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- W4237543695 abstract "This chapter presents some basic concepts and ideas of number theory, computation theory, computational number theory, and modern number-theoretic cryptography. Whether or not the Riemann Hypothesis is true is one of the most important open problems in mathematics, and is one of the seven Millennium Prize Problems proposed by the Clay Mathematics Institute in Boston in 2000. A Chinese mathematician has reportedly shown that there are in?nitely many pairs of integers, with n prime and n+2 a product of at most two primes, using very complicated arguments based on sieve methods, in his work on the Goldbach conjecture. Computation theory, or the theory of computation, is a branch that deals with whether and how ef?ciently problems can be solved on a model of computation, using an algorithm. The Church-Turing thesis thus provides us with a powerful tool to distinguish what is computation and what is not computation, what function is computable and what function is not computable, and more generally, what computers can do and what computers cannot do. Computational number theory is a new branch of mathematics. Informally, it can be regarded as a combined and disciplinary subject of number theory and computer science, particularly computation theory, including the theory of classical electronic computing, quantum computing, and biological computing." @default.
- W4237543695 created "2022-05-12" @default.
- W4237543695 date "2012-11-27" @default.
- W4237543695 modified "2023-09-27" @default.
- W4237543695 title "Introduction" @default.
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- W4237543695 doi "https://doi.org/10.1002/9781118188606.ch1" @default.
- W4237543695 hasPublicationYear "2012" @default.
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