A twin prime cluster of order n is a collection of 2n consecutive prime numbers such that consecutive pairs form twin primes. Twin prime clusters were discussed by Mudge, and N. D. Backhouse found such a cluster of order 7. The smallest twin prime clusters of order n = 1, 2, ... are 3, 5, 5, 9419, 909287, 325267931, 678771479, 1107819732821, 170669145704411, 3324648277099157, ... (OEIS A111950). The cluster of order 7 was found by P. Carmody on Jan. 7, 2001, the cluster of order 8 was found by DeVries, the cluster of order 9 by DeVries, and the cluster of order 10 by G. Levai (in Sept. 2004, pers. comm., Apr. 5, 2005).
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