On Mon, 14 May 2001 20:23:45 -0000, Brian J. Beesley wrote:
>On 14 May 2001, at 8:45, Nathan Russell wrote:
>
>> >First of all, as Jud notes, the 'elitism' is already there, in that different
>> >machines get treated differently in the assignments that they are given.
(To clarify, I did not write the above - Daran did)
>
>Sorry, I don't buy that. Every system has exactly the same chance of
>picking up any given assignment; it's a matter of the time at which
>you make the request. And you _can_ override the assignment type
>which would be the default for your system, if you wish to do so.
That is indeed true. I would have to say that having defaults
different for different systems is a Good Thing; otherwise, you might
have someone using a 486 suddenly realize that their computer was
doing a first-time check that would take over a year, get frustrated,
and give up.
>>
>> >Even readers of this list
>> >get opportunities to acquire exponents or prebeta-test software, etc., that
>> >are not available to the unwashed masses.
>
>AFAIK everyone is entitled to subscribe to this list, whether they
>participate by running assignments or not.
Agreed. Membership to the list indicates a slightly-more-than-casual
interest in the project, specifically a willingness to sift through a
few dozen messages per month in order to learn more about the project.
That interest might well also be a sign of someone who is more likely
to faithfully complete 'special' assignments in a relatively timely
fashion.
>>
>> Additionally, GIMPS,
>> unlike most other projects, has exponents taht are 'better' than
>> others.
>
>In the absence of completed tests, small exponents are more likely to
>be prime than larger ones, as well as taking less effort to test.
>However, note that a considerable number of users have voluntarily
>chosen to run 10 million digit range exponents, thus reducing the
>probability that they will discover a prime. The increased reward for
>being successful counterbalances the reduced chance of success.
True - and probably by a greater margin now that ordinary first-time
testing is getting higher (12,200,000 now as opposed to 9,700,000 when
I joined late in January 2000).
>There is also a theoretical difference between those exponents
>congruent to 1 modulo 4 and those congruent to 3 modulo 4. However I
>believe that this is due to the fact that one of these groups has a
>larger probability of having a small factor; thus this irregularity
>is removed by the time that LL testing begins.
I think I read something similiar. Might it relate to whether the
first potential factor itself is prime, specifically whether it is
divisible by 3? I can't do the arithmetic in my head, but I have a
hunch...
>
>> >Secondly, if - when I ask the server to give me "whatever kind of work makes
>> >most sense" - it gives me something else, whether out of spurious concern for
>> >my feelings or for any other reason, then not only are the programmers
>> >betraying my trust in them, they are also indicating that they don't trust me
>> >to ask for what I want.
>
>I agree. Either you allow people to choose the type of work they
>want, or you tell people plainly that you will select for them the
>type of work you will ask them to do. Either works, but a mixture is
>inconsistent.
Perhaps clicking the 'give me the work that makes the most sense' box
should immediately set the appearance of the others to the work that
will be chosen, rather than simply graying them out.
>>
>> Note that an exponent given out for triple-checking has a microscopic
>> chance of being prime (something like two in one billion), since it
>> must
>>
>> 1. Be prime (once chance in 60,000-70,000) and
>> 2. Have been missed by both previous tests (1 in 100 for each).
>
>NO! Conditional probability: if we need a third LL test run, it is
>because at least one of the other two _must_ be in error. So the
>probability of finding a prime on the third LL test run is (about)
>one half the probability of finding a prime on the second LL test run
>- irrespective of the error rate, provided it is small.
I stand corrected here.
Nathan Russell
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