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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; internal format)
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OFFSET
| 1,1
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COMMENTS
| 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 iff 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 iff (4*(n-1)!+n+4) mod n*(n+2) = 0. - Stefan Steinerberger (hansibal(AT)hotmail.com), Dec 04 2005
A164292(a(n)) = 1. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 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 7 2011
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REFERENCES
| M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 870.
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
| 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 [alternative scanned copy].
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
| Select[ Prime[ Range[120]], PrimeQ[ # - 2] || PrimeQ[ # + 2] &] (from Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 09 2005)
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PROG
| (PARI) isA001097(n) = (isprime(n) & (isprime(n+2) | isprime(n-2))) [From Michael Porter (michael_b_porter(AT)yahoo.com), Oct 29 2009]
(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
| 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
| nonn,core
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), Sep 19 2000
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