A204189 Benoît Perichon's 26 primes in arithmetic progression.

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

Offset

1,1

Comments

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.

References

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.

Links

Table of n, a(n) for n=1..26.

J. K. Andersen, Primes in Arithmetic Progression Records.

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

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

Formula

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).

Mathematica

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 *)

Prog

(PARI) a(n)=5283234035979900*n+37859512559734291 \\ Charles R Greathouse IV, Jan 15 2012

Crossrefs

Cf. A002110, A033188, A033189, A033290.

Sequence in context: A003934 A038362 A038363 * A317163 A051167 A155057

Adjacent sequences: A204186 A204187 A204188 * A204190 A204191 A204192

Keyword

nonn,fini,full,easy

Author

Jonathan Sondow, Jan 14 2012

Status

approved