Cunningham chains of length n of the first kind are n long sequences of prime numbers p1, p2,. .. , pn so that pi+1 = 2pi + 1 (for 1 ≤ i < n). In [3] we have devised a plan to find large Cunningham chains of the first kind of length 3 where the primes are of the form pi+1 = (h0 + cx) · 2 e+i − 1 for some integer x with h0 = 5 775, c = 30 030 and e = 34 944. The project was executed on the non-uniform memory access (NUMA) supercomputer of NIIF in Pécs , Hungary. In this paper we report on the obtained results and discuss the implementation details. The search consisted of two stages: sieving and the Fermat test. The sieving stage was implemented in a concurrent manner using lockfree queues, while the Fermat test was trivially parallel. On the 27th of April, 2014 we have found the largest known Cunningham chain of length 3 of the first kind which consists of the numbers 5110664609396115 · 2 34944+j − 1 for j = 0, 1, 2. Mathematics Subject Classification (2010): 11Y11. Cunningham chains of length n of the first kind are n long sequences of prime numbers p 1 , p 2 ,. .. , p n so that p i+1 = 2p i +1 (for 1 ≤ i < n). In 2013 we set out to find the largest primes which form a Cunningham chain of the first kind of length 3. The first stage of the plan was to take a large number of candidates, each representing one chain, i.e. three primes, and eliminate most of them using a sieve similar to the sieve of Eratosthenes. In the second stage the Fermat test was used to check if the remaining candidates are probable primes. Finally, that the numbers were actually primes was proven using the OpenPFGW open source implementation of the Brillhart-Lehmer-Selfridge test.