Abstract
The sequence of natural numbers presents itself as a multidimensional array. Two problems are solved on the basis of these arrays:
a) distribution of prime numbers in multidimensional array,
b) factoring of composite numbers.
For solving the problems related to the distribution of prime numbers, there was developed a generator of prime numbers in the Delphi programming language. The program serves as well as a generator of Mersenne composite numbers. While generating a Mersenne composite number, one of its divisors is automatically defined.
The problem of factoring in Delphi is solved for numbers of the form 2i -1, where i is a natural number. Mersenne composite numbers are factoring in particular for the prime i.
References
Bulat, M. (2001) “Isomorfismo de grandes sistemas”, Acta Academia 2001, Evrica, Chisinau: 161–170.
Bulat, M. (2000) “Isomorphic sistems of graphs”, 3rd European Congress of Mathematics, Section 06: Discrete Mathematics and Computer Science, Poster number 236, Barcelona.
Bulat, M. (2002) “Algunas aplicaciones de las matrices multidimensionales”, Anales ATIC-2002, vol.1, Academia de Transportes, Informática y Comunicaciones, Chisinau, Evrica: 30–38 (en rumano).
Bulat,M. (2003) “La distribución de los números primos en matrices multidimensionales”, Anales ATIC-2003, vol.1, Academia de Transportes, Informática y Comunicaciones, Chisinau, Evrica: 74–82 (en rumano).
Minuts, P. (1997) Teoria de los Números, Vol.1, Editorial Crengutsa Galdau, Iasi (en rumano).
Oleinik, W.(1999) “Métodos de obtención de los números primos. La situación actual y las perspectivas.” Acta Academia 1999, Evrica, Chisinau: 101–126 (en ruso).
Bajandin, E.(2003) La distribución de los Números Primos en la Serie de los Números Naturales. Editorial Nauka, Novosibirsk (en ruso).
Bulat, M.; Zgureanu, A.; Ciobanu, I.; Bivol, L. (2006) “A method for obtaining arbitrary form prime numbers”, Satellite Conference of the ICM 2006. The XIVth Conference on Applied and Industrial Mathematics, Chisinau: 70–73.