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%I #37 Sep 08 2022 08:45:27
%S -1705829,-1313701,-991127,-729173,-519643,-355049,-228581,-134077,
%T -65993,-19373,10181,26539,33073,32687,27847,20611,12659,5323,-383,
%U -3733,-4259,-1721,3923,12547,23887,37571,53149,70123,87977,106207,124351,142019,158923,174907,189977,204331,218389
%N a(n) = (n^5 - 133*n^4 + 6729*n^3 - 158379*n^2 + 1720294*n - 6823316)/4.
%C Prime generating polynomial found by Shyam Sunder Gupta. The first 57 values (n=0..56) are primes.
%C In fact, this polynomial was first found by F. Dress and B. Landreau in 2002 and not by Gupta. See, e.g., Ribenboim's book, page 148. - _Hugo Pfoertner_, Dec 12 2019
%D Paulo Ribenboim, The Little Book of Bigger Primes, Second Edition, Springer-Verlag New York, 2004.
%H G. C. Greubel, <a href="/A121887/b121887.txt">Table of n, a(n) for n = 0..1000</a>
%H Ed Pegg Jr., <a href="http://web.archive.org/web/20120702053057/http://www.maa.org/editorial/mathgames/mathgames_07_17_06.html">Prime generating polynomial</a>, July 17, 2006.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Prime-GeneratingPolynomial.html">Prime-Generating Polynomial</a>.
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F G.f.: (-1705829 + 8921273*x - 18696356*x^2 + 19628654*x^3 - 10324925*x^4 + 2177213*x^5)/(1-x)^6. - _R. J. Mathar_, Sep 13 2011
%F E.g.f.: (-6823316 + 1568512 x - 139108 x^2 + 5956 x^3 - 123 x^4 + x^5)*exp(x)/4. - _G. C. Greubel_, Oct 07 2019
%p seq((n^5 -133*n^4 +6729*n^3 -158379*n^2 +1720294*n -6823316)/4, n=0..35); # _G. C. Greubel_, Oct 07 2019
%t Table[(n^5 -133*n^4 +6729*n^3 -158379*n^2 +1720294*n -6823316)/4, {n, 0, 35}]
%o (PARI) vector(35, n, my(m=n-1); (m^5 -133*m^4 +6729*m^3 -158379*m^2 +1720294*m -6823316)/4) \\ _G. C. Greubel_, Oct 07 2019
%o (Magma) [(n^5 -133*n^4 +6729*n^3 -158379*n^2 +1720294*n -6823316)/4: n in [0..35]]; // _G. C. Greubel_, Oct 07 2019
%o (Sage) [(n^5 -133*n^4 +6729*n^3 -158379*n^2 +1720294*n -6823316)/4 for n in (0..35)] # _G. C. Greubel_, Oct 07 2019
%o (GAP) List([0..35], n-> (n^5 -133*n^4 +6729*n^3 -158379*n^2 +1720294*n -6823316)/4); # _G. C. Greubel_, Oct 07 2019
%Y Cf. A330363 for a polynomial improving the record to 58 consecutive primes.
%K sign,easy
%O 0,1
%A _Roger L. Bagula_, Aug 31 2006
%E Edited by _N. J. A. Sloane_, Sep 05 2006
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