Matches in DBpedia 2014 for { <http://dbpedia.org/resource/Cunningham_chain> ?p ?o. }
Showing items 1 to 44 of
44
with 100 items per page.
- Cunningham_chain abstract "In mathematics, a Cunningham chain is a certain sequence of prime numbers. Cunningham chains are named after mathematician A. J. C. Cunningham. They are also called chains of nearly doubled primes.A Cunningham chain of the first kind of length n is a sequence of prime numbers (p1, ..., pn) such that for all 1 ≤ i < n, pi+1 = 2pi + 1. (Hence each term of such a chain except the last one is a Sophie Germain prime, and each term except the first is a safe prime).It follows that Or, by setting (the number is not part of the sequence and need not be a prime number), we have Similarly, a Cunningham chain of the second kind of length n is a sequence of prime numbers (p1,...,pn) such that for all 1 ≤ i < n, pi+1 = 2pi − 1.It follows that the general term is Now, by setting , we have .Cunningham chains are also sometimes generalized to sequences of prime numbers (p1, ..., pn) such that for all 1 ≤ i ≤ n, pi+1 = api + b for fixed coprime integers a, b; the resulting chains are called generalized Cunningham chains.A Cunningham chain is called complete if it cannot be further extended, i.e., if the previous or next term in the chain would not be a prime number anymore.Examples of complete Cunningham chains of the first kind include these: 2, 5, 11, 23, 47 (The next number would be 95, but that is not prime.) 3, 7 (The next number would be 15, but that is not prime.) 29, 59 (The next number would be 119=7*17, but that is not prime.) 41, 83, 167 (The next number would be 335, but that is not prime.)Examples of complete Cunningham chains of the second kind include these: 2, 3, 5 (The next number would be 9, but that is not prime.) 7, 13 (The next number would be 25, but that is not prime.) 19, 37, 73 (The next number would be 145, but that is not prime.) 31, 61 (The next number would be 121, but that is not prime.)Cunningham chains are now considered useful in cryptographic systems since "they provide two concurrent suitable settings for the ElGamal cryptosystem ... [which] can be implemented in any field where the discrete logarithm problem is difficult."".
- Cunningham_chain wikiPageExternalLink A005602.
- Cunningham_chain wikiPageExternalLink A005603.
- Cunningham_chain wikiPageExternalLink index.php?block_height=182690.
- Cunningham_chain wikiPageExternalLink index.php?block_height=239833.
- Cunningham_chain wikiPageExternalLink index.php?block_height=323183.
- Cunningham_chain wikiPageExternalLink index.php?block_height=365304.
- Cunningham_chain wikiPageExternalLink index.php?block_height=368051.
- Cunningham_chain wikiPageExternalLink index.php?block_height=519253.
- Cunningham_chain wikiPageExternalLink index.php?block_height=519344.
- Cunningham_chain wikiPageExternalLink index.php?block_height=79349.
- Cunningham_chain wikiPageExternalLink index.php?block_height=95569.
- Cunningham_chain wikiPageExternalLink page.php?sort=CunninghamChain.
- Cunningham_chain wikiPageExternalLink Cunningham_chains.
- Cunningham_chain wikiPageID "321790".
- Cunningham_chain wikiPageRevisionID "606695252".
- Cunningham_chain hasPhotoCollection Cunningham_chain.
- Cunningham_chain subject Category:Prime_numbers.
- Cunningham_chain type Abstraction100002137.
- Cunningham_chain type DefiniteQuantity113576101.
- Cunningham_chain type Measure100033615.
- Cunningham_chain type Number113582013.
- Cunningham_chain type Prime113594005.
- Cunningham_chain type PrimeNumber113594302.
- Cunningham_chain type PrimeNumbers.
- Cunningham_chain comment "In mathematics, a Cunningham chain is a certain sequence of prime numbers. Cunningham chains are named after mathematician A. J. C. Cunningham. They are also called chains of nearly doubled primes.A Cunningham chain of the first kind of length n is a sequence of prime numbers (p1, ..., pn) such that for all 1 ≤ i < n, pi+1 = 2pi + 1.".
- Cunningham_chain label "Cadena de Cunningham".
- Cunningham_chain label "Catena di Cunningham".
- Cunningham_chain label "Chaîne de Cunningham".
- Cunningham_chain label "Cunningham chain".
- Cunningham_chain label "Cunningham-Kette".
- Cunningham_chain label "Cunningham-ketting".
- Cunningham_chain label "Последовательности Куннингама".
- Cunningham_chain sameAs Cunningham-Kette.
- Cunningham_chain sameAs Cadena_de_Cunningham.
- Cunningham_chain sameAs Chaîne_de_Cunningham.
- Cunningham_chain sameAs Catena_di_Cunningham.
- Cunningham_chain sameAs Cunningham-ketting.
- Cunningham_chain sameAs m.01vlx8.
- Cunningham_chain sameAs Q1144029.
- Cunningham_chain sameAs Q1144029.
- Cunningham_chain sameAs Cunningham_chain.
- Cunningham_chain wasDerivedFrom Cunningham_chain?oldid=606695252.
- Cunningham_chain isPrimaryTopicOf Cunningham_chain.