202 Form and Symmetry: Art and Science Buenos Aires Congress, 2007 HIDDEN SYMMETRIES AMONG PRIMES GUSTAVO FUNES, DAMIAN GULICH, LEOPOLDO GARAVAGLIA AND MARIO GARAVAGLIA Name: Gustavo Funes Address: Laboratorio de Procesamiento Láser, Centro de investigaciones Ópticas, La Plata, Argentina. Email: gfunes@ciop.unlp.edu.ar Name: Damián Gulich Address: Laboratorio de Procesamiento Láser, Centro de investigaciones Ópticas, La Plata, Argentina. Email: dgulich@ciop.unlp.edu.ar Name: Leopoldo Garavaglia Address: Aranjuez, España. Name: Mario Garavaglia Address: Laboratorio de Procesamiento Láser, Centro de investigaciones Ópticas, La Plata, Argentina. Email: garavagliam@ciop.unlp.edu.ar Abstract: We have established a new way of studying simple mathematical problems in a graphical way. Copying Eratosthenes we introduce a sieve in the form of layers of prime multiples represented as binary bands. Those layers have a totally determined frequency and they are fully symmetric. By means of this method we will see that the position of prime numbers is far away from being random, on the contrary, it has a totally determined structure, at least not directly. Finally we will see that some unsolved problems like Goldbach conjecture and related ones, are based in hidden symmetries to be proved. 1 INTRODUCTION For centuries many mathematicians, scientists and erudits studied the problem of the location of prime numbers. Some of them found formulas that based on natural numbers will give possible primes, like Fermat and Merssene. Nevertheless, no one has found a single formula that gives all prime numbers as a result. Nowadays, prime search algorithms are based on probabilistic mathematic structures, although some mathematicians think that prime structure is totally determined by certain rules. The location of prime numbers does not follow a defned pattern, and it has an evident lack of symmetry. For that reason it is remarkable the existence of twin primes, (prime numbers separated by 2), Cousin primes (primes separated by 4), sexy primes (primes separated by 6), and even triplets and cuadruplets of primes. Recently, it has been demonstrated that there exist arbitrary large arithmetic progressions of primes (Terence Tao). It is evident that these groups of primes, or constellations, are amazing because the