Binary BBP-Formulae for Logarithms and Generalized Gaussian-Mersenne Primes

Constants of the form C = 1 X k=0 p(k) q(k)b k where p and q are integer polynomials, degp < degq, and p(k)=q(k) is non-singular for nonnegative k and b‚ 2, have special properties. The n th digit (base b) of C may be calculated in (essentially) linear time without computing its preceding digits, and constants of this form are conjectured to be either rational or normal to base b. This paper constructs such formulae for constants of the form logp for many primes p. This holds for all Gaussian-Mersenne primes and for a larger class of \generalized GuassianMersenne primes". Finally, connections to Aurifeuillian factorizations are made.