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gptkbp:instanceOf
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gptkb:mathematical_concept
prime number pair
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gptkbp:Brun's_constant
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sum of reciprocals of twin primes
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gptkbp:Brun's_constant_value
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approximately 1.902160583104
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gptkbp:defines
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pair of prime numbers that differ by 2
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gptkbp:example
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(11, 13)
(17, 19)
(29, 31)
(3, 5)
(41, 43)
(5, 7)
(59, 61)
(71, 73)
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gptkbp:first_twin_prime_pair
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(3, 5)
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gptkbp:hasConjecture
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There are infinitely many twin primes (twin prime conjecture)
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https://www.w3.org/2000/01/rdf-schema#label
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twin primes
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gptkbp:largest_known_twin_prime_pair
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(2996863034895·2^1290000±1)
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gptkbp:openProblem
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twin prime conjecture is unproven
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gptkbp:property
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both numbers are odd except (3, 5)
gaps between twin primes can be arbitrarily large
except for (3, 5), all twin primes are of the form (6n-1, 6n+1)
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gptkbp:relatedTo
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gptkb:Polignac's_conjecture
gptkb:Goldbach's_conjecture
gptkb:Brun's_constant
prime numbers
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gptkbp:sequence
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gptkb:A001097_(OEIS)
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gptkbp:studiedBy
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gptkb:Paul_Erdős
gptkb:Alphonse_de_Polignac
gptkb:Yitang_Zhang
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gptkbp:bfsParent
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gptkb:Twin_prime_conjecture
gptkb:twin_prime_conjecture
gptkb:Twin_prime_conjecture_(partial_results)
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gptkbp:bfsLayer
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6
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