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%I #38 Aug 17 2024 23:24:36
%S 43142746595714191,48425980631694091,53709214667673991,
%T 58992448703653891,64275682739633791,69558916775613691,
%U 74842150811593591,80125384847573491,85408618883553391,90691852919533291,95975086955513191,101258320991493091,106541555027472991,111824789063452891,117108023099432791,122391257135412691,127674491171392591,132957725207372491,138240959243352391,143524193279332291,148807427315312191,154090661351292091,159373895387271991,164657129423251891,169940363459231791,175223597495211691
%N Benoît Perichon's 26 primes in arithmetic progression.
%C Longest known arithmetic progression of primes as of Jan 14, 2012.
%C Discovered on Apr 12 2010 by Benoît Perichon using software by Jaroslaw Wroblewski and Geoff Reynolds in a distributed PrimeGrid project.
%D R. K. Guy, Unsolved Problems in Number Theory, 2nd ed., Springer-Verlag, 1994, A5 and A6.
%D P. Ribenboim, The New Book of Prime Number Records, Springer-Verlag, 1989, p. 224.
%H J. K. Andersen, <a href="http://primerecords.dk/aprecords.htm">Primes in Arithmetic Progression Records</a>.
%H T. Eisner and R. Nagel, <a href="http://dx.doi.org/10.3934/dcdss.2013.6.657">Arithmetic progressions-an operator theoretic view</a>, 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
%H A. Granville, <a href="http://www.dms.umontreal.ca/~andrew/PDF/PrimePattMonthly.pdf">Prime Number Patterns</a>, Amer. Math. Monthly 115 (2008), 279-296.
%H B. Green and T. Tao, <a href="http://arxiv.org/abs/math.NT/0404188">The primes contain arbitrarily long arithmetic progressions</a>, Annals of Math. 167 (2008), 481-547.
%H PrimeGrid, <a href="http://www.primegrid.com/download/AP26.pdf">AP26 Search</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimeArithmeticProgression.html">Prime Arithmetic Progression</a>.
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Primes_in_arithmetic_progression">Primes in arithmetic progression</a>.
%H J. Wroblewski, <a href="http://www.math.uni.wroc.pl/~jwr/AP26/AP26v3.pdf">How to search for 26 primes in arithmetic progression?</a>, May 23, 2008.
%H <a href="/index/Pri#primes_AP">Index entries for sequences related to primes in arithmetic progressions</a>
%F a(n) = 43142746595714191 + 5283234035979900*(n-1) for n = 1, 2, ..., 26.
%F 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).
%t a[1] := 43142746595714191; a[n_] := a[n] = a[n - 1] + 5283234035979900; Table[a[n], {n, 26}] (* _Alonso del Arte_, Jan 14 2012 *)
%t Range[ 43142746595714191, 175223597495211691, 5283234035979900] (* _Michael Somos_, Jan 15 2012 *)
%o (PARI) a(n)=5283234035979900*n+37859512559734291 \\ _Charles R Greathouse IV_, Jan 15 2012
%Y Cf. A002110, A033188, A033189, A033290, A260751, A261140, A327760, A363980, A374949.
%K nonn,fini,full,easy
%O 1,1
%A _Jonathan Sondow_, Jan 14 2012