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Max0526

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**"logic of the set" analyzer**

Hi;

I'll start from an example.

There's a given set of positive integers: {2, 4, 6, 8, 10}. The problem is to estimate a (relative) probability for any number (not included into the set) to follow the logic of the set. For the example above, the probable logic is: even numbers only. Following this conclusion one can say that numbers 12, 14, 16, 18, 20 have the same and higher probability (=1) to follow set's logic, then numbers 1, 3, 5, 7, 9 (probability=0).

But the problem can be not so simple for a different set of data. E.g.: the set is {1, 3, 7, 11, 19, 21, 28, 31, 47, 53, 62, 69, 75, 76, 82, 98}. The problem is to estimate the relative probability for numbers 700, 800 and 900 to follow the logic of the set.

Now, my question is:

Does anybody know about existing piece of software (computer algebra of any kind - Mathematica, Maple, Mathcad, etc., Excel add-in, graph analyzer, some stand-alone product) that can perform that kind of estimation?

I would be very grateful,

Max

P.S. The application of this is number theory, specifically prime numbers. Examples of crazy unpredictable sets are available for example here: http://www.prothsearch.net/riesel2.html [Broken].

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