|
%I #79 Mar 23 2024 19:22:39
%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
|
