Computing twin primes and Brun´s constant: a distributed approach

The paper describes an implementation of a large heterogeneous distributed parallel computation that counts the distribution of twin primes and calculates Brun´s constant and maximal distances between pairs of twin primes. Two primes are twins if they differ by two. It is not known if there are infinitely many twin primes but it was proven that the sum of their inverses converges to the value defined as Brun´s constant. Prior to this work, the number of twins and their contribution to Brun´s constant was known for all twins up to 10¹⁴. The authors have advanced this calculation to 2·10¹⁵ and are planning to continue to 10¹⁶. The computation is distributed using the farmer-workers paradigm. The farmer divides the numerical range into intervals of 10 billion. Workers are assigned intervals to analyze and return results. If a worker fails, e.g., it does not return results within a given time period, the farmer reassigns its intervals to other workers. The farmer also frequently saves its state. If the farmer dies, a new one can be started up with minimal loss of work. The paper describes the algorithm for locating twin primes, a modified Sieve of Eratosthenes. It also discusses the method for distributing the work to clients, time and space saving optimizations, and multi-platform support. They conclude by presenting some preliminary results up to 1.8·10¹⁵ future directions for the system