The issue is when you talk chess you talk _very_ large data-sets. You can keep track of games (both table state and players move) and build out your statistical pool every game that is played. Given a very large number of games with that player you may pick up statistical anomalies vs a large set of other players games. There are so many combinations of moves and board states that you wold be hard pressed to find a large enough population of data on one player to build a "ok" data-set against. And even then it is really only useful if you have that same volume from a ton of different people.
To bring this back to your example, where we may near instantly recognize the small set of primes that you listed above, can that really be said of 6 random board states from historical Karpov games? Yes, your mind is trained to grasp patterns such as the one above. Yes, your computer can run tests on the numbers above and come back and tell you that they are prime -- but only if tests are written to do so. The problem with attaching those principals directly with chess are great. Chess is more complex. Chess is played by humans (the first time I play you is not the same as the second time. I learn, think and evolve) which makes the data-sets less than static. At most you would be able to derive Fingerprints for players with large enough statistical anomalies -- but then again if they continue to play the same way their opponents will eventually learn and overtake.
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