The game name: Prediction of Prime Number
The game rules as you mentioned:
The number is very big, and is not possible to be done with regular factorization, and needs a better algorithm to do the decomposition of it. The basic idea is to decompose it into two big factors which cant be done by regular integer numbers and this concept will be more or less based on the RSA Decryption algorithm. Player will win the game if he/she guess from a list what prime numbers are in it.
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In this paper I intend to analyze a theoretical subject involving game theory, regarding mathematical approach. Although this is a well-studied area, there are still new things to notice involving the prime numbers and their influence on computer gaming. As technical considerations, I first say that can be used several methods to predict the integer prime numbers, such as Cartesian Genetic Programming and multi-chromosome CGP to evolve a digital circuit, which represents a polynomial function. These built functions are able to find arrays of consecutive prime numbers, but usually are hard to obtain. From theory, the prime numbers distribution among the natural numbers is 1/lnN, for 1->N range....
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