks, or run LL tests in those
>ranges; I guess not many, 8 months is a long time to wait for a result !!
Benchmarks have probably been done, but last time I checked, nobody had
turned in a completed LL test. There are also no people doing only
factoring assignments in that range, that I recall (getting the list that
far down takes a LONG time on my dialup connection, and here at school I
have fairly limited time online). This seems to make sense, since the
factoring people are (presumably often) intersted in immediate gratification
rather than boosting their producer standing.
>
>Dave
>
>"And the winning ticket in this year's Christmas Raffle is number
>111111111111111111111111111......"
I wonder whether any of the newspapers will publish the entire decimal text
of the next prime.... It'd be funny to watch people open the newspaper on
the bus and see that :-)
Nathan
______________________________________________________
Get Your Private, Free Email at http://www.hotmail.com
_________________________________________________________________
Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm
Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
