On 1 Jul 99, at 12:06, Jeff Woods wrote:
> Very well -- I will now predict that the NEXT Mersenne prime we find will
> be discovered very shortly (within 60 days, sans verification time), and
> will be PRECISELY:
>
> 2^7682383 - 1
If I were a bookie, I'd happily offer you odds of 1000-1 on that
prediction.
>
> I say this only because I have that number reserved, and because it falls
> within the subjective "Mersenne Island" that p=6972593 makes possible.
>
> (If you take the LARGEST Mersennes, M30 and up, and calculate the gap
> between them, you will find that the percentage is .8806259 through
> .9850544. Thus, if I arbitrarily choose 87% either way from the current
> discovery, this gives an "Island" potential (if such exists) of another
> prime possibly between p = 6066155 and p = 7879030. I choose to guess
> that this is the lower of the two primes in this island, if it exists,
> SOLELY because I'm too stink'n proud to think I might have missed out on
> the discovery of a WORLD RECORD find. ;-)
>
My reading of the "island" theory is that the centre of the next
"island" should be closer to 6 million than 7 million. Therefore, if
"M38" has a mate, the "island" theory predicts that "M38" is the
higher of a pair. _If_ a pair exists. _If_ the "island" theory really
does hold water. I'd very much like to see the "island" theory
proved; however, to the best of my knowledge, there isn't even a half-
formed heuristic argument as to why "islands" should exist - it's
just an observation of a (statistically insignificant) pattern.
There are still plenty of untested exponents in the 6 millions, so
there's plenty of opportunity to find another Mersenne prime
somewhere amongst them. Also, we aren't sure that there are no
Mersenne primes in the high 3 millions, the 4 millions or the low to
mid 5 millions; finding one in the "gap" would do the "island theory"
serious damage.
Irrespective of the "island" theory, I'll predict that exactly one
more Mersenne prime will be found with an exponent less than 10
million, but I wouldn't risk more than $10 on a bet at even money
odds, or venture to hazard an estimate of the value of its exponent
in the event that my prediction turns out to be true.
Regards
Brian Beesley
________________________________________________________________
Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm
