Large primes in generalized Pascal triangles

In this paper, after presenting the results of the generalization of Pascal triangle (using powers of base numbers), we examine some properties of the 112-based triangle, most of all regarding to prime numbers. Additionally, an effective implementation of ECPP method is presented which enables Magma computer algebra system to prove the primality of numbers with more than 1000 decimal digits. 1 Generalized Pascal triangles using the powers of base numbers As it is a well-known fact, the classic Pascal triangle has served as a model for various generalizations. Among the broad variety of ideas of generalizations we can find e.g.: the generalized binomial coefficients of s order (leading to generalized Pascal triangles of s order), the multinomial coefficients (leading to Pascal pyramids and hyperpyramids), special arithmetical sequences (leading to resulting triangles which we might call as Lucas, Fibonacci, Gaussian, Catalan, ... triangle) (details in [3]). One of the present authors has devised, and then worked out in detail and published such a type of generalization, which is based on the idea of using Computing Classification System 1998: G.4 Mathematics Subject Classification 2010: 05A10, 11Y11