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Bitwin Chain

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A bitwin chain of length one consists of two pairs of twin primes with the property that they are related by being of the form:

(n-1,n+1) and (2n-1,2n+1).
(1)

The first few values of n generating bitwin chains are 6, 30, 660, 810, 2130, 2550, 3330, ... (OEIS A066388).

In general a chain of length i consists of i+1 pairs of twin primes,

(n-1,n+1),(2n-1,2n+1),...,(2^i·n-1,2^i·n+1).
(2)

Bitwin chains can also be viewed as consisting of two related Cunningham chains of the first and second kinds,

(n-1,2n-1,4n-1,...) and (n+1,2n+1,4n+1,...).
(3)

P. Jobling (1999) found the largest known chain of length six,

337190719854678690·2^n+/-1,
(4)

where n=0 to 6.

See also

Cunningham Chain, Twin Primes

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References

Jobling, P. "A BiTwin Chain of Length 6 Discovered." 4 Oct 1999. http://listserv.nodak.edu/scripts/wa.exe?A2=ind9910&L=NMBRTHRY&P=151.Lifchitz, H. "New Chains of Prime Numbers." http://ourworld.compuserve.com/homepages/hlifchitz/Henri/us/NouvChPus.htm.Sloane, N. J. A. Sequence A066388 in "The On-Line Encyclopedia of Integer Sequences."

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Bitwin Chain

Cite this as:

Weisstein, Eric W. "Bitwin Chain." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/BitwinChain.html

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