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A204189
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Benoît Perichon's 26 primes in arithmetic progression.
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2
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43142746595714191, 48425980631694091, 53709214667673991, 58992448703653891, 64275682739633791, 69558916775613691, 74842150811593591, 80125384847573491, 85408618883553391, 90691852919533291, 95975086955513191, 101258320991493091, 106541555027472991, 111824789063452891, 117108023099432791, 122391257135412691, 127674491171392591, 132957725207372491, 138240959243352391, 143524193279332291, 148807427315312191, 154090661351292091, 159373895387271991, 164657129423251891, 169940363459231791, 175223597495211691
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OFFSET
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1,1
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COMMENTS
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Longest known arithmetic progression of primes as of Jan 14, 2012.
Discovered on Apr 12 2010 by Benoît Perichon using software by Jaroslaw Wroblewski and Geoff Reynolds in a distributed PrimeGrid project.
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REFERENCES
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T. Eisner and R. Nagel, Arithmetic progressions-an operator theoretic view, Discrete and continuous dynamical systems series S, Volume 6, Number 3, June 2013 pp. 657-667; doi:10.3934/dcdss.2013.6.657. - From N. J. A. Sloane, Feb 03 2013
R. K. Guy, Unsolved Problems in Number Theory, 2nd ed., Springer-Verlag, 1994, A5 and A6.
P. Ribenboim, The New Book of Prime Number Records, Springer-Verlag, 1989, p. 224.
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LINKS
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Table of n, a(n) for n=1..26.
J. K. Andersen, Primes in Arithmetic Progression Records.
A. Granville, Prime Number Patterns, Amer. Math. Monthly 115 (2008), 279-296.
B. Green and T. Tao, The primes contain arbitrarily long arithmetic progressions, Annals of Math. 167 (2008), 481-547.
PrimeGrid, AP26 Search.
Eric Weisstein's World of Mathematics, Prime Arithmetic Progression.
Wikipedia, Primes in arithmetic progression.
J. Wroblewski, How to search for 26 primes in arithmetic progression?, May 23, 2008.
Index entries for sequences related to primes in arithmetic progressions
Index to sequences with linear recurrences with constant coefficients, signature (2,-1).
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FORMULA
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a(n) = 43142746595714191 + 5283234035979900*(n-1) for n = 1, 2, ..., 26.
a(n) = 43142746595714191 + 23681770*23#*(n-1) for n = 1..26, where 23# = 2*3*5*7*11*13*17*19*23 = 223092870 = A002110(9).
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MATHEMATICA
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a[1] := 43142746595714191; a[n_] := a[n] = a[n - 1] + 5283234035979900; Table[a[n], {n, 26}] (* Alonso del Arte, Jan 14 2012 *)
Range[ 43142746595714191, 175223597495211691, 5283234035979900] (* Michael Somos, Jan 15 2012 *)
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PROG
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(PARI) a(n)=5283234035979900*n+37859512559734291 \\ Charles R Greathouse IV, Jan 15 2012
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CROSSREFS
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Cf. A002110, A033188, A033189, A033290.
Sequence in context: A003934 A038362 A038363 * A051167 A155057 A083105
Adjacent sequences: A204186 A204187 A204188 * A204190 A204191 A204192
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KEYWORD
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nonn,fini,full,easy,changed
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AUTHOR
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Jonathan Sondow, Jan 14 2012
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STATUS
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approved
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