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    STUDIA MATHEMATICA - Issue no. 4 / 2014  
         
  Article:   THE LARGEST KNOWN CUNNINGHAM CHAIN OF LENGTH 3 OF THE FIRST KIND.

Authors:  . 		 
       
         
  Abstract:   Cunningham chains of length n of the fi rst 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 fi nd large Cunningham chains of the fi rst kind of length 3 where the primes are of the form pi +1 = (h0 +cx) • 2e+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 Pecs, 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 fi rst kind which consists of the numbers 5110664609396115 • 234944+ j 􀀀 -1 for j = 0, 1, 2.

Mathematics Subject Classifi cation (2010): 11Y11.
Keywords: Cunningham chains, primality, computational number theory.
 
         
     
         
         
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