2010/03/21 by Marek Wolf, Wolf, Marek
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #History and Overview (math.HO) #Mathematical Dynamics and Fractals #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.1003.4015
openalex publication_date 2010/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give 50 digits values of the simple continued fractions whose denominators are formed from a) prime numbers, b) twin primes, c) generalized d-twins, d) primes of the form m2+n4, e)primes of the form m2+1, f) Mersenne primes and g) primorial primes. All these continued fractions belong to the set of measure zero of exceptions to the theorems of Khinchin and Levy. We claim that all these continued fractions are transcendental numbers. Next we propose the conjecture which indicates the way to deduce the transcendence of some continued fractions from transcendence of another ones.