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3, 5, 7, 11, 13, 17, 19, 29, 31, 41, 43, 59, 61, 71, 73, 101, 103, 107, 109, 137, 139, 149, 151, 179, 181, 191, 193, 197, 199, 227, 229, 239, 241, 269, 271, 281, 283, 311, 313, 347, 349, 419, 421, 431, 433, 461, 463, 521, 523, 569, 571, 599, 601, 617, 619, 641, 643
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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Union of A001359 and A006512.
The only twin primes that are Fibonacci numbers are 3, 5 and 13 [MacKinnon]. - Emeric Deutsch, Apr 24 2005
(p, p+2) are twin primes if and only if p + 2 can be represented as the sum of two primes. Brun (1919): Even if there are infinitely many twin primes, the series of all twin prime reciprocals does converges against Brun's constant (A065421). Clement (1949): (n, n+2) are twin primes if and only if (4*(n-1)!+n+4) mod n(n+2) = 0. - Stefan Steinerberger, Dec 04 2005
A164292(a(n)) = 1. [From Reinhard Zumkeller, Mar 29 2010]
The 100355-digit numbers, 65516468355 ยท 2^333333 +/- 1, are currently the largest known twin primes. They were discovered by Twin Prime Search and Primegrid in August 2009. - Paul Muljadi, Mar 07 2011
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REFERENCES
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Harvey Dubner, Twin Prime Statistics, Journal of Integer Sequences, Vol. 8 (2005), Article 05.4.2.
N. MacKinnon, Problem 10844, Amer. Math. Monthly 109, (2002), p. 78.
P. Ribenboim, The New Book of Prime Number Records, Springer-Verlag, p. 259-265.
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..10000
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972, p. 870.
J. P. Delahaye, Twin Primes:Enemy Brothers?
Eric Weisstein's World of Mathematics, Twin Primes
Index entries for primes, gaps between
O. E. Pol, Determinacion geometrica de los numeros primos y perfectos.
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MATHEMATICA
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Select[ Prime[ Range[120]], PrimeQ[ # - 2] || PrimeQ[ # + 2] &] (* Robert G. Wilson v, Jun 09 2005 *)
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PROG
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(PARI) isA001097(n) = (isprime(n) & (isprime(n+2) | isprime(n-2))) \\ Michael B. Porter, Oct 29 2009
(PARI) a(n)=if(n==1, return(3)); my(p); forprime(q=3, default(primelimit), if(q-p==2 && (n-=2)<0, return(if(n==-1, q, p))); p=q) \\ Charles R Greathouse IV, Aug 22 2012
(Haskell)
a001097 n = a001097_list !! (n-1)
a001097_list = head a077800_list : drop 2 a077800_list
-- Reinhard Zumkeller, Nov 27 2011
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CROSSREFS
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Cf. A070076. See A077800 for another version.
Sequence in context: A186884 A045393 A132143 * A117243 A179679 A059362
Adjacent sequences: A001094 A001095 A001096 * A001098 A001099 A001100
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KEYWORD
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nonn,core
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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More terms from James A. Sellers, Sep 19 2000
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STATUS
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approved
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