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The HP Prime Graphing Calculator is a graphing calculator introduced by Hewlett-Packard in 2013 and manufactured by HP Inc. until the licensees Moravia Consulting spol. s r.o. and Royal Consumer Information Products, Inc. took over the continued development, manufacturing, distribution, marketing and support in 2022.
A prime sieve works by creating a list of all integers up to a desired limit and progressively removing composite numbers (which it directly generates) until only primes are left. This is the most efficient way to obtain a large range of primes; however, to find individual primes, direct primality tests are more efficient [ citation needed ] .
The system was also chosen by Hewlett-Packard as the CAS for their HP Prime calculator, which utilizes the Giac/Xcas 1.5.0 engine under a dual-license scheme. In 2013, the mathematical software Xcas was also integrated into GeoGebra 's CAS view.
Because the set of primes is a computably enumerable set, by Matiyasevich's theorem, it can be obtained from a system of Diophantine equations. Jones et al. (1976) found an explicit set of 14 Diophantine equations in 26 variables, such that a given number k + 2 is prime if and only if that system has a solution in nonnegative integers: [7]
The multiples of a given prime are generated as a sequence of numbers starting from that prime, with constant difference between them that is equal to that prime. [1] This is the sieve's key distinction from using trial division to sequentially test each candidate number for divisibility by each prime. [ 2 ]
The following tables provide a comparison of computer algebra systems (CAS). [1] [2] [3] A CAS is a package comprising a set of algorithms for performing symbolic manipulations on algebraic objects, a language to implement them, and an environment in which to use the language.
Prime ideals, which generalize prime elements in the sense that the principal ideal generated by a prime element is a prime ideal, are an important tool and object of study in commutative algebra, algebraic number theory and algebraic geometry.
The calculator was officially discontinued in 2015. [8] [9] [10] It was HP's last calculator to support RPL, later calculators like the HP Prime support RPN only, although in a variant named Advanced RPN.