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**1 - 2**of**2**### Theoretical Computer ScienceThe Complexity of Goldbach’s Conjecture and Riemann’s Hypothesis

, 2009

"... In this paper we obtain better upper bounds on the complexities of Goldbach’s Conjecture and Riemann’s Hypothesis in [3] and [8] by improving the register machine language used as well as the optimisation technique. 1 ..."

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In this paper we obtain better upper bounds on the complexities of Goldbach’s Conjecture and Riemann’s Hypothesis in [3] and [8] by improving the register machine language used as well as the optimisation technique. 1

### A Program-Size Complexity Measure for Mathematical Problems and Conjectures

"... Abstract. Cristian Calude et al. in [5] have recently introduced the idea of measuring the degree of difficulty of a mathematical problem (even those still given as conjectures) by the length of a program to verify or refute the statement. The method to evaluate and compare problems, in some objecti ..."

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Abstract. Cristian Calude et al. in [5] have recently introduced the idea of measuring the degree of difficulty of a mathematical problem (even those still given as conjectures) by the length of a program to verify or refute the statement. The method to evaluate and compare problems, in some objective way, will be discussed in this note. For the practitioner, wishing to apply this method using a standard universal register machine language, we provide (for the first time) some “small ” core subroutines or library for dealing with array data structures. These can be used to ease the development of full programs to check mathematical problems that require more than a predetermined finite number of variables. 1