The deterministic error limit in probability theory: On the probability method for the Goldbach conjecture, the 8th problem of Hilbert and Fermat's last theorem (Q2704427)

This paper is related to the well-known Goldbach conjecture [cp. e.g. \textit{Chendong Pan} and \textit{Chengbiao Pan}, ``Goldbach conjecture'' (1992; Zbl 0849.11080)], to the 8th problem of Hilbert [cp. e.g. \textit{J. Kaczorowski}, in: Hilbert's problems, 85-118 (1997)] and to Fermat's last theorem [cp. e.g. \textit{A. Wiles}, Ann. Math., II. Ser. 141, No. 3, 443-551 (1995; Zbl 0823.11029) or \textit{S. Singh}, ``Fermat's last theorem. The story of a riddle that confounded the world's greatest minds for 358 years'' (1997; Zbl 0930.00001); German translation (1998; Zbl 0930.00002)].NEWLINENEWLINENEWLINEThe paper contains more than 20 theorems on questions involving primes and number theory and using probability methods to solve some deterministic problems. The English abstract begins with the definitions on event of absolute small probability, natural ordinal experiment, \(n\)th natural ordinal experiment and \(n\)th \(k\)-variable natural ordinal experiment and later a prime generating element of an arithmetical series. E.g., Theorem 4 is a law of large number for events with absolute small probabilities. In other theorems the occurrence number of events has to obey the normal distribution. A further author's paper is published one year ago [J. Shenzhen, Univ., Sci. Eng. 16, No. 2/3, 1-21 (1999)].