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A077800 List of twin primes {p, p+2}. 88

%I

%S 3,5,5,7,11,13,17,19,29,31,41,43,59,61,71,73,101,103,107,109,137,139,

%T 149,151,179,181,191,193,197,199,227,229,239,241,269,271,281,283,311,

%U 313,347,349,419,421,431,433,461,463,521,523,569,571,599,601,617,619

%N List of twin primes {p, p+2}.

%C Union (with repetition) of A001359 and A006512.

%D 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.

%H Vincenzo Librandi, <a href="/A077800/b077800.txt">Table of n, a(n) for n = 1..1000</a>

%H M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

%H Jean-Paul Delahaye, <a href="http://www.lifl.fr/~delahaye/SIME/JPD/PLS_Nb_premiers_jumeaux.pdf">Premiers jumeaux: frères ennemis?</a> [Twin primes: Enemy Brothers?], Pour la science, No. 260 (Juin 1999), 102-106.

%H Jean-Claude Evard, <a href="http://web.archive.org/web/20110726012847/http://www.math.utoledo.edu/~jevard/Page012.htm">Twin primes and their applications</a>. [Cached copy on the Wayback Machine]

%H Jean-Claude Evard, <a href="/A077800/a077800.html">Twin primes and their applications</a>. [Local cached copy]

%H Jean-Claude Evard, <a href="/A077800/a077800.pdf">Twin primes and their applications</a>. [Pdf file of cached copy]

%H Dave Platt and Tim Trudgian, <a href="https://doi.org/10.1007/978-3-030-36568-4_25">Improved bounds on Brun's constant</a>, in: David H. Bailey et al. (eds), From Analysis to Visualization, JBCC 2017, Springer Proceedings in Mathematics & Statistics, Vol 313, Springer, Cham, 2020, <a href="https://arxiv.org/abs/1803.01925">preprint</a>, arXiv:1803.01925 [math.NT], 2018.

%H Hayden Tronnolone, <a href="https://www.semanticscholar.org/paper/A-tale-of-two-primes-Tronnolone/2576b80d487c909639c98a1e3cb255658c40d699">A tale of two primes</a>, COLAUMS Space, #3, 2013.

%H Wikipedia, <a href="http://www.wikipedia.org/wiki/Twin_prime">Twin prime</a>.

%H <a href="/index/Pri#gaps">Index entries for primes, gaps between</a>

%F Sum_{n>=1} 1/a(n) is in the interval (1.840503, 2.288490) (Platt and Trudgian, 2020). The conjectured value based on assumptions about the distribution of twin primes is A065421. - _Amiram Eldar_, Oct 15 2020

%t Sort[ Join[ Select[ Prime[ Range[ 115]], PrimeQ[ # - 2] &], Select[ Prime[ Range[ 115]], PrimeQ[ # + 2] &]]] (* _Robert G. Wilson v_, Jun 09 2005 *)

%t Select[ Partition[ Prime@ Range@ 115, 2, 1], #[[1]] + 2 == #[[2]] &] // Flatten

%t Flatten[Select[{#, # + 2} & /@Prime[Range[1000]], PrimeQ[Last[#]]&]] (* _Vincenzo Librandi_, Nov 01 2012 *)

%o (Haskell)

%o a077800 n = a077800_list !! (n-1)

%o a077800_list = concat $ zipWith (\p q -> if p == q+2 then [q,p] else [])

%o (tail a000040_list) a000040_list

%o -- _Reinhard Zumkeller_, Nov 27 2011

%o (PARI) p=2;forprime(q=3,1e3,if(q-p==2,print1(p", "q", "));p=q) \\ _Charles R Greathouse IV_, Mar 22 2013

%Y Cf. A065421, A070076, A095958. See A001097 for another version.

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_, Dec 03 2002

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Last modified April 14 12:11 EDT 2021. Contains 342949 sequences. (Running on oeis4.)