Polynomial splines interpolating prime series
  Differentiable real function reproducing primes up to a given number and having a differentiable inverse function is constructed. This inverse function is compared with the Riemann-Von Mangoldt exact expression for the number of primes not exceeding a given value. Software for computation of the direct and inverse functions and their derivatives is developed. Examples of approximate solution of Diophantine equations on the primes are given. 
Lumomir Alexandrov, D. B. Baranov, and Plamen Yotov (JINR, BLTP,   Dubna, Russia)