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Cunningham chain
A sequence of prime numbers in which each member is twice the previous one plus one. For example, {2, 5, 11, 23, 47} is the first Cunningham chain of length 5 and {89, 179, 359, 719, 1439, 2879} is the first of length 6. More generally, a Cunningham chain of length k of the first kind is a sequence of k prime numbers, each of which is twice the preceding one plus one. A Cunningham chain of length k of the second kind is a sequence of k primes, each of which is twice the preceding one minus one. For example, {2, 3, 5} is a Cunningham chain of length 3 of the second kind and {1531, 3061, 6121, 12241, 24481} is a Cunningham chain of length 5 of the second kind. Primes of both these forms are called complete chains if they can't be extended by adding either the next larger or the next smaller terms.
Related entry
• Sophie Germain prime
Related category
• PRIME NUMBERS
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