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- Title
The largest known Cunningham chain of length 3 of the first kind.
- Authors
Farkas, Gábor; Gévay, Gábor E.; Járai, Antal; Vatai, Emil
- Abstract
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) · 2e+i - 1 for some integer x with h0 = 5 775, c = 30030 and e = 34944. 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 · 234944+j - 1 for j = 0, 1, 2.
- Subjects
HUNGARY; PRIME numbers; NON-uniform memory access; SUPERCOMPUTERS; FERMAT numbers; RESEARCH institutes
- Publication
Studia Universitatis Babeş-Bolyai, Mathematica, 2014, Vol 59, Issue 4, p457
- ISSN
0252-1938
- Publication type
Article