A077800 List of twin primes {p, p+2}.
3, 5, 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
Offset: 1
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.
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..1000
- 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].
- Nicholas John Bizzell-Browning, LIE scales: Composing with scales of linear intervallic expansion, Ph. D. Thesis, Brunel Univ. (UK, 2024). See p. 144.
- Jean-Paul Delahaye, Premiers jumeaux: frères ennemis? [Twin primes: Enemy Brothers?], Pour la science, No. 260 (Juin 1999), 102-106.
- Jean-Claude Evard, Twin primes and their applications. [Cached copy on the Wayback Machine]
- Jean-Claude Evard, Twin primes and their applications. [Local cached copy]
- Jean-Claude Evard, Twin primes and their applications. [Pdf file of cached copy]
- Dave Platt and Tim Trudgian, Improved bounds on Brun's constant, in: David H. Bailey et al. (eds), From Analysis to Visualization, JBCC 2017, Springer Proceedings in Mathematics & Statistics, Vol 313, Springer, Cham, 2020, preprint, arXiv:1803.01925 [math.NT], 2018.
- Mario Raso, Integer Sequences in Cryptography: A New Generalized Family and its Application, Ph. D. Thesis, Sapienza University of Rome (Italy 2025). See p. 114.
- Hayden Tronnolone, A tale of two primes, COLAUMS Space, #3, 2013.
- Wikipedia, Twin prime.
- Index entries for primes, gaps between
Programs
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Haskell
a077800 n = a077800_list !! (n-1) a077800_list = concat $ zipWith (\p q -> if p == q+2 then [q,p] else []) (tail a000040_list) a000040_list -- Reinhard Zumkeller, Nov 27 2011 -
Mathematica
Sort[ Join[ Select[ Prime[ Range[ 115]], PrimeQ[ # - 2] &], Select[ Prime[ Range[ 115]], PrimeQ[ # + 2] &]]] (* Robert G. Wilson v, Jun 09 2005 *) Select[ Partition[ Prime@ Range@ 115, 2, 1], #[[1]] + 2 == #[[2]] &] // Flatten Flatten[Select[{#, # + 2} & /@Prime[Range[1000]], PrimeQ[Last[#]]&]] (* Vincenzo Librandi, Nov 01 2012 *) Splice[{#,#+2}]& /@ Select[Prime[Range[PrimePi[619]]], PrimeQ[#+2]&] (* Oliver Seipel, Sep 04 2024 *)
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PARI
p=2;forprime(q=3,1e3,if(q-p==2,print1(p", "q", "));p=q) \\ Charles R Greathouse IV, Mar 22 2013
Formula
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
Comments