On 3 Mar 00, at 17:42, Dave Mullen wrote:
> Now a number of 10 million decimals is approx. 33 million bits long i.e.
> the Prime Exponent would be approx. 33 million.
Yes, this is perfectly true.
>
> 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.
Ah, but ... theories being theories ...
Suppose you have an object whose colour is such that it appears red
until 4th March 2000 but blue from that date onwards. So far, every
time you've observed it, it's proved to be red. Past observations are
not neccessarily a good predictor of what you will observe tomorrow!
No-one seems to seriously doubt that the underlying distribution of
Mersenne primes is at least fairly random, and that the density falls
off with increasing exponents. So the chance of any particular
exponent in the region of 48 million yielding a Mersenne prime is
less than the chance of any particular exponent "just big enough" for
the Mersenne number to have 10 million digits. To test an exponent
around 48 million will take about twice as long; so (given the
current state of the art) it looks as though testing the smallest
eligible exponents is the better strategy.
If you really want to have a go at the 48 million range, fair enough -
but please tell someone (George?) so that nobody else wastes time by
duplicating work on the same exponents - there are plenty of
candidates available!!!
>
> 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 !!
The existing v19 program is quite capable of running 10 timed
iterations on an arbitary exponent up to at least 79 million.
Extrapolation of the full test run time is a simple job, in fact
"Advanced/Time" does it for you.
No-one has reported any completed LL tests for any "10 million digit"
exponent yet; v19 hasn't been out that long, so that even anyone who
started on Release Day & has religiously followed the processor speed
leapfrog game is probably still some way from completing the first
one.
>
> "And the winning ticket in this year's Christmas Raffle is number
> 111111111111111111111111111......"
How many 1's?
Regards
Brian Beesley
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