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A077800 List of twin primes {p, p+2}. 87
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Union (with repetition) of A001359 and A006512.

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].

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.

Hayden Tronnolone, A tale of two primes, COLAUMS Space, #3, 2013.

Wikipedia, Twin prime.

Index entries for primes, gaps between

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

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 *)

PROG

(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

(PARI) p=2; forprime(q=3, 1e3, if(q-p==2, print1(p", "q", ")); p=q) \\ Charles R Greathouse IV, Mar 22 2013

CROSSREFS

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

Sequence in context: A058020 A069201 A272882 * A073340 A118409 A162779

Adjacent sequences:  A077797 A077798 A077799 * A077801 A077802 A077803

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Dec 03 2002

STATUS

approved

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Last modified February 26 07:51 EST 2021. Contains 341631 sequences. (Running on oeis4.)