Prime numbers beckon to the beginner, the basic notion of primality being accessible to a child. Yet, some of the simplest questions about primes have stumped humankind for millennia. In this book,… Expand

By using number-theoretical analysis and extended computations, the transcendency of the Kempner--Mahler number {summation}{sub n{ge}0}1/2{sup 2{sup n}}, yet the authors can also handle numbers with a substantially denser occurrence of 1's.Expand

The concept of Discrete Weighted Transforms (DWTs) are introduced which substantially improve the speed of multiplication by obviating costly zero-padding of digits.Expand

A theory to explain random behavior for the digits in the expansions of fundamental mathematical constants and proofs of base-2 normality for a collection of celebrated constants, including π, log 2, ζ(3), and others are proposed.Expand

It is an open conjecture that for any positive odd integer m the function C(m) = (3m + 1)/2e(m) where e(m) is chosen so that C(m) is again an odd integer, satisfies Ce(m) = 1 for some h. Here we show… Expand

From an experimental-mathematical perspective, Ising-class integrals are analyzed, which involvedextreme-precision, multidimensional quadrature on intricate integrands and highly parallel computation was required.Expand

An uncountable class of explicit normals that succumb to the PRNG approach is described, and b-normality is established for constants of the form Σ 1/(b mi c ni) for certain sequences (mi), (ni) of integers.Expand