Possibility to Construct a Machine for Primality Testing of Numbers

Like the optical prism to break white light up into its constituent spectral colors, the machine to show a prime as a single spectrum is proposed. From the theoretical analysis, it can be shown that the machine to recognize the prime number as a single spectrum can be realized by using the correlation function of Riemann zeta function. Moreover, this method can be used for a factorization of the integer consisted of two primes.

Autistic Savants and large number primality detection.

In a sequel to the paper on small number primality detection by mental arithmetic.In this paper, we consider primality detection of four digit prime numbers, leading next to larger six digit and eight digit numbers, optionally scaled to arbitrary sized numbers. Several mental arithmetic techniques as mental arithmetic exercises from literature are cited, towards effective primality detection, by mental arithmetic only.The “large primes” mental arithmetic skill is developed both as a web based UI and as a UI based on slack, using the Wolfram Alpha nd Wolfram API , for primality testing and for Easter Eggs on prime numbers.Keywords: ASD, prime number determination, autistic savants, mathematical testing, Alexa Skills, learning and Cognition, Rabin-Miller test, Lucas test, fermat primes.

Probabilistic and deterministic analogues of the Miller – Rabin algorithm for ideals of rings of integer algebraic elements of finite extensions of the field 

In this paper, we obtained the primality criteria for ideals of rings of integer algebraic elements of finite extensions of the field Q, which are analogues of Miller and Euler’s primality criteria for rings of integers. Also advanced analogues of these criteria were obtained, assuming the extended Riemann hypothesis. Arithmetic and modular operations for ideals of rings of integer algebraic elements of finite extensions of the field Q were elaborated. Using these criteria, the polynomial probabilistic and deterministic algorithms for the primality testing in rings of integer algebraic elements of finite extensions of the field Q were offered.