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Old 2005-06-17, 17:35   #1
Numbers
 
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Question Number Projects

This isn’t exactly a maths question, but close to it, so I hope no one is offended by my posting it here.
I have seen a number of threads in various forums on this site that start with a guy saying that he is looking for numbers up to some big integer N that have properties x, y, and z, would anyone like to help? Several people respond and reserve some of the numbers being searched and after a few days or weeks they post back their results and reserve a few more.
In one typical example, a guy posted back what the originator thought was a highly unexpected result. The details don’t matter, but it was thought that low values for the variable k would not be successful, but this guy found a result when k = -15. No one suggested that this should be verified, or checked on another computer. The immediate response was that this should be emailed to Chris Caldwell’s Prime Pages.
So my question is this: bearing in mind that I can post a message to this forum from a Blackberry, where is the mathematical rigour in this. How do we know that these guys even have computers, never mind whether these routines they have written themselves actually do what they claim?
GIMPS itself has rigorous protocols for verifying everything, and every number is LL tested twice on a known program that sends back standard reports to the server. I am not talking about that, I mean the other “Projects” that are going on. Fun as they are, do they actually have any point if nothing is verified or checked to confirm these results?
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Old 2005-06-17, 17:57   #2
R.D. Silverman
 
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Quote:
Originally Posted by Numbers
This isn’t exactly a maths question, but close to it, so I hope no one is offended by my posting it here.
I have seen a number of threads in various forums on this site that start with a guy saying that he is looking for numbers up to some big integer N that have properties x, y, and z, would anyone like to help? Several people respond and reserve some of the numbers being searched and after a few days or weeks they post back their results and reserve a few more.
In one typical example, a guy posted back what the originator thought was a highly unexpected result. The details don’t matter, but it was thought that low values for the variable k would not be successful, but this guy found a result when k = -15. No one suggested that this should be verified, or checked on another computer. The immediate response was that this should be emailed to Chris Caldwell’s Prime Pages.
So my question is this: bearing in mind that I can post a message to this forum from a Blackberry, where is the mathematical rigour in this. How do we know that these guys even have computers, never mind whether these routines they have written themselves actually do what they claim?
GIMPS itself has rigorous protocols for verifying everything, and every number is LL tested twice on a known program that sends back standard reports to the server. I am not talking about that, I mean the other “Projects” that are going on. Fun as they are, do they actually have any point if nothing is verified or checked to confirm these results?

With NFS projects it is easy to check for invalid results. And I believe that
NFSNET does so check.

SeventeenorBust uses protocols similar to GIMPS.

With ECMNET, we simply have to take people at their word that they did
actaully run the curves they report. But what would be the point in lying?
When curve counts are accumulated, only the total is presented in public.
Individual credit isn't assigned. Only when a factor is found is credit given,
and I assure you that factors are checked.

But to answer your question in general: sometimes results get verified,
sometimes they are not. It depends on whether the reported results
are important to others. It's just like the report on any scientific experiment.
It is likely that some experiments do *not* get repeated.
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Old 2005-06-17, 18:56   #3
Wacky
 
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Just to further elaborate on what Bob has said,

Whenever anyone claims that they have a factor of a larger number, it is very easy for anyone to verify it -- Just do the division and check the remainder.

As for NFSNET, like factors, the relations can be verified with far less effort than the effort required to find them. Initially, we make some limited checks to catch the obvious problems such as including relations from another project (That has happened a few times because we are handling a lot of data and it does occasionally get "miss-filed").

Since we are using the Numeric Field Sieve, we don't need to find ALL of the "relations" within a certain region. Our objective is to collect a SUFFICIENT number of them by searching a two dimensional space. Although, like primes, the suitable relations are more densely packed closer to the origin, there are plenty more than we need within a short distance of the designed search area.

In the general scheme of data collection and processing, some of the relations get missed or corrupted. Unless there is a significant area involved, it is easier to extend the perimeter by a small amount rather than try to figure out just which relations were missed.

During data collection, we can take advantage of the statistical properties of the distribution. If someone reports unexpectedly many, or few, relations, that is a flag which leads to closer scrutiny.

During the post-processing, we discard a large number of the relations anyway. This is because we can only use those which can be paired with others. (We have to collect "too many" because during collection we don't know which ones are the ones that we will be able to pair and which we will be discarding).

At that point, all of the survivors are verified as a part of the processing.

Thus minor data problems are simply discarded and replaced from the "extra" relations collected elsewhere. The only time that I have encountered a major problem, (a software error on one particular platform), I went back to the original data, discarded the offending relations, and reassigned the sieving space.

I hope that this has helped you understand a bit more about our process.
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Old 2005-06-17, 20:34   #4
Numbers
 
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Default Thank you

Thank you. Dr. Silverman of course requires no introduction, and a quick trip to the NFSNET website revealed my second respondent wrote the infrastructure code for that record-setting project. I couldn’t have asked for two more eligible experts. Thank you both for taking the time.
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