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Bi-twin chain : ウィキペディア英語版
Bi-twin chain
In number theory, a bi-twin chain of length ''k'' + 1 is a sequence of natural numbers
: n-1,n+1,2n-1,2n+1, \dots, 2^k n - 1, 2^k n + 1 \,
in which every number is prime.〔Eric W. Weisstein, ''CRC Concise Encyclopedia of Mathematics'', CRC Press, 2010, page 249.〕
The numbers n-1, 2n-1, \dots, 2^kn - 1 form a Cunningham chain of the first kind of length k + 1, while n+1, 2n + 1, \dots, 2^kn + 1 forms a Cunningham chain of the second kind. Each of the pairs 2^in - 1, 2^in+ 1 is a pair of twin primes. Each of the primes 2^in - 1 for 0 \le i \le k - 1 is a Sophie Germain prime and each of the primes 2^in - 1 for 1 \le i \le k is a safe prime.
== Largest known bi-twin chains ==

''q''# denotes the primorial 2×3×5×7×...×''q''.
, the longest known bi-twin chain is of length 8.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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