Twin Prime Cluster

A twin prime cluster of order  is a collection of  consecutive prime numbers such that consecutive pairs form twin primes. Twin prime clusters were discussed by Mudge (around 1995), and N. D. Backhouse found such a cluster of order 7. The smallest twin prime clusters of order , 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 (2001), the cluster of order 9 by DeVries (2002), and the cluster of order 10 by G. Levai (in Sept. 2004, pers. comm., Apr. 5, 2005).

REFERENCES:

Mudge, M. "Some Sequences of Smarandache Contrasted with a Permutations Problem Relating to Class/student Allocation." Personal Computer World, London, England. pp. 674-675, June 1995.

Mudge, M. "Smarandache Sequences and Related Open Problems." Personal Computer World. Numbers Count, February 1997.

DeVries, D. "Twin Prime Groups." 26 Jan 2001. https://listserv.nodak.edu/scripts/wa.exe?A2=ind0101&L=nmbrthry&P=4377.

DeVries, D. "Twin Prime Constellation--9." 1 Apr 2002. https://listserv.nodak.edu/scripts/wa.exe?A2=ind0204&L=nmbrthry&P=146.

Rivera, C. "Problems & Puzzles: Puzzle 122-Consecutive Twin Primes in A.P." https://www.primepuzzles.net/puzzles/puzz_122.htm.

Sloane, N. J. A. Sequence A111950 in "The On-Line Encyclopedia of Integer Sequences."