Search: id:A001097
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%I A001097
%S A001097 3,5,7,11,13,17,19,29,31,41,43,59,61,71,73,101,103,107,109,137,139,149,
%T A001097 151,179,181,191,193,197,199,227,229,239,241,269,271,281,283,311,313,
%U A001097 347,349,419,421,431,433,461,463,521,523,569,571,599,601,617,619,641,643
%N A001097 Twin primes.
%C A001097 Union of A001359 and A006512.
%C A001097 The only twin primes that are Fibonacci numbers are 3, 5 and 13 [MacKinnon]. 
               - Emeric Deutsch, Apr 24 2005
%C A001097 (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
%D A001097 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.
%D A001097 Harvey Dubner, Twin Prime Statistics, Journal of Integer Sequences, Vol. 
               8 (2005), Article 05.4.2.
%D A001097 N. MacKinnon, Problem 10844, Amer. Math. Monthly 109, (2002), p. 78.
%D A001097 P. Ribenboim, The New Book of Prime Number Records, Springer-Verlag, 
               p. 259-265.
%H A001097 T. D. Noe, <a href="b001097.txt">Table of n, a(n) for n = 1..10000</a>
%H A001097 M. Abramowitz and I. A. Stegun, eds., <a href="http://www.nrbook.com/
               abramowitz_and_stegun/">Handbook of Mathematical Functions</a>, National 
               Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 
               [alternative scanned copy].
%H A001097 J. P. Delahaye, <a href="http://tr.voila.fr/ano?anolg=65544&anourl=http:/
               /www.pour-la-science.com/numeros/pls-260/logique.htm">Twin Primes:Enemy 
               Brothers?</a>
%H A001097 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               TwinPrimes.html">Twin Primes</a>
%H A001097 <a href="Sindx_Pri.html#gaps">Index entries for primes, gaps between</
               a>
%H A001097 O. E. Pol, <a href="http://www.polprimos.com">Determinacion geometrica 
               de los numeros primos y perfectos</a>.
%t A001097 Select[ Prime[ Range[120]], PrimeQ[ # - 2] || PrimeQ[ # + 2] &] (from 
               Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 09 2005)
%o A001097 (PARI) isA001097(n) = (isprime(n) & (isprime(n+2) | isprime(n-2))) [From 
               Michael Porter (michael_b_porter(AT)yahoo.com), Oct 29 2009]
%Y A001097 Cf. A070076. See A077800 for another version.
%Y A001097 Sequence in context: A065393 A132143 A045393 this_sequence A117243 A059362 
               A059264
%Y A001097 Adjacent sequences: A001094 A001095 A001096 this_sequence A001098 A001099 
               A001100
%K A001097 nonn,core
%O A001097 1,1
%A A001097 N. J. A. Sloane (njas(AT)research.att.com).
%E A001097 More terms from James A. Sellers (sellersj(AT)math.psu.edu), Sep 19 2000

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