Sieving for large Cunningham chains of length \(3\) of the first kind

Abstract. In this paper we study the details of sieving for Cunningham chains of the first kind of length 3. To find such prime triplets larger than the ones already known, we have to investigate the primality of \(2^{37}\) numbers, each in the magnitude of \(2^{34944}\) (more than 10 500 decimal digits). This would not be feasible if it weren't for the sieving process which reduces the estimated time of completion to only a few weeks on a grid or a supercomputer with multiple cores.